amount of heat
The method of setting temperature values is the temperature scale. Several temperature scales are known.
- Kelvin scale(named after the English physicist W. Thomson, Lord Kelvin).
Unit designation: K(not "degree Kelvin" and not °K).
1 K \u003d 1/273.16 - part of the thermodynamic temperature of the triple point of water, corresponding to the thermodynamic equilibrium of a system consisting of ice, water and steam. - Celsius(named after the Swedish astronomer and physicist A. Celsius).
Unit designation: °C .
In this scale, the melting temperature of ice at normal pressure is taken equal to 0°C, the boiling point of water is 100°C.
The Kelvin and Celsius scales are related by the equation: t (°C) \u003d T (K) - 273.15. - Fahrenheit(D. G. Fahrenheit - German physicist).
Unit designation: °F. It is widely used, in particular in the USA.
The Fahrenheit scale and the Celsius scale are related: t (°F) = 1.8 t (°C) + 32°C. By absolute value 1 (°F) = 1 (°C). - Reaumur scale(named after the French physicist R.A. Reaumur).
Designation: °R and °r.
This scale has almost fallen into disuse.
Relationship with degrees Celsius: t (°R) = 0.8 t (°C). - Rankin scale (Rankine)- named after the Scottish engineer and physicist W. J. Rankin.
Designation: °R (sometimes: °Rank).
The scale is also used in the USA.
The temperature on the Rankin scale corresponds to the temperature on the Kelvin scale: t (°R) = 9/5 T (K).
The main temperature indicators in units of measurement of different scales:
The SI unit of measurement is the meter (m).
- Off-system unit: angstrom (Å). 1Å = 1 10-10 m.
- Inch(from Dutch duim - thumb); inch; in; ´´; 1´ = 25.4 mm.
- Hand(English hand - hand); 1 hand=101.6mm.
- Link(English link - link); 1 li = 201.168 mm.
- Span(English span - span, range); 1 span = 228.6mm.
- Foot(English foot - foot, feet - feet); 1 ft = 304.8 mm.
- Yard(English yard - yard, paddock); 1 yd = 914.4 mm.
- Fatom, face(English fathom - a measure of length (= 6 ft), or a measure of the volume of wood (= 216 ft 3), or a mountain measure of area (= 36 ft 2), or a fathom (Ft)); fath or fth or Ft or ƒfm; 1 Ft = 1.8288 m.
- chain(English chain - chain); 1 ch = 66 ft = 22 yd = = 20.117 m.
- Furlong(English furlong) - 1 fur = 220 yd = 1/8 mile.
- Mile(English mile; international). 1 ml (mi, MI) = 5280 ft = 1760 yd = 1609.344 m.
The unit of measure in SI is m 2 .
- square foot; 1 ft 2 (also sq ft) = 929.03 cm 2.
- Square inch; 1 in 2 (sq in) = 645.16 mm 2.
- Square veil (face); 1 fath 2 (ft 2; Ft 2; sq Ft) \u003d 3.34451 m 2.
- square yard; 1 yd 2 (sq yd) \u003d 0.836127 m 2 .
Sq (square) - square.
The unit of measure in SI is m 3 .
- Cubic foot; 1 ft 3 (also cu ft) = 28.3169 dm 3.
- Cubic Fathom; 1 fath 3 (fth 3; Ft 3; cu Ft) = 6.11644 m 3.
- cubic yard; 1 yd 3 (cu yd) = 0.764555 m 3.
- cubic inch; 1 in 3 (cu in) \u003d 16.3871 cm 3.
- Bushel (UK); 1 bu (uk, also UK) = 36.3687 dm 3.
- Bushel (USA); 1 bu (us, also US) = 35.2391 dm 3.
- Gallon (UK); 1 gal (uk, also UK) = 4.54609 dm 3.
- Gallon liquid (US); 1 gal (us, also US) = 3.78541 dm 3.
- US gallon dry; 1 gal dry (us, also US) = 4.40488 dm3.
- Jill (gill); 1 gi = 0.12 L (US), 0.14 L (UK).
- Barrel (USA); 1bbl \u003d 0.16 m 3.
UK - United Kingdom - United Kingdom (Great Britain); US - United Stats (USA).
Specific volume
The unit of measurement in SI is m 3 / kg.
- ft 3 /lb; 1 ft3 / lb = 62.428 dm3 / kg .
The unit of measurement in SI is kg.
- Pound (trading) (English libra, pound - weighing, pound); 1 lb = 453.592 g; lbs - pounds. In the system of old Russian measures 1 lb = 409.512 g.
- Gran (English grain - grain, grain, pellet); 1 gr = 64.799 mg.
- Stone (English stone - stone); 1 st = 14 lb = 6.350 kg.
Density, incl. bulk
The unit of measurement in SI is kg / m 3.
- lb/ft 3 ; 1 lb / ft 3 \u003d 16.0185 kg / m 3.
Line Density
The unit of measure in SI is kg/m.
- lb/ft; 1 lb / ft = 1.48816 kg/m
- Pound/yard; 1 lb / yd = 0.496055 kg/m
Surface density
The unit of measurement in SI is kg / m 2.
- lb/ft 2 ; 1 lb / ft 2 (also lb / sq ft - pound per square foot) = 4.88249 kg / m 2.
Line speed
The SI unit is m/s.
- ft/h; 1 ft / h = 0.3048 m/h.
- ft/s; 1 ft/s = 0.3048 m/s.
The SI unit is m/s 2 .
- ft/s 2 ; 1 ft / s 2 \u003d 0.3048 m / s 2.
Mass flow
The SI unit is kg/s.
- Pound/h; 1 lb / h = 0.453592 kg/h.
- Pound/s; 1 lb/s = 0.453592 kg/s.
Volume flow
The SI unit is m 3 / s.
- ft 3 /min; 1 ft 3 / min = 28.3168 dm 3 / min.
- Yard 3 /min; 1 yd 3 / min = 0.764555 dm 3 / min.
- Gallon/min; 1 gal/ min (also GPM - gallon per min) = 3.78541 dm3/min.
Specific volume flow
- GPM/(sq ft) - gallon (G) per (P) minute (M)/(square (sq) foot (ft)) - gallon per minute per square foot;
1 GPM / (sq ft) \u003d 2445 l / (m 2 h) 1 l / (m 2 h) \u003d 10 -3 m / h. - gpd - gallons per day - gallons per day (days); 1 gpd \u003d 0.1577 dm 3 / h.
- gpm - gallons per minute - gallons per minute; 1 gpm \u003d 0.0026 dm 3 / min.
- gps - gallons per second - gallons per second; 1 gps \u003d 438 10 -6 dm 3 / s.
