Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 2 of 37
Water flows smoothly from a pipe with a diameter of \( 6.0 \text{ cm} \) into a wider pipe with a diameter of \( 8.0 \text{ cm} \). If the speed of the water in the narrower pipe is \( 5.0 \text{ m/s} \), what is its speed in the wider pipe?
A
\( 1.4 \text{ m/s} \)
B
\( 2.8 \text{ m/s} \)
C
\( 3.7 \text{ m/s} \)
D
\( 8.8 \text{ m/s} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 2.8 \text{ m/s} \)
Concept:

According to the Equation of Continuity for an incompressible fluid, the volume flow rate must remain constant.

Formula:

$$ A_1 v_1 = A_2 v_2 \implies d_1^2 v_1 = d_2^2 v_2 $$

Solution:

  • Given diameters: \( d_1 = 6 \text{ cm} \), \( d_2 = 8 \text{ cm} \).
  • Given initial speed: \( v_1 = 5.0 \text{ m/s} \).
  • Setup the equation: \( (6)^2 \times 5.0 = (8)^2 \times v_2 \).
  • \( 36 \times 5.0 = 64 \times v_2 \).
  • \( 180 = 64 v_2 \implies v_2 = \frac{180}{64} = \frac{45}{16} \approx 2.8 \text{ m/s} \).


Why other options are incorrect:

Using the ratio of diameters linearly instead of squaring them leads to incorrect speeds like 3.7 m/s. Assuming speed increases in a wider pipe would lead to Option D.

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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