QuestionJune 4, 2025

8. Water flows with a volume flow rate of 1.50m^3/s in a pipe. Find the water speed where the pipe radius is 050 m.

8. Water flows with a volume flow rate of 1.50m^3/s in a pipe. Find the water speed where the pipe radius is 050 m.
8. Water flows with a volume flow rate of 1.50m^3/s in a pipe. Find the water speed where the pipe radius is 050 m.

Solution
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Answer

1.91 \, \text{m/s} Explanation 1. Calculate the Cross-sectional Area The cross-sectional area A of a pipe is given by **A = \pi r^2**. Here, r = 0.50 \, \text{m}, so A = \pi (0.50)^2 = 0.785 \, \text{m}^2. 2. Calculate Water Speed Use the formula for volume flow rate **Q = A \cdot v**, where Q = 1.50 \, \text{m}^3/\text{s}. Solve for v: v = \frac{Q}{A} = \frac{1.50}{0.785} = 1.91 \, \text{m/s}.

Explanation

1. Calculate the Cross-sectional Area<br /> The cross-sectional area $A$ of a pipe is given by **$A = \pi r^2$**. Here, $r = 0.50 \, \text{m}$, so $A = \pi (0.50)^2 = 0.785 \, \text{m}^2$.<br />2. Calculate Water Speed<br /> Use the formula for volume flow rate **$Q = A \cdot v$**, where $Q = 1.50 \, \text{m}^3/\text{s}$. Solve for $v$: $v = \frac{Q}{A} = \frac{1.50}{0.785} = 1.91 \, \text{m/s}$.
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