Sorbate consumption (for example, Cl 2) when filtering through a layer of sorbent (for example, active carbon)
- Gals/cu ft (gal/ft 3) - gallons/cubic foot (gallons per cubic foot); 1 Gals/cu ft = 0.13365 dm 3 per 1 dm 3 sorbent.
The unit of measure in SI is N.
- Pound-force; 1 lbf – 4.44822 N .44822 N 1N \u003d 1 kg m / s 2
- Poundal (English: poundal); 1 pdl \u003d 0.138255 N. (Poundal is the force that gives a mass of one pound an acceleration of 1 ft / s 2, lb ft / s 2.)
Specific gravity
The unit of measure in SI is N/m 3 .
- Pound-force/ft 3 ; 1 lbf/ft 3 = 157.087 N/m 3.
- Poundal/ft 3 ; 1 pdl / ft 3 \u003d 4.87985 N / m 3.
SI unit - Pa, multiple units: MPa, kPa.
Specialists in their work continue to use obsolete, canceled or previously optionally allowed pressure units: kgf / cm 2; bar; atm. (physical atmosphere); at(technical atmosphere); ata; ati; m of water. Art.; mmHg st; torr.
Concepts are used: "absolute pressure", "excessive pressure". There are errors when converting some units of pressure into Pa and into its multiple units. It should be taken into account that 1 kgf / cm 2 is equal to 98066.5 Pa (exactly), that is, for small (up to about 14 kgf / cm 2) pressures, with sufficient accuracy for work, we can take: 1 Pa \u003d 1 kg / (m s 2) \u003d 1 N / m 2. 1 kgf / cm 2 ≈ 105 Pa = 0.1 MPa. But already at medium and high pressures: 24 kgf / cm 2 ≈ 23.5 105 Pa = 2.35 MPa; 40 kgf / cm 2 ≈ 39 105 Pa = 3.9 MPa; 100 kgf / cm 2 ≈ 98 105 Pa = 9.8 MPa etc.
Ratios:
- 1 atm (physical) ≈ 101325 Pa ≈ 1.013 105 Pa ≈ ≈ 0.1 MPa.
- 1 at (technical) \u003d 1 kgf / cm 2 \u003d 980066.5 Pa ≈ 105 Pa ≈ 0.09806 MPa ≈ 0.1 MPa.
- 0.1 MPa ≈ 760 mmHg Art. ≈ 10 m w.c. Art. ≈ 1 bar.
- 1 Torr (torus, tor) \u003d 1 mm Hg. Art.
- Pound-force/inch 2 ; 1 lbf/in 2 = 6.89476 kPa (see below: PSI).
- Pound-force/ft 2 ; 1 lbf/ft 2 = 47.8803 Pa.
- Pound-force/yard 2 ; 1 lbf/yd 2 = 5.32003 Pa.
- Poundal/ft 2 ; 1 pdl/ft 2 = 1.48816 Pa.
- Foot of water column; 1 ft H 2 O = 2.98907 kPa.
- An inch of water column; 1 in H 2 O = 249.089 Pa.
- inch of mercury; 1 in Hg = 3.38639 kPa.
- PSI (also psi) - pounds (P) per square (S) inch (I) - pounds per square inch; 1 PSI = 1 lbƒ/in 2 = 6.89476 kPa.
Sometimes in the literature there is a designation for the pressure unit lb / in 2 - this unit does not take into account lbƒ (pound-force), but lb (pound-mass). Therefore, in numerical terms, 1 lb / in 2 is somewhat different from 1 lbf / in 2, since when determining 1 lbƒ, it is taken into account: g \u003d 9.80665 m / s 2 (at the latitude of London). 1 lb / in 2 \u003d 0.454592 kg / (2.54 cm) 2 \u003d 0.07046 kg / cm 2 \u003d 7.046 kPa. Calculation 1 lbƒ - see above. 1 lbf / in 2 \u003d 4.44822 N / (2.54 cm) 2 \u003d 4.44822 kg m / (2.54 0.01 m) 2 s 2 \u003d 6894.754 kg / (m s 2) = 6894.754 Pa ≈ 6.895 kPa.
For practical calculations, you can take: 1 lbf / in 2 ≈ 1 lb / in 2 ≈ 7 kPa. But, in fact, equality is illegal, as well as 1 lbƒ = 1 lb, 1 kgf = 1 kg. PSIg (psig) - same as PSI, but indicates overpressure; PSIa (psia) - the same as PSI, but emphasizes: absolute pressure; a - absolute, g - gauge (measure, size).
Water pressure
The unit of measure in SI is m.
- Head in feet (feet-head); 1 ft hd = 0.3048 m
Pressure loss during filtration
- PSI/ft - pounds (P) per square (S) inch (I)/foot (ft) - pounds per square inch/foot; 1 PSI/ft = 22.62 kPa per 1 m of filter bed.
WORK, ENERGY, AMOUNT OF HEAT |
SI unit - Joule(named after the English physicist J.P. Joule).
- 1 J is the mechanical work of a force of 1 N when a body moves a distance of 1 m.
- Newton (N) - SI unit of force and weight; 1 N is equal to the force imparting to a body with a mass of 1 kg an acceleration of 1 m 2 / s in the direction of the force. 1 J = 1 N m.
In heat engineering, the canceled unit of measurement of the amount of heat, the calorie (cal, cal), continues to be used.
- 1 J (J) = 0.23885 cal. 1 kJ = 0.2388 kcal.
- 1 lbf ft (lbf ft) = 1.35582 J.
- 1 pdl ft (poundal foot) = 42.1401 mJ.
- 1 Btu (British Heat Unit) = 1.05506 kJ (1 kJ = 0.2388 kcal).
- 1 Therm (therma - British big calorie) = 1 10 -5 Btu.
The SI unit is Watt (W)- named after the English inventor J. Watt - mechanical power at which 1 J work is done in 1 s, or a heat flux equivalent to 1 W mechanical power.
- 1 W (W) \u003d 1 J / s \u003d 0.859985 kcal / h (kcal / h).
- 1 lbf ft/s (lbf ft/s) = 1.33582 watts.
- 1 lbf ft / min (lbf ft/min) = 22.597 mW.
- 1 lbf ft / h (lbf ft/h) = 376.616 µW.
- 1 pdl ft/s (poundal feet/s) = 42.1401 mW.
- 1 hp (horsepower British / s) \u003d 745.7 watts.
- 1 Btu/s (British Heat Unit/s) = 1055.06 W.
- 1 Btu/h (Btu/h) = 0.293067 W.
Surface heat flux density
The unit of measure in SI is W / m 2.
