Question

What is the speed of water flowing through a hole located at a depth \(h\) from the surface of water in a tank?

• A. \(\sqrt{2gh}\)
• B. \(\sqrt{gh}\)
• C. \(2gh\)
• D. \(gh\)

Hint:

When determining the speed of fluid flowing through a hole, use Torricelli’s law, which gives the speed as \(\sqrt{2gh}\), where \(g\) is the acceleration due to gravity and \(h\) is the depth.

Answer 1

The Correct Option is A

The speed of water flowing through a hole in a tank can be determined using the Torricelli’s law, which is derived from the principle of conservation of energy. The speed \(v\) of the water flowing through the hole at a depth \(h\) is given by the equation: \[ v = \sqrt{2gh} \] Where: - \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)), - \(h\) is the height of the water above the hole. This formula is derived by equating the potential energy per unit volume of the water at depth \(h\) to the kinetic energy per unit volume of the water exiting the hole. Thus, the speed of water flowing through the hole is \(\sqrt{2gh}\).