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 $)

Question

Water is being poured at the rate of 36 m$^3$/min into a cylindrical vessel whose circular base is of radius 3 meters. Then the water level in the cylinder increases at the rate of:

Answer 1

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.

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 \( g = 10 \, \text{m/s}^2 \))

Show Hint

The Correct Option is A

Solution and Explanation

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