Topic: Fluid Mechanics
Two pipe lines at a different pressures, $p_{A}$ and $p_{B}$, each carrying the same liquid of specific gravity of $S_{1}$ are connected to a U tube with a liquid of specific gravity of $S_{2}$ resulting in the level differences $h_{1}$, $h_{2}$ and $h_{3}$ as shown in the figure. The difference is pressure head between points A and B in terms of head of water is.
- A. $h_{1}S_{2}+h_{2}S_{1}+h_{3}S_{1}$
- B. $h_{1}S_{1}+h_{2}S_{2}-h_{3}S_{1}$
- C. $h_{1}S_{1}-h_{2}S_{2}-h_{3}S_{1}$
- D. $h_{1}S_{1}+h_{2}S_{2}+h_{3}S_{1}$
Answer: D. $h_{1}S_{1}+h_{2}S_{2}+h_{3}S_{1}$
Explanation: Starting from point A and writing the manometric equation towards B: $P_{A} - h_{1}S_{1} - h_{2}S_{2} - h_{3}S_{1} = P_{B}$. Rearranging to find the pressure difference: $P_{A} - P_{B} = h_{1}S_{1} + h_{2}S_{2} + h_{3}S_{1}$.