In a cement factory, a viscous liquid flows through a pipe with an area of cross-section 6 m2 at a velocity of 8 m/s.When this fluid moves forward, the area of cross-section of the pipe decreases to 4 m2 The velocity of the liquid will now be
Correct answer: B. 12 m/s.
- A. 3 m/s.
- B. 12 m/s.
- C. 18 m/s.
- D. 24 m/s.
Explanation
The principle of continuity for incompressible fluid flow states that the product of the cross-sectional area and velocity must remain constant. Initially, the flow rate is 6 m2 × 8 m/s = 48 m3/s. When the cross-sectional area decreases to 4 m2, the velocity must increase to maintain the same flow rate. Therefore, the new velocity is 48 m3/s ÷ 4 m2 = 12 m/s. Hence, option B is correct. Options A, C, and D are incorrect because they do not satisfy the continuity equation given the change in cross-sectional area.
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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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