5. Consider an incompressible flow of air with a constant density of ρ = 1.23 kg/m³ through the

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Question

5. Consider an incompressible flow of air with a constant density of $\rho$ = 1.23 kg/m³ through the a pipe bent into a U shape. The pipe inlet is 5 cm in diameter. Air is injected with velocity of 120 m/s and exits the opposite end with the same velocity in the opposite direction. The pipe inlet and outlet are at atmospheric conditions. (a) What is the mass flow rate of air at the exit plane? (b) What force does the air exert on the pipe? (c) Assume that the flow is adiabatic and reversible, and no body forces are applied to the flow. By how much does the internal energy of air change across the control volume? Make sure to show the derivations supporting your answer.

          5. Consider an incompressible flow of air with a constant density of $\rho$ = 1.23 kg/m³ through the a pipe
bent into a U shape. The pipe inlet is 5 cm in diameter. Air is injected with velocity of 120 m/s and
exits the opposite end with the same velocity in the opposite direction. The pipe inlet and outlet are
at atmospheric conditions.
(a) What is the mass flow rate of air at the exit plane?
(b) What force does the air exert on the pipe?
(c) Assume that the flow is adiabatic and reversible, and no body forces are applied to the flow. By
how much does the internal energy of air change across the control volume? Make sure to show
the derivations supporting your answer.

5. Consider an incompressible flow of air with a constant density of ρ = 1.23 kg/m³ through the a pipe
bent into a U shape. The pipe inlet is 5 cm in diameter. Air is injected with velocity of 120 m/s and
exits the opposite end with the same velocity in the opposite direction. The pipe inlet and outlet are
at atmospheric conditions.
(a) What is the mass flow rate of air at the exit plane?
(b) What force does the air exert on the pipe?
(c) Assume that the flow is adiabatic and reversible, and no body forces are applied to the flow. By
how much does the internal energy of air change across the control volume? Make sure to show
the derivations supporting your answer.

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