Question

Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and disregarding minor losses, determine the ratio of the flow rates in the two pipes.

Answer 1

Answer:

$\frac{\dot V_{A}}{\dot V_{B}}\approx 5.657$

Explanation:

The head loss due to friction has the following model:

$\Delta h_{l} = f\cdot \frac{L}{D}\cdot \frac{v^{2}}{2\cdot g}$

$\Delta h_{l} = f \cdot \frac{L}{D} \cdot \frac{1}{2\cdot g}\cdot \frac{\dot V^{2}}{\frac{\pi^{2}}{16}\cdot D^{4} }$

$\Delta h_{l} = \frac{8\cdot f\cdot L \cdot \dot V^{2}}{\pi^{2}\cdot g \cdot D^{5}}$

Given that both pipes are connected parallel:

$\frac{f\cdot L \cdot \dot V_{A}^{2}}{4\cdot \pi^{2}\cdot g \cdot D^{5}} = \frac{8\cdot f\cdot L \cdot \dot V_{B}^{2}}{\pi^{2}\cdot g \cdot D^{5}}$

$\dot V_{A}^{2} = 32\cdot \dot V_{B}^{2}$

$\frac{\dot V_{A}}{\dot V_{B}}= \sqrt{32}$

$\frac{\dot V_{A}}{\dot V_{B}}\approx 5.657$