- 1 W / m 2 (W / m 2) \u003d 0.859985 kcal / (m 2 h) (kcal / (m 2 h)).
- 1 Btu / (ft 2 h) \u003d 2.69 kcal / (m 2 h) \u003d 3.1546 kW / m 2.
Dynamic viscosity (viscosity factor), η.
SI unit - Pa s. 1 Pa s \u003d 1 N s / m 2;
off-system unit - poise (P). 1 P \u003d 1 dyne s / m 2 \u003d 0.1 Pa s.
- Dina (dyn) - (from the Greek dynamic - strength). 1 dyne \u003d 10 -5 N \u003d 1 g cm / s 2 \u003d 1.02 10 -6 kgf.
- 1 lbf h / ft 2 (lbf h/ft 2) = 172.369 kPa s.
- 1 lbf s / ft 2 (lbf s / ft 2) = 47.8803 Pa s.
- 1 pdl s / ft 2 (poundal s / ft 2) = 1.48816 Pa s.
- 1 slug /(ft s) (slug/(ft s)) = 47.8803 Pa s. Slug (slug) - a technical unit of mass in English system measures.
Kinematic viscosity, ν.
Unit of measurement in SI - m 2 / s; The unit cm 2 / s is called "Stokes" (after the English physicist and mathematician J. G. Stokes).
Kinematic and dynamic viscosities are related by the equation: ν = η / ρ, where ρ is the density, g/cm 3 .
- 1 m 2 / s = Stokes / 104.
- 1 ft 2 / h (ft 2 / h) \u003d 25.8064 mm 2 / s.
- 1 ft 2 /s (ft 2 /s) \u003d 929.030 cm 2 /s.
Tension unit magnetic field in SI - A/m(Ammeter). Ampère (A) is the surname of the French physicist A.M. Ampere.
Previously, the Oersted unit (E) was used - named after the Danish physicist H.K. Oersted.
1 A / m (A / m, At / m) \u003d 0.0125663 Oe (Oe)
The resistance to crushing and abrasion of mineral filter materials and, in general, of all minerals and rocks is indirectly determined on the Mohs scale (F. Moos is a German mineralogist).
In this scale, the numbers in ascending order indicate minerals arranged in such a way that each subsequent one is able to leave a scratch on the previous one. Extreme substances in the Mohs scale: talc (hardness unit - 1, the softest) and diamond (10, the hardest).
- Hardness 1-2.5 (drawn with a fingernail): wolskoite, vermiculite, halite, gypsum, glauconite, graphite, clay materials, pyrolusite, talc, etc.
- Hardness> 2.5-4.5 (not drawn with a fingernail, but drawn with glass): anhydrite, aragonite, barite, glauconite, dolomite, calcite, magnesite, muscovite, siderite, chalcopyrite, chabazite, etc.
- Hardness >4.5-5.5 (not drawn with glass, but drawn with a steel knife): apatite, vernadite, nepheline, pyrolusite, chabazite, etc.
- Hardness > 5.5-7.0 (not drawn with a steel knife, but drawn with quartz): vernadite, garnet, ilmenite, magnetite, pyrite, feldspars, etc.
- Hardness >7.0 (not drawn with quartz): diamond, garnet, corundum, etc.
The hardness of minerals and rocks can also be determined on the Knoop scale (A. Knup is a German mineralogist). In this scale, the values are determined by the size of the imprint left on the mineral when a diamond pyramid is pressed into its sample under a certain load.
Ratios of indicators on the Mohs (M) and Knoop (K) scales:
SI unit - Bq(Becquerel, named after the French physicist A.A. Becquerel).
Bq (Bq) is a unit of nuclide activity in a radioactive source (isotope activity). 1 Bq is equal to the activity of the nuclide, at which one decay event occurs in 1 s.
Radioactivity concentration: Bq/m 3 or Bq/l.
Activity is the number of radioactive decays per unit of time. Activity per unit mass is called specific activity.
- Curie (Ku, Ci, Cu) is a unit of nuclide activity in a radioactive source (isotope activity). 1 Ku is the activity of an isotope in which 3.7000 1010 decay events occur in 1 s. 1 Ku = 3.7000 1010 Bq.
- Rutherford (Rd, Rd) is an obsolete unit of activity of nuclides (isotopes) in radioactive sources, named after the English physicist E. Rutherford. 1 Rd \u003d 1 106 Bq \u003d 1/37000 Ci.
Radiation dose
Radiation dose - the energy of ionizing radiation absorbed by the irradiated substance and calculated per unit of its mass (absorbed dose). The dose accumulates over time of exposure. Dose rate ≡ Dose/time.
The unit of absorbed dose in SI is Gray (Gy, Gy). The off-system unit is Rad (rad), corresponding to a radiation energy of 100 erg absorbed by a substance weighing 1 g.
Erg (erg - from Greek: ergon - work) is a unit of work and energy in the non-recommended CGS system.
- 1 erg \u003d 10 -7 J \u003d 1.02 10 -8 kgf m \u003d 2.39 10 -8 cal \u003d 2.78 10 -14 kWh.
- 1 rad (rad) \u003d 10 -2 Gy.
- 1 rad (rad) \u003d 100 erg / g \u003d 0.01 Gy \u003d 2.388 10 -6 cal / g \u003d 10 -2 J / kg.
Kerma (abbreviated English: kinetic energy released in matter) - the kinetic energy released in matter, measured in grays.
The equivalent dose is determined by comparing the radiation of nuclides with X-rays. The radiation quality factor (K) shows how many times the radiation hazard in the case of chronic human exposure (in relatively small doses) for a given type of radiation is greater than in the case of X-rays with the same absorbed dose. For X-ray and γ-radiation K = 1. For all other types of radiation, K is established according to radiobiological data.
Deq = Dpogl K.
The absorbed dose unit in SI is 1 Sv(Sievert) = 1 J/kg = 102 rem.
- REM (rem, ri - until 1963 was defined as the biological equivalent of an roentgen) - a unit of equivalent dose of ionizing radiation.
- Roentgen (Р, R) - unit of measure, exposure dose of X-ray and γ-radiation. 1 P \u003d 2.58 10 -4 C / kg.
- Coulomb (C) - a unit in the SI system, the amount of electricity, electric charge. 1 rem = 0.01 J/kg.
Dose equivalent rate - Sv/s.
Permeability of porous media (including rocks and minerals)
Darcy (D) - named after the French engineer A. Darcy, darsy (D) 1 D \u003d 1.01972 μm 2.
1 D is the permeability of such a porous medium, when filtered through a sample of which with an area of 1 cm 2, a thickness of 1 cm and a pressure drop of 0.1 MPa, the flow rate of a liquid with a viscosity of 1 cP is 1 cm 3 / s.
