Air enters a 5-cm-diameter, 4-m-long adiabatic duct with inlet conditions of
FIGURE P12-102
Velocity, temperature and pressure at the duct exit.
Answer to Problem 102P
Explanation of Solution
Given:
The properties of air to be,
Temperature
Pressure at Inlet
The average friction factor is given to be
Calculation:
The Fanno flow functions corresponding to the inlet Mach number of
First we check that the flow in everywhere shock at upstream is supersonic. The required length of duct from the inlet
This is higher than the actual length of
Therefore, the flow is indeed supersonic when the normal shock appears at the indicated location. Then, using the actual duct length
Taking the value
From
Calculating the temperature, pressure, and velocity before the shock,
The normal shock functions corresponding to Mach number
Then the temperature after the shock will be,
Pressure after the shock will be,
Sonic conditions exist at the exit of duct, and the flow downstream the shock will be Fanno flow. From
Calculating the temperature at the duct exit is given by,
Therefore, the temperature at the duct exit is
Calculating the pressure at the duct exit is given by,
Therefore, the pressure at the duct exit is
Calculating the velocity at the duct exit is given by,
Therefore, the velocity at the duct exit is
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Chapter 12 Solutions
Fluid Mechanics: Fundamentals and Applications
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