In a cement factory, a viscous liquid flows through a pipe with an area of cross-section 6 m2at 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: A. 12 m/s.
- A. 12 m/s.
- B. 3 m/s.
- C. 18 m/s.
- D. 24 m/s.
Explanation
To solve this problem, use the principle of continuity, which states that the product of the cross-sectional area and velocity of a fluid is constant across any two points in a streamline. Mathematically, this is expressed as A1 * V1 = A2 * V2. Here, the initial area A1 is 6 m2 and the initial velocity V1 is 8 m/s. The new area A2 is 4 m2. Setting up the equation 6 * 8 = 4 * V2, we solve for V2, yielding V2 = 12 m/s. Therefore, the correct answer is 12 m/s. The other options do not satisfy the continuity equation.
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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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