Sizes of particles, grains (granules) of filter materials according to SI and standards of other countries
In the USA, Canada, Great Britain, Japan, France and Germany, grain sizes are estimated in meshes (English mesh - hole, cell, network), that is, by the number (number) of holes per inch of the finest sieve through which they can pass grains. And the effective grain diameter is considered to be the hole size in microns. IN last years US and UK mesh systems are more commonly used.
The ratio between the units of measurement of the grain (granule) size of filter materials according to SI and the standards of other countries:
Mass fraction
Mass fraction shows what mass amount of a substance is contained in 100 mass parts of a solution. Units of measurement: fractions of a unit; percentage (%); ppm (‰); parts per million (ppm).
Concentration of solutions and solubility
The concentration of the solution must be distinguished from the solubility - the concentration of a saturated solution, which is expressed by the mass amount of a substance in 100 mass parts of the solvent (for example, g / 100 g).
Volume concentration
Volume concentration is the mass amount of a solute in a certain volume of solution (for example: mg / l, g / m 3).
Molar concentration
Molar concentration - the number of moles of a given substance dissolved in a certain volume of solution (mol / m 3, mmol / l, μmol / ml).
Molar concentration
Molar concentration - the number of moles of a substance contained in 1000 g of a solvent (mol / kg).
normal solution
A normal solution is one that contains one equivalent of a substance per unit volume, expressed in mass units: 1H = 1 mg equiv / l = = 1 mmol / l (indicating the equivalent of a particular substance).
Equivalent
Equivalent is equal to the ratio part of the mass of an element (substance) that adds or replaces in chemical compound one atomic mass of hydrogen or half an atomic mass of oxygen, to 1/12 of the mass of carbon 12 . Thus, the equivalent of an acid is equal to its molecular weight, expressed in grams, divided by the basicity (the number of hydrogen ions); base equivalent - molecular weight divided by acidity (number of hydrogen ions, and for inorganic bases - divided by the number of hydroxyl groups); salt equivalent - molecular weight divided by the sum of charges (valency of cations or anions); the equivalent of a compound participating in redox reactions is the quotient of dividing the molecular weight of the compound by the number of electrons accepted (given away) by the atom of the reducing (oxidizing) element.
Relationships between units of measurement of the concentration of solutions
(Formulas for the transition from one expression of the concentration of solutions to another):
Accepted designations:
- ρ is the density of the solution, g/cm 3 ;
- m is the molecular weight of the solute, g/mol;
- E is the equivalent mass of a solute, that is, the amount of a substance in grams that interacts in a given reaction with one gram of hydrogen or corresponds to the transition of one electron.
According to GOST 8.417-2002 the unit of quantity of a substance is established: mole, multiples and submultiples ( kmol, mmol, µmol).
The unit of measure for hardness in SI is mmol/l; µmol/l.
In different countries, the canceled units of water hardness often continue to be used:
- Russia and CIS countries - mg-eq / l, mcg-eq / l, g-eq / m 3;
- Germany, Austria, Denmark and some other countries of the Germanic group of languages - 1 German degree - (H ° - Harte - hardness) ≡ 1 hour CaO / 100 thousand hours of water ≡ 10 mg CaO / l ≡ 7.14 mg MgO / l ≡ 17.9 mg CaCO 3 / l ≡ 28.9 mg Ca (HCO 3) 2 / l ≡ 15.1 mg MgCO 3 / l ≡ 0.357 mmol / l.
- 1 French degree ≡ 1 hour CaCO 3 / 100 thousand hours of water ≡ 10 mg CaCO 3 / l ≡ 5.2 mg CaO / l ≡ 0.2 mmol / l.
- 1 English degree ≡ 1 grain / 1 gallon of water ≡ 1 h CaCO 3 / 70 thousand hours of water ≡ 0.0648 g CaCO 3 / 4.546 l ≡ 100 mg CaCO 3 / 7 l ≡ 7.42 mg CaO / l ≡ 0.285 mmol / l. Sometimes the English degree of hardness is referred to as Clark.
- 1 American degree ≡ 1 hour CaCO 3 / 1 million hours of water ≡ 1 mg CaCO 3 / l ≡ 0.52 mg CaO / l ≡ 0.02 mmol / l.
Here: h - part; the conversion of degrees to their corresponding amounts of CaO, MgO, CaCO 3 , Ca(HCO 3) 2 , MgCO 3 is shown as examples mainly for German degrees; the dimensions of degrees are tied to calcium-containing compounds, since in the composition of hardness ions calcium, as a rule, is 75-95%, in rare cases - 40-60%. Numbers are rounded mostly to the second decimal place.
Relationship between water hardness units:
1 mmol/L = 1 mg equiv/L = 2.80°N (German degrees) = 5.00 French degrees = 3.51 English degrees = 50.04 US degrees.
The new unit of measure for water hardness is the Russian degree of hardness - °F, defined as the concentration of an alkaline earth element (mainly Ca 2+ and Mg 2+), numerically equal to ½ of its mole in mg / dm 3 (g / m 3).
Alkalinity units - mmol, µmol.
The unit of measure for electrical conductivity in SI is µS/cm.
The electrical conductivity of solutions and the reverse electrical resistance characterize the mineralization of solutions, but only the presence of ions. When measuring electrical conductivity, non-ionic organic substances, neutral suspended impurities, interferences that distort the results - gases, etc. cannot be taken into account. In natural water, different ions have different electrical conductivity, which simultaneously depends on the salinity of the solution and its temperature. To establish such a dependence, it is necessary to experimentally establish the ratio between these quantities for each specific object several times a year.
- 1 µS/cm = 1 MΩ cm; 1 S/m = 1 ohm m.
For pure solutions of sodium chloride (NaCl) in distillate, the approximate ratio is:
- 1 µS/cm ≈ 0.5 mg NaCl/l.
The same ratio (approximately), subject to the above reservations, can be taken for most natural waters with mineralization up to 500 mg/l (all salts are converted to NaCl).
With a mineralization of natural water of 0.8-1.5 g / l, you can take:
- 1 μS / cm ≈ 0.65 mg salts / l,
and with mineralization - 3-5 g / l:
- 1 µS/cm ≈ 0.8 mg salts/l.
The content of suspended impurities in water, transparency and turbidity of water
The turbidity of water is expressed in units:
- JTU (Jackson Turbidity Unit) - Jackson turbidity unit;
- FTU (Formasin Turbidity Unit, also referred to as EMF) - formazin turbidity unit;
- NTU (Nephelometric Turbidity Unit) - nephelometric turbidity unit.
