# Obtain an expression for pressure difference [closed] The question is "For the two-liquid manometer, shown below, obtain an expression for $$p_1 – p_2$$. Let $$\mathcal A$$ be the area of each tank and $$\mathcal S$$ the area of the tube. Let $$S_3$$ be the relative density of the manometric liquid, $$S_2$$ the relative density of liquid in the tanks and $$S_1$$ the relative density in which the pressure difference is to be measured."

I am struggling with line below because I don't understand why it should be $$\gamma S_1 (x_1+\Delta y)$$ and $$\gamma S_1 (x_1-\Delta y)$$. Any clarification is appreciated.

\begin{aligned} p_1= \gamma S_1 (x_1+\Delta y)+ \gamma S_2(x_3-\Delta y+x/2)-\gamma S_3x&\\ -\gamma S_2(x_3+\Delta y-x/2)-\gamma S_1 (x_1-\Delta y)=p_2 & \end{aligned}

Final answer $$p_1-p_2=\gamma x(S_3-S_2)$$.

## closed as off-topic by ZeroTheHero, John Rennie, Jon Custer, stafusa, Aaron StevensAug 15 at 14:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ZeroTheHero, John Rennie, Jon Custer, stafusa, Aaron Stevens
If this question can be reworded to fit the rules in the help center, please edit the question.