13. (a) The two water reservoirs shown in the figure are open to the atmosphere,

Question

13. (a) The two water reservoirs shown in the figure are open to the atmosphere, and the water has density p1 = 1000 kg m^3. The manometer contains incompressible mercury with a density of p2 = 13,600 kg m^3. 1f necessary, you can use the atmospheric pressure Po and the gravitational acceleration on Earth g to answer the following questions. (i) Write down the expression for the water pressures at A and B. and define them as PA and PB, respectively. You can use the parameters defined in the problem. [4]

Explanation / Answer

The pressure only depend on deep, density of the fluid and gravity. So at point A we have pA=y1*g*rhowater and at point B pB=y2*g*rhowater. These pressure are "gauge pressure" or "manometric pressure". To obtain absolute presure we only need to sum atmospheric pressure po.

Note that pA=pA' because both points are at the same deep, so we can write pA'=pA=y2*g*rhowater+h2*g*rhomercury or pA=pB+h2*g*rhomercury, finally pA-pB=h2*g*rhomercury

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