Handout 1 - Clemson University

where y: ratio of specific heats air, (for the value y = 1.4 can be used for the range of
temperatures of interest)
By using Equations 3.2-7, and 3.2-8 3.2-9, the following equation is derived, which is
used as the equation of state for ideal gas instead of Equation 3.2-7 thus closing the
system of equations:
e = -P I -> e - P
p RIC, -1 p
By introducing the Mach number [34]:
U
M =- Equa tion 3.2-11
a
where a is the speed of sound in ideal gas given by
a 2 __
ap
_ yRT = y -
Equation 3.2-10
Equation 3.2-12
The energy equation (Equation 3.2-6) can be written in terms of the Mach number as
a, 21+ LM a2 1+ 21MM 2 Equation 3.2-13
After some algebraic manipulations, the following set of equations with the ratios of the
physical parameters that are of interest to us are calculated: