Question

A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.8 m below the water level. The rate of flow from the leak is found to be 3.00 10-3 m3/min. (a) Determine the speed at which the water leaves the hole. 22.22 Incorrect: Your answer is incorrect. The water speed at the top of the tank can be assumed to be zero since the flow rate from the hole is relatively small. m/s (b) Determine the diameter of the hole. 1.692e-3 Incorrect: Your answer is incorrect. How is the flow rate related to the area of the hole and the speed of the flow? mm

Answer 1

Pressure at the top of the tank = P_a

Pressure at the small hole on the side of the tank = P_b

The pressure at the top of the tank and at small hole on the side of the tank are equal to the atmospheric pressure as both of them are directly open to atmosphere.

P_a = P_b

Speed of flow at the top of the tank = V_a = 0 m/s (Assumed from question)

Speed of flow from the small hole = V_b

Height of water above the small hole = h = 16.8 m

By applying Bernoulli's equation at the top of the tank and at the small hole,

V_b = 18.15 m/s

Flow rate of water throught the small hole = Q = 3 x 10^-3 m³/min = 5 x 10^-5 m³/s

Diameter of the small hole = d

Area of the small hole = A = d²/4

Q = AV_b

5x10^-5 = (d²/4)(18.15)

d² = 3.507 x 10^-6

d = 1.872 x 10^-3 m

d = 1.872 mm

a) Speed of water at which it leaves the hole = 18.15 m/s

b) Diameter of the hole = 1.872 mm