Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 9 of 37
An incompressible liquid flows along a pipe featuring two distinct cross-sectional areas, \( A_1 \) and \( A_2 \), with fluid velocities \( V_1 \) and \( V_2 \) respectively. The ratio of the speeds \( V_1 / V_2 \) is strictly equal to:
A
\( A_1 / A_2 \)
B
\( A_2 / A_1 \)
C
\( (A_2 / A_1)^2 \)
D
\( (A_1 / A_2)^2 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( A_2 / A_1 \)
Concept:

The Equation of Continuity governs the mass flow rate of an incompressible fluid, ensuring it remains constant throughout a closed pipe.

Formula:

$$ A_1 V_1 = A_2 V_2 $$

Solution:

  • Divide both sides by \( A_1 \): \( V_1 = \frac{A_2 V_2}{A_1} \).
  • Divide both sides by \( V_2 \): \( \frac{V_1}{V_2} = \frac{A_2}{A_1} \).
  • This shows that the fluid's velocity is inversely proportional to the cross-sectional area.


Why other options are incorrect:

Option A falsely implies a direct relationship. Options C and D wrongly suggest a squared relationship concerning the area itself, rather than the radius/diameter.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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