Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 11 of 37
A nurse uses two different hypodermic needles of identical length. The first needle has an inside diameter of \( 0.30 \text{ mm} \), and the second has an inside diameter of \( 0.60 \text{ mm} \). To administer an injection at the exact same volume flow rate, how much more thumb pressure must be applied to the smaller needle compared to the larger one?
A
Twice as much
B
4 times as much
C
8 times as much
D
16 times as much
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 16 times as much
Concept:

Poiseuille's Law describes the pressure difference required to drive a viscous fluid through a narrow cylindrical pipe.

Formula:

$$ Q = \frac{\pi \Delta P r^4}{8 \eta L} \implies \Delta P \propto \frac{1}{r^4} $$

Solution:

  • Since volume flow rate (\( Q \)), length (\( L \)), and viscosity (\( \eta \)) are constant, pressure \( P \) is inversely proportional to \( r^4 \).
  • The ratio of diameters is \( 0.60 / 0.30 = 2 \). Thus, the ratio of radii is also 2.
  • Comparing pressures: \( \frac{P_1}{P_2} = \left(\frac{r_2}{r_1}\right)^4 = (2)^4 = 16 \).
  • The smaller needle requires 16 times more pressure.


Why other options are incorrect:

Option A assumes a linear relation. Option B assumes an area relation (\( r^2 \)). Poiseuille's flow strictly scales with the fourth power of the radius.

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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