Question

A hole of area 1 mm\(^2\) opens in the pipe near the lower end of a large water storage tank, and a stream of water shoots from it. If the top of the water in the tank is 20 m above the point of the leak, the amount of water escapes in 1 s is:

• A. 87.5 cm\(^3\)/s
• B. 43.1 cm\(^3\)/s
• C. 27.5 cm\(^3\)/s
• D. 19.8 cm\(^3\)/s

Hint:

Use Torricelli’s Law to calculate the speed of a fluid exiting a hole under the influence of gravity.

Answer 1

The Correct Option is A

The velocity of water exiting the hole is given by Torricelli's Law: \[ v = \sqrt{2gh} \] where \( h = 20 \, \text{m} \) and \( g = 9.81 \, \text{m/s}^2 \). Thus, the velocity of the water is: \[ v = \sqrt{2 \times 9.81 \times 20} = 19.8 \, \text{m/s} \] The flow rate \( Q \) is given by: \[ Q = A \cdot v \] where \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \). Therefore: \[ Q = 1 \times 10^{-6} \times 19.8 = 1.98 \times 10^{-5} \, \text{m}^3/\text{s} = 87.5 \, \text{cm}^3/\text{s} \]