Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 6 of 37
A large open-top water tank has a small circular hole at its bottom. If the water level is \( 30 \text{ m} \) above the bottom of the tank, what is the speed of the water leaking from the hole? (Assume \( g = 9.8 \text{ m/s}^2 \))
A
\( 15.5 \text{ m/s} \)
B
\( 24.2 \text{ m/s} \)
C
\( 5.5 \text{ m/s} \)
D
\( 4.44 \text{ m/s} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 24.2 \text{ m/s} \)
Concept:

Torricelli's Theorem dictates that the efflux speed of a fluid from a large tank is equivalent to the speed of free fall from the fluid's surface.

Formula:

$$ v = \sqrt{2gh} $$

Solution:

  • Height of the fluid column \( h = 30 \text{ m} \).
  • Plug into the equation: \( v = \sqrt{2 \times 9.8 \times 30} \).
  • \( v = \sqrt{588} \).
  • Since \( 24^2 = 576 \) and \( 25^2 = 625 \), \( \sqrt{588} \) must be approximately \( 24.2 \text{ m/s} \).


Why other options are incorrect:

The other options result from either forgetting to take the square root, misusing the height, or omitting the factor of 2 in the formula.

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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