The correct difference $(\frac{P_{A}}{w}-\frac{P_{B}}{w})$ is given by

Question

A differential manometer as shown in figure below is used to measure the difference in pressure at points A and B in terms specific weight of water w. The specific gravities of the liquids X, Y and Z are respectively S₁, S₂ and S₃

The correct difference $(\frac{P_{A}}{w}-\frac{P_{B}}{w})$  is given by

(a) $h_{3}S_{3}-h_{1}S_{1}+h_{2}S_{2}$

(b) $h_{1}S_{1}+h_{2}S_{3}-h_{3}S_{2}$

(c) $h_{3}S_{1}-h_{1}S_{2}+h_{2}S_{3}$

(d) $h_{1}S_{1}+h_{2}S_{2}-h_{3}S_{3}$