A large storage tank, open to the atmosphere at the top and fi lled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of fl ow from the leak is 2.50 103 m3 /min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole

The speed at which the water leaves the hole = 4.21

The value of  diameter of the hole d = 0.112 m = 11.2 cm

Step-by-step explanation:

Given data

Flow rate = 2.5 × = 0.0416 ×

Height (h) = 16 m

(a) The speed at which the water leaves the hole :-

Apply bernouli equation for the water tank at point 1 & 2

------ (1)

Since = , &

Equation (1) becomes

=

This is the speed at which the water leaves the hole.

Put the values of g & h in the above formula

⇒ 2 g h = 2 × 9.81 × 16 = 17.71

= =

= 4.21

This is the speed at which the water leaves the hole.  

(b)Diameter of the hole :-

We know that flow rate Q = A × V

Put the values of Q & V in the above formula we get

A =   ×

A = 9.88 ×

We know that area A =

⇒ = × 9.88 ×

⇒ = 0.01258

⇒ d = 0.112 m = 11.2 cm

this is the value of  diameter of the hole.