Give exact ratio units of turbidity and suspended matter content is impossible. For each series of determinations, it is necessary to build a calibration graph that allows you to determine the turbidity of the analyzed water compared to the control sample.
Approximately you can imagine: 1 mg / l (suspended solids) ≡ 1-5 NTU.
If the cloudy mixture (diatomaceous earth) has a particle size of 325 mesh, then: 10 units. NTU ≡ 4 units JTU.
GOST 3351-74 and SanPiN 2.1.4.1074-01 equate 1.5 units. NTU (or 1.5 mg/l as silica or kaolin) 2.6 units FTU (EMF).
The relationship between font transparency and haze:
The ratio between the transparency of the "cross" (in cm) and turbidity (in mg / l):
The unit of measure in SI is mg / l, g / m 3, μg / l.
In the USA and in some other countries, mineralization is expressed in relative units (sometimes in grains per gallon, gr / gal):
- ppm (parts per million) - parts per million (1 10 -6) units; sometimes ppm (parts per mille) also denotes a thousandth (1 10 -3) of a unit;
- ppb - (parts per billion) billionth (billionth) share (1 10 -9) units;
- ppt - (parts per trillion) trillionth (1 10 -12) units;
- ‰ - ppm (also used in Russia) - a thousandth (1 10 -3) units.
The ratio between the units of measurement of mineralization: 1mg / l \u003d 1ppm \u003d 1 10 3 ppb \u003d 1 10 6 ppt \u003d 1 10 -3 ‰ = 1 10 -4%; 1 gr/gal = 17.1 ppm = 17.1 mg/l = 0.142 lb/1000 gal.
For measuring salinity of salt waters, brines and salinity of condensates The correct units to use are: mg/kg. In laboratories, water samples are measured by volume, not mass fractions, therefore it is advisable in most cases to refer the amount of impurities to a liter. But for large or very small mineralization values, the error will be sensitive.
According to SI, volume is measured in dm 3, but the measurement is also allowed in liters, because 1 l \u003d 1.000028 dm 3. Since 1964 1 liter is equal to 1 dm 3 (exactly).
For salt water and brines sometimes salinity units are used in degrees Baumé(for mineralization >50 g/kg):
- 1°Be corresponds to a solution concentration of 1% in terms of NaCl.
- 1% NaCl = 10 g NaCl/kg.
Dry and calcined residue
Dry and calcined residue are measured in mg/l. The dry residue does not fully characterize the mineralization of the solution, since the conditions for its determination (boiling, drying the solid residue in an oven at a temperature of 102-110 ° C to constant weight) distort the result: in particular, part of the bicarbonates (conventionally accepted - half) decomposes and volatilizes in the form of CO 2 .
Decimal multiples and submultiples of quantities
Decimal multiples and submultiple units of measurement of quantities, as well as their names and designations, should be formed using multipliers and prefixes given in the table:
(based on materials from the site https://aqua-therm.ru/).
This guide has been compiled from various sources. But its creation was prompted by a small book "Mass Radio Library" published in 1964, as a translation of the book by O. Kroneger in the GDR in 1961. Despite its antiquity, it is my reference book (along with several other reference books). I think time has no power over such books, because the foundations of physics, electrical and radio engineering (electronics) are unshakable and eternal.
Units of measurement of mechanical and thermal quantities.
Units of measurement of electromagnetic quantities
|
Relations between units of magnetic quantities
in CGSM and SI systems
| In electrical and reference literature published before the introduction of the SI system, the magnitude of the magnetic field strength H often expressed in oersteds (uh) magnetic induction value IN - in gauss (gs), magnetic flux Ф and flux linkage ψ - in maxwells (µs). |
| 1e \u003d 1/4 π × 10 3 a / m; 1a / m \u003d 4π × 10 -3 e; 1gf=10 -4 t; 1tl=104 gs; 1mks=10 -8 wb; 1vb=10 8 ms |
| It should be noted that the equalities are written for the case of a rationalized practical MKSA system, which was included in the SI system as an integral part. From a theoretical point of view, it would be better to O in all six relationships, replace the equal sign (=) with the match sign (^). For example |
|
1e \u003d 1 / 4π × 10 3 a / m |
| which means: a field strength of 1 Oe corresponds to a strength of 1/4π × 10 3 a/m = 79.6 a/m |
| The point is that the units gs And ms belong to the CGMS system. In this system, the unit of current strength is not the main one, as in the SI system, but a derivative. Therefore, the dimensions of the quantities characterizing the same concept in the CGSM and SI systems turn out to be different, which can lead to misunderstandings and paradoxes, if we forget about this circumstance. When performing engineering calculations, when there is no basis for misunderstandings of this kind |
Off-system units
Some mathematical and physical concepts
applied to radio engineering
| Like the concept - the speed of movement, in mechanics, in radio engineering there are similar concepts, such as the rate of change of current and voltage. They can be either averaged over the course of the process, or instantaneous. |
|
i \u003d (I 1 -I 0) / (t 2 -t 1) \u003d ΔI / Δt |
| With Δt -> 0, we get the instantaneous values of the current change rate. It most accurately characterizes the nature of the change in the quantity and can be written as: |
|
i=lim ΔI/Δt =dI/dt |
| And you should pay attention - the average values and instantaneous values \u200b\u200bcan differ by dozens of times. This is especially evident when a changing current flows through circuits with a sufficiently large inductance. |
decibell |
| To assess the ratio of two quantities of the same dimension in radio engineering, a special unit is used - the decibel. |
| K u \u003d U 2 / U 1 Voltage gain; K u [dB] = 20 log U 2 / U 1 Voltage gain in decibels. Ki [dB] = 20 log I 2 / I 1 Current gain in decibels. Kp[dB] = 10 log P 2 / P 1 Power gain in decibels. |
| The logarithmic scale also allows, on a graph of normal sizes, to depict functions that have a dynamic range of parameter changes in several orders of magnitude. |
| To determine the signal strength in the reception area, another logarithmic unit of DBM is used - dicibells per meter. |
| P [dbm] = 10 log U 2 / R +30 = 10 log P + 30. [dbm]; |
| The effective load voltage at a known P[dBm] can be determined by the formula: |
 |
Dimensional coefficients of basic physical quantities
| In accordance with state standards, the following multiple and submultiple units - prefixes are allowed: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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In principle, one can imagine any number of different systems of units, but only a few have become widespread. All over the world for scientific and technical measurements and in most countries in industry and everyday use the metric system.
Basic units.
In the system of units for each measured physical quantity, an appropriate unit of measurement must be provided. Thus, a separate unit of measure is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are chosen as the main ones, and the rest are determined through the main ones. So, if the unit of length is a meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered square meter, the unit of volume is a cubic meter, the unit of speed is a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who are much more likely to deal with measurements than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. At the same time, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation, it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the "dimension" of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to define units for quantities such as pressure or electric current.) Such relationships are general and hold regardless of which units (meter, foot, or arshin) are measured in length and which units are chosen for other quantities.
