Effect of nozzle friction on jet speed How does internal friction (irreversibility) within a steam nozzle influence the exit velocity of the steam jet for a given inlet and back pressure?
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AIt decreases the exit velocity due to kinetic energy loss
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BIt has no effect on the exit velocity once the flow is choked
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CIt increases the exit velocity by heating the steam
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DIt increases mass flow enough to raise velocity
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EIt only changes the direction, not the magnitude, of velocity
Answer
Correct Answer: It decreases the exit velocity due to kinetic energy loss
Explanation
Introduction / Context:Nozzle friction converts part of the available enthalpy drop into entropy rather than directed kinetic energy. Appreciating this effect is crucial for predicting jet speed and turbine work.
Given Data / Assumptions:
- Same inlet state and back pressure for the comparison.
- Real nozzle with friction vs. ideal isentropic nozzle.
- Negligible heat transfer to surroundings.
Concept / Approach:In an ideal nozzle, the isentropic enthalpy drop fully converts to kinetic energy: V^2/2 = Δh_isentropic. With friction, the actual kinetic energy equals η_nozzle * Δh_isentropic, where 0 < η_nozzle < 1. Thus, exit velocity is lower.
Step-by-Step Solution:Write V_actual^2 / 2 = η_nozzle * Δh_isentropic.For fixed inlet and exit pressures, friction raises entropy and reduces effective Δh to kinetic energy.Therefore, V_actual < V_isentropic; exit velocity decreases.
Verification / Alternative check:Measured nozzle coefficients (velocity coefficient < 1) quantify this reduction; test data show lower exit Mach numbers and speeds than ideal predictions.
Why Other Options Are Wrong:
- (b) Choking does not eliminate friction losses; it limits mass flow but velocity still falls from the ideal.
- (c) Internal viscous heating increases entropy, not useful kinetic energy.
- (d) Mass flow changes are secondary and do not increase exit kinetic energy beyond ideal.
- (e) Friction affects magnitude strongly.
Common Pitfalls:Assuming choked flow guarantees ideal velocity; choking fixes Mach at the throat, not exit losses.
Final Answer:It decreases the exit velocity due to kinetic energy loss