Question

A pipe through which water is flowing is having diameters 20 cm and 10 cm at the cross-sections 1 and 2 respectively. The velocity of water at section 1 is given 4 m/s. Find the velocity head at sections 1 and 2 and also rate of discharge.

Answer 1

8 m/s is the answer....

Answer 2

Answer:

Velocity head at sections 1 =  0.815 m

Velocity head at sections 2 =  13.04 m

Rate of Discharge = 0.12568 m3/s

Explanation:

Given:

Cross section 1 diameter = D1= 0.2 m

Cross section 2 diameter = D2= 0.1 m

Velocity at cross section 1 = v1 = 4m/s

Velocity at cross section 2 = v2

We know that,

A1*v1 = A2* v2

π(D1)^2/4 * v1 = π(D2)^2/4 * v2

So,

v2 = (D1/D2)^2 * v1 = 4*4 = 16 m/s

Velocity head at sections 1 = v1 ^ 2/ 2g = 16/(2*9.81) = 0.815 m

Velocity head at sections 2 = v2 ^ 2/ 2g = 256/(2*9.81) = 13.04 m

Rate of Discharge = A1v1 = A2v2

                              = π(D1)^2/4 * v1

                              = (3.142*0.2*0.2 *4)/4

                              =  0.12568 m3/s

So,

Rate of Discharge = 0.12568 m3/s