Page 100 - 48Fundamentals of Compressible Fluid Mechanics

62 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

( %

With known Mach number, and temperature at the exit the velocity can be calcu-

'33

%

lated. The exit temperature is

'33

. The exit velocity, then,
is #

3'

%

(

Even for the isothermal model, the initial stagnation temperature is given

3 (
& 1
as

. With the area ratio by using the Figure 4.6 or using the Potto–GDC
obtains the following table is obtained
# #

%(

The exit Mach number is known and the initial temperature to the throat tempera-

ture ratio can be calculated as following:
'*3
0
(4.88)

%

% %

Thus the stagnation temperature at the exit is %
)('(('(('('((/%

%

The exit stagnation temperature is

(/3 . The exit velocity deter-

mined by utilizing the following equation #

)('('(('(('(*(*%

As it was discussed before the velocity in copper nozzle will be larger than

%(

3 *
& 1

velocity in the wood nozzle. However, the maximum velocity can not exceed the
# #

3 '
& 1
4.5 The Impulse Function
4.5.1 Impulse in Isentropic Adiabatic Nozzle

One of the function that used in calculation of the forces is the Impulse function.
The Impulse Function is denoted here as , but in the literature some denote this
function as . To explain the motivation for using this definition consider calculation

of the net forces that acting on section shown in Figure (4.9). To calculate the
net forces that acting on the section shown in the Figure in the x direction the
momentum equation has to be applied as
(4.89)