Pipe Velocity When Diameter Is Halved
Easycontinuitypipe flow
A circular pipes diameter is halved while its volumetric flow rate remains constant. How does its average velocity change?
- AIt becomes half as large
- BIt stays the same
- CIt doubles
- DIt becomes four times as large
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Answer: D. It becomes four times as large
Equation: continuity, Q = A·V, with A = πD²/4 for a circular pipe. Values: Q is the same in both pipes (stated, and shown by the same Q in each). The first pipe has diameter D; the second has D/2. Step 1: area goes with diameter squared, so A₂/A₁ = (D/2 ÷ D)² = (1/2)² = 1/4. Step 2: with Q fixed, V = Q/A, so V₂/V₁ = A₁/A₂ = 4. The velocity becomes four times as large. Answering "doubles" scales velocity with diameter instead of with area.
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