If a device consists of one inlet and one outlet and the volume flow rates at the inlet and at the outlet are equal, then the flow through the device:
- Amust be laminar
- Bmust be steady
- Cmust be uniform
- Dis not necessarily steadyCorrect
Solution
Concept
Equal inlet and outlet volume flow rates only show conservation of mass (for incompressible flow). They do not prove that the flow is steady.
Formula
Qin = Qout = A V
Step-by-step solution
1. For incompressible flow, continuity gives Qin = Qout at every instant. 2. This equality can hold even when Q changes with time, for example when a pump speeds up. 3. Steady flow means flow properties do not change with time at a point. 4. Equal flow rates at inlet and outlet do not prove there is no change with time. 5. So the flow is not necessarily steady.
Explanation
Equal inlet and outlet flow rates only mean that no mass is stored inside the device. The flow rate can still rise or fall with time, so the flow may be unsteady. It also need not be laminar or uniform.
Why the other options are wrong
A: Laminar or turbulent depends on Reynolds number, not on equal flow rates. B: Flow rate can change with time while staying equal at both ends, so steady flow is not guaranteed. C: Uniform flow means velocity does not change with position. The inlet and outlet areas may be different, so velocities may differ.
Shortcut
Equal Q at inlet and outlet means continuity only, not steady flow.
Common mistake
Thinking that equal inflow and outflow always means steady flow.
Correct answer: D) is not necessarily steady