Manometer U Tube Homework: Solving Pressure in B

[tsslaporte]

Homework Statement

The U-tube in the figure is sealed at both ends. It contains a gas in A, another gas in B, and mercury in C. The heights of the mercury in the two arms are as shown. The density of mercury is 13.6 g/cm3. If the pressure in A is 1 × 10^4 dyn/cm2, the pressure in B is


The attempt at a solution

4-7 = 3CM

0.03m * 9.81 * 13600 kg/m^3 which = 4000 Pa which converts to 4x10^4 dyn/cm^2

But the answer given was 5x10^4 dyn/cm^2


I am not sure what I am doing wrong?


Edit: 4x10E4 is the pressure difference. So I have to add A which is 1x10E4 and that gives B = 5x10E4.

Could someone explain why I add A?

 

[RTW69]

One way to think about this problem is to calculate the pressure at the bottom of the U-tube. Look at the left U-tube column the pressure at the bottom is P_b+ h_b*density*g that will equal the right U-tube P_a+h_a*density*g

It is easy to see why you must add P_a if you are measuring the pressures at the bottom of the U-tube