Question

Two pipes of identical diameter and material are connected in parallel. The length of pipe A is five times the length of pipe B. Assuming the flow is fully turbulent in both pipes and thus the friction factor is independent of the Reynolds number and disregarding minor losses, determine the ratio of the flow rates in the two pipes.

Answer 1

Answer:

$\dfrac{Q_B}{Q_A}=\sqrt{5}$

Explanation:

Lets take

Length of pipe B = L

Length of pipe A = 5 L

Discharge in pipe A = Q₁

Discharge in pipe B = Q₂

We know that head loss in the pipe given as

$h_f=\dfrac{FLQ^2}{12.1d^5}$

F=Friction factor, Q=Discharge,L=length

d=Diameter of pipe

here all only Q and L is varying and all other quantity is constant

So we can say that

LQ²= Constant

L₁Q₁²=L₂Q²₂

By putting the values

5LQ₁²=LQ²₂

$\dfrac{Q_2}{Q_1}=\sqrt{5}$

Therefore

$\dfrac{Q_B}{Q_A}=\sqrt{5}$