Air enters a 15-m-long, 4-cm-diameter adiabatic duct at
The exit Mach number, the exit velocity and the mass flow rate of air.
Answer to Problem 106P
The exit Mach number is
The exit velocity is
The mass flow rate of air is
Explanation of Solution
Given information:
The length of pipe is
Calculation:
Expression for inlet Mach number
Here, inlet velocity is
Expression for length required for sonic flow for inlet condition
Here, friction factor is
Expression for inlet density
Here, inlet pressure is
Expression for length required for sonic flow for outlet condition
Here, length of pipe is
Expression for mass flow rate of air
Refer to Table-A-1 “Molar mass, gas constant, and ideal gas specific heat of some substances” to obtain gas constant of air as
Substitute
Refer to Table-A-15 “Rayleigh flow function for an ideal gas with
Relation of velocity at initial state and sonic state
Here, inlet velocity at sonic state is
Substitute
Substitute
Substitute
Refer to Table-A-16 “Fanno flow function for an ideal gas with
Relation of velocity at exit and sonic state
Substitute
Substitute
Substitute
Conclusion:
The exit Mach number is
The exit velocity is
The mass flow rate of air is
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Chapter 12 Solutions
Connect 1 Semester Access Card For Fluid Mechanics Fundamentals And Applications
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