In engineering, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most used in physical research, a metal cylinder is taken as a standard of mass, then in a technical system it is considered as a standard of force that balances the force of gravity acting on it. But since the force of gravity is not the same at different points on the surface of the Earth, for the exact implementation of the standard, it is necessary to indicate the location. Historically, the location was taken at sea level at a geographic latitude of 45°. At present, such a standard is defined as the force necessary to give the indicated cylinder a certain acceleration. It is true that measurements in technology are, as a rule, not carried out with such a high accuracy that it would be necessary to take care of variations in the force of gravity (if we are not talking about the calibration of measuring instruments).
A lot of confusion is associated with the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same name. Mass is the inertial characteristic of a body, showing how difficult it is to derive it external force from a state of rest or uniform and rectilinear motion. A unit of force is a force that, acting on a unit of mass, changes its speed by a unit of speed per unit of time.
All bodies are attracted to each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as mentioned above, is not the same at different points on the surface of the Earth and at different heights above sea level due to differences in gravitational attraction and in the manifestation of the rotation of the Earth. However, the total mass of a given amount of substance is unchanged; it is the same in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies (i.e. their weight) is proportional to their mass. Therefore, masses can be compared on a balance, and masses that are the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of the displaced air). If a certain body is weighed on a spring balance, balancing the force of gravity with the force of an extended spring, then the results of the weight measurement will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly show the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the reference mass was taken as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is common name international decimal system of units, the basic units of which are the meter and the kilogram. With some differences in details, the elements of the system are the same all over the world.
Story.
The metric system grew out of the decrees adopted by the National Assembly of France in 1791 and 1795 to define the meter as one ten-millionth of a section of the earth's meridian from North Pole to the equator.
By a decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It has gradually supplanted local and national systems elsewhere in Europe and has been legally accepted in the UK and the US. An agreement signed on May 20, 1875 by seventeen countries created an international organization designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten millionth of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and exact reproducibility of the system. They took the gram as a unit of mass, defining it as the mass of one millionth cubic meter water at its maximum density. Since it would not be very convenient to make geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes in the market with an appropriate amount of water, metal standards were created that reproduce these ideal definitions with the utmost accuracy.
It soon became clear that metal standards of length could be compared with each other, introducing a much smaller error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to take the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission took the archival platinum-iridium kilogram as the standard of mass, “considering that the simple ratio established by the creators of the metric system between a unit of weight and a unit of volume represents the existing kilogram with an accuracy sufficient for ordinary uses in industry and commerce, and accurate science needs not a simple numerical ratio of this kind, but an extremely perfect definition of this ratio. In 1875, many countries of the world signed an agreement on the meter, and this agreement established the procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately took up the development of international standards of length and mass and the transfer of their copies to all participating countries.
Length and mass standards, international prototypes.
International prototypes of standards of length and mass - meters and kilograms - were deposited with the International Bureau of Weights and Measures, located in Sevres, a suburb of Paris. The standard meter was a ruler made of an alloy of platinum with 10% iridium, the cross section of which was given a special X-shape to increase flexural rigidity with a minimum volume of metal. There was a longitudinal flat surface in the groove of such a ruler, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made from the same platinum was taken as the international prototype of the kilogram. iridium alloy, which is the standard of the meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at a geographical latitude of 45 °, is sometimes called a kilogram-force. Thus, it can be used either as a standard of mass for the absolute system of units, or as a standard of force for the technical system of units, in which one of the basic units is the unit of force.
The International Prototypes were selected from a significant batch of identical standards made at the same time. The other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made in different time since then, show that they do not detect deviations (from international standards) that go beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically supposed to be independently reproducible, and also because of its simplicity. Scientists began to derive new units for the various physical quantities they were dealing with, based on the elementary laws of physics and relating these units to the units of length and mass of the metric system. The latter increasingly conquered various European countries, in which many unrelated units for different quantities used to be in circulation.
Although in all countries that adopted the metric system of units, the standards of metric units were almost the same, there were various discrepancies in the derived units between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units have emerged: the electrostatic one, based on the force with which two electric charges act on each other, and the electromagnetic one, based on the force of the interaction of two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called. practical electrical units, introduced in the middle of the 19th century. British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of the two systems named above, but differ from the units of the electromagnetic system only by factors equal to integer powers of ten.
Thus, for such common electrical quantities as voltage, current and resistance, there were several options for accepted units of measurement, and each scientist, engineer, teacher had to decide for himself which of these options he should use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. more and more practical units were used, which eventually came to dominate the field.
To eliminate such confusion in the early 20th century. a proposal was put forward to combine practical electrical units with the corresponding mechanical units based on metric units of length and mass, and to build some kind of consistent (coherent) system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of some derived units, "without prejudice to the question of others that may be added in the future." Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is now accepted as the legal system of units of measurement by most countries in the world.
The International System of Units (SI) is a harmonized system in which for any physical quantity such as length, time or force, there is one and only one unit of measure. Some of the units are given specific names, such as the pascal for pressure, while others are named after the units from which they are derived, such as the unit of speed, the meter per second. The main units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in Table. 2. Of all the derived mechanical units, the most important are the newton unit of force, the joule unit of energy, and the watt unit of power. Newton is defined as the force that gives a mass of one kilogram an acceleration equal to one meter per second squared. A joule is equal to the work done when the point of application of a force equal to one Newton moves one meter in the direction of the force. A watt is the power at which work of one joule is done in one second. Electrical and other derived units will be discussed below. The official definitions of primary and secondary units are as follows.
A meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
The kilogram is equal to the mass of the international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
A mole is equal to the amount of a substance that contains the same amount structural elements, how many atoms are in the carbon-12 isotope with a mass of 0.012 kg.
A radian is a flat angle between two radii of a circle, the length of the arc between which is equal to the radius.
The steradian is equal to the solid angle with the vertex at the center of the sphere, which cuts out an area on its surface, equal to the area a square with a side equal to the radius of the sphere.
For the formation of decimal multiples and submultiples, a number of prefixes and multipliers are prescribed, indicated in Table. 3.
|
Table 3 INTERNATIONAL SI DECIMAL MULTIPLES AND MULTIPLE UNITS AND MULTIPLIERS |
|||||
| exa | deci | ||||
| peta | centi | ||||
| tera | Milli | ||||
| giga | micro |
mk |
|||
| mega | nano | ||||
| kilo | pico | ||||
| hecto | femto | ||||
| soundboard |
Yes |
atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
Initially, one of the basic units was supposed to be the gram, and this was reflected in the names of the units of mass, but now the basic unit is the kilogram. Instead of the name of megagrams, the word "ton" is used. In physical disciplines, for example, to measure the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as x-rays, in scientific publications it is allowed to use a picometer and x-unit (1 x-unit = 10 -13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (l).
