ENB221 Lecture Fluid Mechanics
The Ideal Gas Law
Equation of State of a Perfect Gas
M = mass P=ρRT
R = Characteristic Gas Constant P = pressure
T = Temperature Ρ=Density
The Universal Gas Constant (R)
M = Molar mass (molecular weight) -1 -1
RU= Universal Gas Constant = 8.314 kJ kMol K
Thermal Total Energy
Kinetic Total energy is the sum of all energies of a system (E).
Denoted by e, if given on a per mass basis
Internal Energy Microscopic Energy
The forms of energy related to the molecular structure of The microscopic energy of a system is related to motion
a system and the degree of molecular activity are and the influence of some external effects such as,
referred to as microscopic energy. The sum of all Temperature change
microscopic forms of energy is called the Internal Energy
of a system (U) Magnetism
Denoted by, u, if given on a per mass basis. Electricity
Thermal Energy Heat
What we think of systems heat content is actually A system cannot contain heat. Heat only exists as energy
Thermal Energy. Thermal energy is the sensible and crossing a system boundary through a temperature
latent forms of internal energy. difference. All other forms of energy transfer are work.
In systems that involve fluid flow we frequently
encounter enthalpy, the combination of internal energy
and flow energy.
The flow energy, or flow work, is the energy per unit
mass needed to move the fluid and maintain flow.
Using Enthalpy instead of internal energy to represent
the energy associated with the flow work is already
taken care of.
1 Week 3 Tuesday, 27 August 2013 ENB221 Lecture Fluid Mechanics
Specific heat is the energy required to raise the temperature of a unit of mass of a substance by one degree in a
specified way. (kJ kg K ).
Specific heat at constant volume, c Specific heat at constant pressure, c
The energy required to raise the temperature of The energy required to raise the temperature of the unit mass
the unit mass of a substance by one degree as the of a substance by one degree as the pressure is maintained
volume is maintained constant. Used for change in constant. Used for change in enthalpy. In an ideal system:
internal energy. In an ideal system
∫ ( )
∫ ( )
Formal Definition: ( ) Formal Definition: ( )
Specific Heat for Incompressible Substances
For incompressible substances the constant-volume and constant-pressure specific heats are identical
Therefore C vC pC
For liquids the internal energy can be defined as: Δu=C ΔT
The specific heat of an ideal gas changes with temperature. In fact C and C are only dependent on temperature
For instance it takes 0.718 kJ of energy to heat air at 300 K by 1 degree, but it takes 0.855 kJ at 1000K
At low pressure, relative to the critical point, all real gases approach ideal-gas behaviour, and therefore their specific
heat depends on temperature only. The specific heats of real gases at low pressures are called ideal-gas specific
heats, or zero-pressure specific heats, and are often denoted c and c .
Values for u, internal energy, h enthalpy and p and cvfor many gases have been tabulated
Internal energy and enthalpy change can be calculated when specific heat is taken constant at an average value.
For small temperature intervals the specific heats may be assumed to vary linearly with temperature.
2 Week 3 Tuesday, 27 August 2013 ENB221 Lecture Fluid Mechanics
Specific Heat relations of ideal gases
We know that olume of a fluid changes with a
change in its temperature of pressure. Fluids
typically expand when heated or
depressurised and contract when they are
cooled or pressurised. This change in volume
is different for different fluids.
Bulk Modulus of Elasticity (Coefficient of compressibility, or the bulk modulus of compressibility)
It can also be expressed approximately in terms of finite changes:
As Δv/v and similiarly Δρ/ρ are dimensionless κ has the same dimension as
Represents the change in pressure corresponding to a fractional change in volume or density, of a fluid (for T =
constant.) For a truly incompressible substance, κ =∞.
Large values of κ indicate that a large change in pressure is needed to cause a small change in volume.
Fluids with large κ can be treated as incompressible – most liquids.
The normal force exerted by a fluid per unit area, only meaningful for a gas or a liquid. In solids we talked about
Normal stress measured in Pascals (Pa). The dimensions of Pascals are normally denoted as Newtons per square
meter (Nm ). Commonly spoken in terms of kPa or MPa. Pressure is always positive.
Defined as “The force acting perpendicular to the surface per unit area”.
Absolute Pressure Gauge Pressure
The actual pressure at a given position, measured relative Most devices do not measure absolute pressure,
to an absolute vacuum typically devices are calibrated to read zero at
atmospheric pressure. They therefore indicate the
difference between absolute pressure and the local
3 Week 3 Tuesday, 27 August 2013 ENB221