Question 122
Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled ?
Solution
Water is flowing at the rate of 3 km/hr = 3000m/hr
circular pipe's internal radius = 20/2 cm = $$\frac{1}{10}$$ m
Volume of water that flows out = $$\pi r^{2}h$$ = $$\pi (\frac{1}{10})^{2}3000$$ = 30π
Volume of the cylinder tank is = $$\pi r^{2}h$$ = $$\pi \frac{10^2}{2} = 50\pi$$
To fill the tank ,
Volume of water flowing out in T hrs = volume of tank
$$30\piT = 50\pi$$
T = 1.66 hrs
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