Mass, length and time.
All the basic units of the SI system, except for the kilogram, are currently defined in terms of physical constants or phenomena, which are considered to be invariable and reproducible with high accuracy. As for the kilogram, a method for its implementation with the degree of reproducibility that is achieved in the procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1×10–8. The standards of multiples and submultiples for a kilogram are established by combined weighing on a balance.
Because the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. So, by the interference method, dashed and end gauges, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods under optimal conditions does not exceed one billionth (1×10–9). With the development of laser technology, such measurements have been greatly simplified and their range has been substantially extended.
Similarly, the second, in accordance with its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam atoms are excited by a high-frequency generator tuned to the atomic frequency, and the electronic circuit measures time by counting the oscillation periods in the generator circuit. Such measurements can be carried out with an accuracy of the order of 1×10 -12 - much better than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their references can be transmitted by radio. Thanks to this, anyone with the appropriate radio receiving equipment can receive accurate time and reference frequency signals that are almost identical in accuracy to those transmitted on the air.
Mechanics.
temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other ratios. Although the work done when moving a mass against the action of a force and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The thermodynamic temperature unit Kelvin (K), called the kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken equal to 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two heat reservoirs with constant temperature and a reversible heat engine transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by the equality T 2 /T 1 = –Q 2 Q 1 , where Q 2 and Q 1 - the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice the heat transferred to another reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the energy of the gas has been converted into mechanical energy in the adiabatic expansion section of the cycle. This temperature is called absolute zero. The thermodynamic temperature, usually used in scientific research, coincides with the temperature included in the ideal gas equation of state PV = RT, Where P- pressure, V- volume and R is the gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. For any of the real gases, this law is not exactly fulfilled. But if we make corrections for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the above definition, the temperature can be measured with a very high accuracy (up to about 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a heat-insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the tank rises (in accordance with the equation of state), and when cooled, the opposite is observed. By simultaneously measuring resistance and pressure, it is possible to calibrate a thermometer according to gas pressure, which is proportional to temperature. The thermometer is then placed in a thermostat in which liquid water can be maintained in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). The Celsius temperature is obtained from the Kelvin temperature by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of work and time. Therefore, in 1968 the International Practical Temperature Scale (IPTS) was introduced. Using this scale, thermometers of various types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer used in the temperature intervals between some pairs of constant reference points (temperature reference points). The MTS was supposed to correspond with the greatest possible accuracy to the thermodynamic scale, but, as it turned out later, its deviations are very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in combination with the British technical system of units, as well as in non-scientific measurements in many countries, is usually determined by two constant reference points - the temperature of ice melting (32 ° F) and the boiling point of water (212 ° F) at normal (atmospheric) pressure. Therefore, to get the Celsius temperature from the Fahrenheit temperature, subtract 32 from the latter and multiply the result by 5/9.
Heat units.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by changing the temperature of a certain amount of water, a unit called a calorie and equal to the amount of heat required to raise the temperature of one gram of water by 1 ° C became widespread. Due to the fact that the heat capacity of water depends on temperature , I had to specify the value of the calorie. At least two different calories appeared - "thermochemical" (4.1840 J) and "steam" (4.1868 J). The “calorie” used in dieting is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most areas of science and technology.
electricity and magnetism.
All common electrical and magnetic units of measurement are based on the metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units derived from certain physical formulas from metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was considered that it was more convenient to establish, by appropriate experiments, derived standards for some of the indicated quantities, and measure others using such standards.
SI units.
Below is a list of electrical and magnetic units of the SI system.
The ampere, the unit of electric current, is one of the six basic units of the SI system. Ampere - the strength of an unchanging current, which, when passing through two parallel rectilinear conductors of infinite length with a negligible circular cross-sectional area, located in vacuum at a distance of 1 m from one another, would cause an interaction force equal to 2 × 10 on each section of the conductor 1 m long - 7 N.
Volt, unit of potential difference and electromotive force. Volt - electric voltage in a section of an electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb - the amount of electricity passing through the cross section of the conductor at a constant current of 1 A in a time of 1 s.
Farad, unit of electrical capacitance. Farad is the capacitance of a capacitor, on the plates of which, with a charge of 1 C, an electric voltage of 1 V arises.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which an EMF of self-induction of 1 V occurs with a uniform change in the current strength in this circuit by 1 A per 1 s.
Weber, unit of magnetic flux. Weber - a magnetic flux, when it decreases to zero in a circuit coupled to it, which has a resistance of 1 Ohm, an electric charge equal to 1 C flows.
Tesla, unit of magnetic induction. Tesla - magnetic induction of a uniform magnetic field, in which the magnetic flux through a flat area of 1 m 2, perpendicular to the lines of induction, is 1 Wb.
Practical standards.
Light and illumination.
The units of luminous intensity and illuminance cannot be determined on the basis of mechanical units alone. It is possible to express the energy flux in a light wave in W/m 2 and the intensity of a light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is essential, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the unit of luminous intensity is the candela (formerly called a candle), equal to strength light in a given direction of a source emitting monochromatic radiation with a frequency of 540×10 12 Hz ( l= 555 nm), energy strength light radiation which in this direction is 1/683 W/sr. This roughly corresponds to the light intensity of the spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens Thus, if this source is located in the center of a sphere with a radius of 1 m, then the illumination of the inner surface of the sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
Roentgen (R) is an obsolete unit of exposure dose of X-ray, gamma and photon radiation, equal to the amount of radiation, which, taking into account secondary electron radiation, forms ions in 0.001 293 g of air, carrying a charge equal to one CGS charge unit of each sign. In the SI system, the unit of absorbed radiation dose is the gray, which is equal to 1 J/kg. The standard of the absorbed dose of radiation is the installation with ionization chambers, which measure the ionization produced by radiation.
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This lesson will not be new for beginners. We all heard from school such things as a centimeter, a meter, a kilometer. And when it came to mass, they usually said grams, kilograms, tons.
Centimeters, meters and kilometers; grams, kilograms and tons have one common name - units of measurement of physical quantities.
In this lesson, we will look at the most popular units of measurement, but we will not go deep into this topic, since units of measurement go into the realm of physics. Today we are forced to study part of physics, as we need it for further study of mathematics.
