(a)
The mass flow rate of air through a duct with
Answer to Problem 9.84P
The mass flow rate is
Explanation of Solution
Given:
Concept Used:
Mass flow rate,
Where,
The temperature at the exit,
The density of air
Local sound speed,
Velocity at the exit,
Where,
Calculation:
Local sound speed,
Velocity of air,
The density of air
Mass flow rate,
Substituting the values of density, area and the velocity in the above relation, we get
Conclusion:
The mass flow rate is
(b)
The Mach number at the section 2.
Answer to Problem 9.84P
The Mach number is
Explanation of Solution
Given:
Concept Used:
Mass flow rate,
Where,
The temperature at the exit,
The density of air
Local sound speed,
Velocity at the exit,
Where,
Calculation:
From section 1 to 2 the flow is isentropic.
For the Mach number
The area ratio
Corresponding to this area ratio, the Mach number
The pressure across the shock is given by
The area ratio is given by
The area ratio is given by
Corresponding to this area ratio, the Mach number
Thus, the Mach number
Conclusion:
The Mach number is
(c)
The stagnation pressure at the section 3.
Answer to Problem 9.84P
The stagnation pressure at the section 3
Explanation of Solution
Given:
Concept Used:
Mass flow rate,
Where,
The temperature at the exit,
The density of air
Local sound speed,
Velocity at the exit,
Where,
Calculation:
The stagnation pressure ratio across the shock can be determined using the Mach number at the section 2
For the Mach number
Thus, the stagnation pressure at the section 3
Conclusion:
The stagnation pressure at the section 3
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Chapter 9 Solutions
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