Alarge storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. if the rate of flow from the leak is 2.50×10−3m3/min, determine the diameter of the hole.

The diameter of the hole is

Explanation:

The velocity at the top of the tank is zero. As depth increases, velocity increases, thus, potential energy is equal to the kinetic energy at the hole level (16-meter depth).

Step 1: We calculate the velocity of water at the hole level

ρgh = ρv²/2

gh = v²/2 (striking the density of water out)

Therefore,

v² = (2)(9.81 m/s²)(16 m)

∴ v = 17.7 m/s (velocity of water at the hole level)

Step 2: We find the area of the hole itself.

Step 3: We calculate the diameter of the hole from its area.

∵

this would be about 43%