Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 25 of 37
For an incompressible fluid, the mathematical product of the cross-sectional area of a pipe and the fluid's speed at any point along the pipe is known to:
A
Exponentially decrease along the pipe.
B
Remain strictly constant.
C
Be exactly zero.
D
Exponentially increase along the pipe.
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Remain strictly constant.
Concept:

This is the fundamental definition of the Equation of Continuity, expressing the conservation of mass.

Formula:

$$ Q = A \cdot v = \text{constant} $$

Solution:

  • Because the fluid is incompressible, its volume cannot be crushed or expanded.
  • Any volume of liquid entering one end must force an identical volume out the other end in the same timeframe.
  • The product of Area (\( A \)) and velocity (\( v \)) defines the volume flow rate (\( Q \)), which must remain constant along any streamline.


Why other options are incorrect:

Flow rate cannot be zero if the fluid is moving. It cannot increase or decrease, as that would imply fluid is being created out of nothing or destroyed/leaked inside the pipe.

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