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Lecture 2:Measurement of Quantities Contents Preamble Standard units of measurement Derived units and quantities Composition of a mixture Derivation of units of universal constant Electrical units Concentration of solids in slurry Conclusion References Key words: unit and dimension, fundamental units, power, pressure Preamble The material balance shows the weights and analysis of input and output materials and the calculated inputs and outputs of each of the important elements and compounds. This accounting serves as a check on plant data in that the various totals of inputs and output should be equal. This lecture discusses the different ways of expression of measured quantities. It is felt that many a times the students have problems in unit and dimensions and to converting one unit to another. Standard units of measurement The adoption of standards has varied greatly as regards unit in different parts of the world. The following table lists some of the commonly used set of fundamental units from which all other units can be derived Quantity Absolute units FPS CGS MKS SI
Engg. Units English Mass Pound gram kg kg Slug (lb) (g) Length ft cm m m ft Time sec sec sec s sec Amount of substance Lb. mole g.mole kg mole mole Lb. mole Temperature o^ F o^ C o^ k(ork) k o^ F
FPS stands for feet, pound and second. It is british system
tension of MKS system
erived units and quantities derived from other physical quantities are called derived quantities.
example area, volume etc.
celeration. เญซเญฑเฌถ
CGS stands for centimeter, gram and second MKS stands for meter, kilogram and second SI stands for international system of units. Ex
D
Physical quantities which can be Derived units: The units of physical quantities which can be expressed in terms of fundamental units, for
Lets us derive (i) unit of force Force =mass x ac
In SI unit force เต เญฉเญฅ^ เต 1N (Newton).
In CGS unit forc e = (^) Cเญซเญฑเฌถเญฅ =
exp ewton( N)
dyne
In MKS unit force is ensed in N
In FPS systems force is Lเญ เญคเญฒเญฑ =1poundal
(ii) Energy =mu^2 we can substitute the units of m and u to derive unit of energy.
In SI system E เต kg เญซเฌถเญฑเฌถ เต 1Joule.
In CGS system E เต g Cเญซเฌถเญฑเฌถ เต 1 er
rgs. Lb ft เฌถ^ /s เฌถ^ เต ft poundal. 1British thermal unit (Btu) =778 ft. Lbf =1054.2 Joule = 252 cal 1kcal = 1000cal.=3.968 Btu (iii) power (watts or W).
g.
1goule = 107 e
In FPS system E เต.
Current =Ampere (A In solids current consists of electron flow. In electrolyte solutios.most of the
current flow by motion of conic species for example cuเต
^ or Na เต
e: flow of 1A/s. s a
as the resistance which ermits flow of 1 A current under an imposed electrical potential difference of 1V. s of electrical flow are:
เต t P เต I 2 Rt. W=energy measured in joules and power in watts Farada is one mole of electrons. faraday 96500 coulomb. One raday will discharge one gram equivalent of ions. The liberation of o bs of electricity
could be discharged in one minute by 1.9 X10^4 A current, if no
loss of current occur.
เฌธ เฌธ d เต เฐฒ
1coulomb is unit of charg SI unit of electrical potential is volt. Volt is the potential in which the charge of 1 coulomb experience force of 1 Newtron. SI unit of resistance is ohm. Ohm is defined p
Some basic equation V เต R. I P เต I. V เต I 2 R P เต power t เต time W A y 1 = fa ne g equivalent of any metal consumes 96500 coulom How many gram moles of Al 3เต
ions
In one minute a current of 1.9X10 A will carry 1.9 X10 X 60 coulombs of electricity.
Gram moles of Al deposite เฌต.เฌตเฌธเตเฌตเฌดเฌทเตเฌฝเฌบเฌนเฌดเฌด เต 3.
Concentration of solids in slurry: Many metallurgical processes have feed and/or product streams that consist of mixtures of solids and lled slurries. The relationship between wt % solid (%x) and specific gravity of solid phase (Ps ) and that of slurry (P (^) m ) an be obtained:
เฎกเฑฃ^ เฌต
liquids. These mixtures are ca
when water is used as a medium c Volume of slurry = Volume of solid x Volume of water. Consider 1 kg slurry with %x as solids weight percent, then
เต (^) เฌตเฌดเฌดเฎก%เญถ (^) เฑฉ เต
แบเฌตเฌดเฌดเฌฟ%เญถเฌตเฌดเฌดเฎก (^) เฑญ^ แป
ฯเญต เต density of water ฯเญฑ เต density of solid ty of mixture แบsolid เต
waterแป
แบWt percent solidแป% x เฌตเฌดเฌดเฎกเฎกเฑฃ เฑฉแบเฎก^ แบเฎกเฑฃเฌฟ (^) เฑฉเฌฟ เฌตเฌดเฌดเฌดเฌตเฌดเฌดเฌด แป^ แป
ฯเญซ เต densi เต (1)
Vo lume % slurry เต % x เฎกเฑฃเฎก (^) เฑฉ
ass flow rate of dry solid in slurry (M) เญดเญญเญชเญณเญซเญฃเญฒเญฐเญงเญก fเญชเญญเญต เญฐเญเญฒเญฃ เตเญฑเญชเญณเญฐเญฐเญท เญขเญฃ เญณเญฌเญฒเญท เต% เญถ เฌตเฌดเฌด
M
M เตเต F เฎกเฑฃเฌตเฌดเฌด^ %เญถ kg/hr
F is volume flow rate in m3/h By1 and 2
M เต F เฎกแบเฎก^ เฑฉ^ แบเฎกเฑฃเฌฟ (^) เฑฉเฌฟ เฌตเฌดเฌดเฌด^ เฌตเฌดเฌดเฌด แป^ แป
r.
Conclusion nsions of physical quantities are derived from fundamental unit of time. Suitable examples are given to illustrate the derivation of units.
Schuhmannโ Me
In this lecture the units and dime mass, length, temperature and Reference: tallurgical engineering principles
