Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 17 of 37
Which of the following mathematical statements correctly expresses the Equation of Continuity for fluid dynamics?
A
\( A_1 V_1 = A_2 V_2 \)
B
\( A_1 V_2 = A_2 V_1 \)
C
\( P_1 V_1 = P_2 V_2 \)
D
\( A_1 / V_1 = A_2 / V_2 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( A_1 V_1 = A_2 V_2 \)
Concept:

The Equation of Continuity represents the conservation of mass in a pipe. For an incompressible fluid, the volume entering one end in a given time equals the volume leaving the other end.

Formula:

$$ A_1 V_1 = A_2 V_2 \implies Q = \text{constant} $$

Solution:

  • \( A \) is the cross-sectional area and \( V \) is the flow velocity.
  • Their product yields the volume flow rate (\( Q \)).
  • The relationship ensures that a decrease in area results in a proportional increase in velocity.


Why other options are incorrect:

Option B represents an inverse proportionality if rearranged. Option C is Boyle's Law for gases (Pressure and Volume). Option D implies a direct relationship between area and velocity, which is physically backwards.

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