Topic: Fluid Mechanics
Two pipe lines of equal length are connected in series. The diameter of second pipe is two times that of first pipe, the ratio of head loss between first and second pipe is
- A. 1:32
- B. 32:1
- C. 1:8
- D. 1:4
Answer: B. 32:1
Explanation: For pipes in series, the discharge $Q$ is constant. The head loss $h_f$ is proportional to $V²/d$. Using $V = Q/A$, $h_f \propto 1/d^5$. Therefore, the ratio of head loss between the first and second pipe is $\frac{h_{f1}}{h_{f2}} = (\frac{d_2}{d_1})^5$. Since $d_2 = 2d_1$, the ratio is $2^5 = 32$. The correct ratio is 32:1.