Discussion
Water is supplied to a tank at the rate of 0.02 m3/s, as shown in the figure below. The cross-sectional area of the tank is 1 m2 and the inner diameter of the outlet pipe is 60 mm. At a time when the water level in the tank is increasing at the rate of 5 mm/s, the average velocity (in m/s) of water in the outlet pipe is approximately
Answer: C
The outlet velocity is about 5.3 m/s.
Mass conservation: inflow equals outflow plus the rate of storage in the tank.
\[ \begin{aligned} Q_{out} &= 0.02 - (1)(0.005) = 0.015\ \text{m}^{3}\text{/s} \\ A_{pipe} &= \tfrac{\pi}{4}(0.06)^{2} = 2.827 \times 10^{-3}\ \text{m}^{2} \\ V &= \frac{0.015}{2.827 \times 10^{-3}} \approx 5.3\ \text{m/s} \end{aligned} \]
Ignoring the rising level and using the full 0.02 m3/s would give about 7.1 m/s, which is not offered. 0.005 is the rate of rise of the level itself, and 0.06 is the pipe diameter in metres, not a velocity.
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