Problems for final exam
Chapter 2: Fundamentals of compressible flow
1. Derive the expression of the speed of sound for a non-reacting ideal gas.
2. Why the flow is considered compressible when Mach number is higher than 0.3?
3. Derive the expressions of stagnation quantities (temperature, pressure and density).
4. Discuss, using appropriate mathematical derivations, the effect of irreversibility on the
stagnation pressure in adiabatic flow.
5. Discuss, using appropriate mathematical derivations, the behavior of iso-lines on P-v and
T-s diagrams.
6. Air enters the diffuser of an aircraft jet engine at a static pressure of 20 kPa and static
temperature 217 K and a Mach number of 0.9. The air leaves the diffuser with a velocity
of 85 m/s. Assuming isentropic operation, determine the exit static temperature and
pressure.
7. Air expands isentropically in a rocket nozzle from 𝑃0 = 3.5 MPa, 𝑇0 = 2700 K to an
ambient pressure of 100 kPa. Determine the exit velocity, Mach number and static
temperature.
Chapter 3: Normal shock waves
1. Starting from the continuity, momentum, energy and entropy equations, show that any
normal shock wave solution has to be compressive.
2. Starting from the continuity, momentum, energy and entropy equations, derive the ratios
of pressure, temperature, density, stagnation pressure and stagnation temperature across a
normal shock wave. Discuss
3. A shock wave advances into stagnant air at a pressure of 100 kPa and 300 K. If the static
pressure downstream of the wave is tripled, what is the shock speed and the absolute
velocity of the air downstream of the shock?
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Chapter 2: Fundamentals of compressible flow
1. Derive the expression of the speed of sound for a non-reacting ideal gas.
2. Why the flow is considered compressible when Mach number is higher than 0.3?
3. Derive the expressions of stagnation quantities (temperature, pressure and density).
4. Discuss, using appropriate mathematical derivations, the effect of irreversibility on the
stagnation pressure in adiabatic flow.
5. Discuss, using appropriate mathematical derivations, the behavior of iso-lines on P-v and
T-s diagrams.
6. Air enters the diffuser of an aircraft jet engine at a static pressure of 20 kPa and static
temperature 217 K and a Mach number of 0.9. The air leaves the diffuser with a velocity
of 85 m/s. Assuming isentropic operation, determine the exit static temperature and
pressure.
7. Air expands isentropically in a rocket nozzle from 𝑃0 = 3.5 MPa, 𝑇0 = 2700 K to an
ambient pressure of 100 kPa. Determine the exit velocity, Mach number and static
temperature.
Chapter 3: Normal shock waves
1. Starting from the continuity, momentum, energy and entropy equations, show that any
normal shock wave solution has to be compressive.
2. Starting from the continuity, momentum, energy and entropy equations, derive the ratios
of pressure, temperature, density, stagnation pressure and stagnation temperature across a
normal shock wave. Discuss
3. A shock wave advances into stagnant air at a pressure of 100 kPa and 300 K. If the static
pressure downstream of the wave is tripled, what is the shock speed and the absolute
velocity of the air downstream of the shock?
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