Question

A water tank is open at the top and has a hole of area \( 10^{-4} \, \text{m}^2 \) at the bottom. The height of the water column is 5 m. What is the speed of the water flowing out of the hole? (Take \( g = 10 \, \text{m/s}^2 \))

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 20 m/s

Hint:

Remember: Torricelli’s law is used to calculate the speed of a fluid flowing out of a hole: \( v = \sqrt{2gh} \).

Answer 1

The Correct Option is A

Given: Height of water column, \( h = 5 \, \text{m} \)
Gravitational acceleration, \( g = 10 \, \text{m/s}^2 \)

Step 1: Apply Torricelli's Law Torricelli's law states that the efflux velocity \( v \) of a fluid from an orifice is: \[ v = \sqrt{2gh} \] where \( g \) is acceleration due to gravity and \( h \) is the fluid column height.
Step 2: Input provided values Substitute the given values into the formula:
\[ v = \sqrt{2(10 \, \text{m/s}^2)(5 \, \text{m})} \]
\[ v = \sqrt{100} = 10 \, \text{m/s} \]

Answer: The correct option is (b): 10 m/s.