Water flows through a first pipe of diameter 3 inches. If it is desired to use another pipe for the same flow rate such that the velocity head in the second pipe is twice the velocity head in the first pipe, determine the diameter of the second pipe.

the diameter of the second pipe is 2.52 in

Explanation:  

Given the data in the question;

We know that; the rate of flow is the same;

so

Av1 = Av2

v ∝ √h

=

 = √(   )

( π/4.D1² / π/4.D2² ) = √(   )

( D1² / D2² ) =  √(   ) since second is double of first

so

( D1² / D2² ) =  √(   )  

3² / D2² =  √2

D2²√2  = 9

D2² = 9/√2

D2² = 9 / 1.4142

D2² = 6.364

D2 = √ 6.364

D2 = 2.52 in

Therefore, the diameter of the second pipe is 2.52 in