Necessary condition for flow through a nozzle:\nIf the inlet steam pressure equals the exit pressure, what happens to pressure drop and flow in the nozzle?

Introduction / Context:
Nozzles convert pressure energy into kinetic energy. A fundamental requirement for any flow through a nozzle is a driving potential—typically a pressure difference. Without a pressure differential, the nozzle cannot accelerate the fluid and sustained flow will not occur (ignoring transient effects).

Given Data / Assumptions:

• Steady operation, no external body forces causing flow.
• Inlet static pressure equals exit static pressure.
• No pump or external device imparting momentum directly within the nozzle.

Concept / Approach:
From basic fluid mechanics, steady flow requires a gradient in total pressure (or head) to overcome friction and to produce acceleration. If inlet and outlet pressures are equal, there is no net driving force; in the ideal, frictionless limit, there is no acceleration; with real friction, any attempt at flow would immediately dissipate energy and eliminate motion, settling at zero flow. Therefore, when p_in = p_out, there is no pressure drop and no flow.

Step-by-Step Solution:

Verification / Alternative check:
Energy equation for steady flow shows V_out^2/2 − V_in^2/2 ≈ (p_in − p_out)/ρ minus losses; with Δp = 0 and nonzero losses, only the trivial solution V_in ≈ V_out ≈ 0 remains steady.

Why Other Options Are Wrong:

• Suggesting pressure drop or flow exists contradicts the premise of equal inlet and outlet pressures under steady, passive conditions.

Common Pitfalls:
Confusing instantaneous transients (e.g., opening a valve briefly) with steady-state; sustained flow requires a pressure difference.

Final Answer:
there is no pressure drop and fluid does not flow through the nozzle