Summary of Week 1

1. Introduction

1. Dimension: a property that can be measured.

Types: Primitive (e.g. Length, Mass, Time, Moles, Temperature) and Derived (e.g. Area, Force, Energy, Power)
 
2. Units: scales used to measure or quantify the dimensions ( based on convention, law or custom )

1. Mass vs Weight: mass is the measure of matter while weight is the force of gravity acting on the mass

 
W = mg
where m is mass (in kg or lb_m)
g is acceleration due to gravity ( 9.8 m/s² or 32.174 ft/s² )
W is weight ( 1 N = 9.8 kg m/s² or 1 lb_f =32.174 lb_m ft/s² )
 
2. Density, specific gravity, specific volume

 
Density of A: mass per unit volume ( usually denoted by r_A)
Specific gravity (SG) of A = ratio of density of A to density of reference fluid
(For liquids and solids, the reference is water at 4^oC )
Specific volume of A= volume occupied by a unit mass of A = 1/r_A
 
3. Mass Flow and Volumetric Flow rates

 
Mass flow rate = amount of mass flowing per unit time ( dm/dt )

Volumetric flow rate = volume flowing per unit time ( dV/dt )

General relationship: dm/dt = (r dV/dt ) + (V dr/dt)

Special case: incompressible fluid (then r=constant or dr/dt = 0)
 

dm/dt = r dV/dt


Also,  volumetric flow of a liquid through a pipe is given by

        dV/dt =  A v

where  A is the crossectional area of the flow
           v is the average velocity of the flow

 
4. Mole vs lb-mole

 
mol ( or gmol ) of A= a unit count equal to N_Avogadro molecules of A
 
where N_Avogadro = 6.023 x 10²³


lb-mol = 454 mol ( approximately )

kg-mol = 1000 mol
 

5. Mass fraction vs Mole fraction

 
mass fraction of A = (mass of A)/(Total mass)

mole fraction of A = (moles of A)/Total moles)

Note: Mole fraction has to do with population fraction:
            Out the total number of molecules, how many are molecules of A ?

While the mass fraction of A has to do with mass contribution of A.
 
 

6. Pressure ( Gage vs Absolute)

 
P_abs = P_gage + P_atm

where
 

P_atm = the pressure of the atmosphere ( surroundings ) usually obtained from
barometric room pressure reading

P_gage = the raw pressure reading obtained from the pressure measuring device.
(usually reported as psi gage or psig)

P_abs = the absolute pressure experience by the system under measurement
( usually reported as psi absolute or psia)
 
 

7. Temperature Reading vs. Change in Temperature