Page 96 - 48Fundamentals of Compressible Fluid Mechanics

58 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW
Isothermal Nozzle
k = 1 4
4
*
P / P
3.5 A / A *
*
P P
0 / 0
3 *
T T
0 / 0
*
2.5 T / T
2

1.5

1

0.5

0
0 0.5 1 1.5 2 2.5 3 3.5 4
M

Tue Apr 5 10:20:36 2005

Fig. 4.6: Various ratios as a function of Mach number for isothermal Nozzle

. All these equations are plotted in Figure

(4.6). From the Figure 4.3 it can be observed that minimum of the curve isn’t
on
. The minimum of the curve is when area is minimum and at the point

Of course in isothermal process
where the flow is choked. It should be noted that the stagnation temperature is not
constant as in the adiabatic case and the critical point is the only one constant.
The mathematical procedure to find the minimum is simply taking the deriva-
tive and equating to zero as following

(4.78)

1

1

Equation (4.78) simplified to

(4.79)

It can be noticed that a similar results are obtained for adiabatic flow. The velocity
at the throat of isothermal model is smaller by a factor of . Thus, dividing the