Question

Air flows in a pipe with a diameter, D=50 mm. The inlet conditions are: M1 = 3; total pressure,
P01 = 1000 kPa absolute; and temperature, T1 = 550 K. The friction coefficient is, f = 0.004. The exit Mach number decreases with the length of the pipe.

Plot the following while the exit Mach number to be changed from 2.5 to 0.99 with decrements of ?M=0.01:
a) L, length of the pipe that is going to give the desired exit Mach number,

b) the P2, pipe exit pressure,

c) T2, pipe exit temperature, and

d) P02, pipe exit total pressure.

Make sure that each plot has a title and that the axes of the plots are labeled. Assume that the flow is steady and adiabatic. Use ?=1.4 and Cp = 1004.5 J / ( kg . K ).

Answer 1

For the fannow flow following relation can be used for length of the pipe -

where M1 is inlet mach no.,M2 is outlet mach no. ,f is friction coefficient ,L is length of pipe and D is the diameter of the pipe..here .

Expanding the equation it becomes-

substituting the values of the parameters we get L.

(b)To get exit pressure we can use following relationship -

(c) To get exit pressure we can use following relationship -

(d) .Total exit pressure can be found by -