A water tank has a hole at a distance of 5m from the free water surface. The velocity of water through the hole is 2mm. What is the rate of flow of water?




We are given the distance of the hole from the free water surface and the velocity of water through the hole. We need to find the rate of flow of water.


To solve this problem, we need to understand the concept of Torricelli's law. According to Torricelli's law, the velocity of water flowing out of a hole in the tank is given by the equation:

v = √(2gh)

Where:
- v is the velocity of water through the hole
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the water column above the hole

We can rearrange the equation to solve for h:

h = (v^2) / (2g)

The rate of flow of water through the hole is given by the equation:

Q = Av

Where:
- Q is the rate of flow of water
- A is the cross-sectional area of the hole
- v is the velocity of water through the hole


First, let's calculate the height of the water column above the hole:

h = (v^2) / (2g)
h = (0.002^2) / (2 * 9.8)
h = 0.000004 / 19.6
h = 0.000000204 m

Next, let's calculate the cross-sectional area of the hole. Since the hole is not specified, we'll assume it is circular with a diameter of 1 cm:

A = πr^2
A = π(0.005^2)
A = 0.00007854 m^2

Finally, let's calculate the rate of flow of water through the hole:

Q = Av
Q = 0.00007854 * 0.002
Q = 0.00000015708 m^3/s

Therefore, the rate of flow of water through the hole is approximately 0.00000015708 cubic meters per second.


The rate of flow of water through the hole is approximately 0.00000015708 cubic meters per second.

I am getting a answer as 12.48× 10^-5 m^3/s........ I am not sure of this answer!!!!