According to the equation of continuity, if the cross-sectional area of a pipe decreases, then the speed of the fluid passing through it
Correct answer: A. Increases
- A. Increases
- B. Decreases
- C. Remains the same
- D. Varies unpredictably
Explanation
The equation of continuity states that the mass flow rate must be constant in a closed system. This means that the product of cross-sectional area and fluid speed at any point in the pipe must remain constant. Therefore, if the cross-sectional area decreases, the fluid speed must increase to maintain the same mass flow rate. Option A is correct. Option B is incorrect because a decrease in area results in an increase in speed, not a decrease. Option C is incorrect because the speed does not remain the same; it changes to conserve mass. Option D is incorrect because the change in speed is predictable and follows the principle of mass conservation.
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About Equation of Continuity
The equation of continuity expresses conservation of mass in fluid flow. For steady incompressible flow, Av remains constant, so fluid speed increases when the cross-sectional area decreases; for compressible flow, ρAv is constant. This relation describes flow rate and area-speed changes without including pressure effects from Bernoulli’s equation.
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