Lesson contentLength units
The following units of measurement are used to measure length:
- millimeters;
- centimeters;
- decimeters;
- meters;
- kilometers.
millimeter(mm). You can even see millimeters with your own eyes if you take the ruler that we used at school every day.
Small lines that follow each other in a row are millimeters. More precisely, the distance between these lines is one millimeter (1 mm):
centimeter(cm). On the ruler, each centimeter is indicated by a number. For example, our ruler, which was in the first figure, had a length of 15 centimeters. The last centimeter on this ruler is marked with the number 15.
There are 10 millimeters in one centimeter. You can put an equal sign between one centimeter and ten millimeters, since they denote the same length:
1cm=10mm
You can see for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distance between lines) is 10.
The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. Between one decimeter and ten centimeters, you can put an equal sign, since they denote the same length:
1 dm = 10 cm
You can verify this if you count the number of centimeters in the following figure:
You will find that the number of centimeters is 10.
The next unit of measure is meter(m). There are ten decimeters in one meter. Between one meter and ten decimeters, you can put an equal sign, since they denote the same length:
1 m = 10 dm
Unfortunately, the meter cannot be illustrated in the figure, because it is rather large. If you want to see the meter live, take a tape measure. Everyone has it in the house. On a tape measure, one meter will be designated as 100 cm. This is because there are ten decimeters in one meter, and one hundred centimeters in ten decimeters:
1 m = 10 dm = 100 cm
100 is obtained by converting one meter to centimeters. This is a separate topic, which we will consider a little later. In the meantime, let's move on to the next unit of length, which is called a kilometer.
A kilometer is considered the most big unit length measurements. Of course, there are other older units, such as a megameter, a gigameter, a terameter, but we will not consider them, since a kilometer is enough for us to further study mathematics.
There are a thousand meters in one kilometer. You can put an equal sign between one kilometer and a thousand meters, since they denote the same length:
1 km = 1000 m
Distances between cities and countries are measured in kilometers. For example, the distance from Moscow to St. Petersburg is about 714 kilometers.
International system of units SI
The international system of units SI is a certain set of generally accepted physical quantities.
The main purpose of the international system of SI units is to reach agreements between countries.
We know that the languages and traditions of the countries of the world are different. There's nothing to be done about it. But the laws of mathematics and physics work the same everywhere. If in one country “twice two is four”, then in another country “twice two is four”.
The main problem was that for each physical quantity there are several units of measurement. For example, we have just learned that there are millimeters, centimeters, decimeters, meters and kilometers for measuring length. If several scientists speaking different languages gather in one place to solve some problem, then such a large variety of length units can give rise to contradictions between these scientists.
One scientist will claim that in their country length is measured in meters. The second might say that in their country, length is measured in kilometers. The third one can offer his own unit of measurement.
Therefore, the international system of units SI was created. SI is an abbreviation for the French phrase Le Système International d'Unités, SI (which in Russian means - the international system of units SI).
The SI lists the most popular physical quantities and each of them has its own generally accepted unit of measurement. For example, in all countries, when solving problems, it was agreed that the length would be measured in meters. Therefore, when solving problems, if the length is given in another unit of measurement (for example, in kilometers), then it must be converted to meters. We will talk about how to convert one unit of measure to another a little later. In the meantime, let's draw our international system of units SI.
Our drawing will be a table of physical quantities. Each studied physical quantity we will include in our table and indicate the unit of measure that is accepted in all countries. Now we have studied the units of measurement of length and learned that meters are defined in the SI system for measuring length. So our table will look like this:
Mass units
Mass is a measure of the amount of matter in a body. In the people, body weight is called weight. Usually, when something is weighed, they say "it weighs so many kilograms" , although we are not talking about weight, but about the mass of this body.
However, mass and weight are different concepts. Weight is the force with which a body acts on a horizontal support. Weight is measured in newtons. And mass is a quantity that shows the amount of matter in this body.
But there is nothing wrong with calling the mass of the body weight. Even in medicine they say "human weight" , although we are talking about the mass of a person. The main thing is to be aware that these are different concepts.
The following units of measure are used to measure mass:
- milligrams;
- grams;
- kilograms;
- centners;
- tons.
The smallest unit of measure is milligram(mg). Milligram most likely you will never put into practice. They are used by chemists and other scientists who work with small substances. It is enough for you to know that such a unit of mass measurement exists.
The next unit of measure is gram(G). In grams, it is customary to measure the amount of a product when compiling a recipe.
There are a thousand milligrams in one gram. You can put an equal sign between one gram and a thousand milligrams, since they denote the same mass:
1 g = 1000 mg
The next unit of measure is kilogram(kg). The kilogram is a common unit of measure. It measures everything. The kilogram is included in the SI system. Let's also include one more physical quantity in our SI table. We will call it "mass":
There are a thousand grams in one kilogram. Between one kilogram and a thousand grams, you can put an equal sign, since they denote the same mass:
1 kg = 1000 g
The next unit of measure is centner(c). In centners, it is convenient to measure the mass of a crop harvested from a small area or the mass of some kind of cargo.
There are one hundred kilograms in one centner. An equal sign can be put between one centner and one hundred kilograms, since they denote the same mass:
1 q = 100 kg
The next unit of measure is ton(T). In tons, large loads and masses of large bodies are usually measured. For example, mass spaceship or car.
There are a thousand kilograms in one ton. You can put an equal sign between one ton and a thousand kilograms, since they denote the same mass:
1 t = 1000 kg
Time units
We don't need to explain what time is. Everyone knows what time is and why it is needed. If we open the discussion to what time is and try to define it, then we will begin to delve into philosophy, and this is not what we need now. Let's start with time units.
The following units of measurement are used to measure time:
- seconds;
- minutes;
- watch;
- day.
The smallest unit of measure is second(With). Of course, there are also smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since at the moment there is no point in this.
In seconds, various indicators are measured. For example, how many seconds does it take an athlete to run 100 meters. The second is included in the international SI system of units for measuring time and is denoted as "s". Let's also include one more physical quantity in our SI table. We will call it "time":
minute(m). There are 60 seconds in one minute. You can put an equal sign between one minute and sixty seconds, since they represent the same time:
1 m = 60 s
The next unit of measure is hour(h). There are 60 minutes in one hour. You can put an equal sign between one hour and sixty minutes, since they represent the same time:
1 h = 60 m
For example, if we studied this lesson for one hour and we are asked how much time we spent studying it, we can answer in two ways: "we studied the lesson for one hour" or so "we studied the lesson for sixty minutes" . In both cases, we will answer correctly.
The next unit of time is day. There are 24 hours in a day. Between one day and twenty-four hours you can put an equal sign, since they denote the same time:
1 day = 24 hours
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