(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the manometer in the figure. If the specific weight of fluid A is 100kN/m^{3}, what is the absolute pressure, in kPa, indicated by the manometer when the local atmospheric pressure is 90kPa?

2. Relevant equations

Specific weight = [itex]\gamma _{s}=\rho g[/itex]

Pressure = [itex]\rho gh[/itex]

3. The attempt at a solution

[tex]\rho_{a}=\left (100,000\frac{N}{m^{3}} \right )/\left (9.81\frac{m}{s^{2}} \right )=10,194\frac{kg}{m^{3}}[/tex]

[tex]\rho_{b}=\left (8,000\frac{N}{m^{3}} \right )/\left (9.81\frac{m}{s^{2}} \right )=815.49\frac{kg}{m^{3}}[/tex]

Find absolute pressure P_{1}.

[tex]P_{1}+\rho_{a}g(.05m)=\rho_{b}g(.12m)+P_{atm}[/tex]

[tex]P_{1}=\rho_{b}g(.12m)+P_{atm}-\rho_{a}g(.05m)[/tex]

[tex]P_{1}=\left (815.49\frac{kg}{m^{3}} \right )\left (9.81\frac{m}{s^{2}} \right )+\left (90,000Pa \right )-\left (10,194\frac{kg}{m^{3}} \right )\left (9.81\frac{m}{s^{2}} \right )\left (.05m \right )[/tex]

[tex]P_{1}=86kPa[/tex]

I'm approaching this problem as a force balance equation. The answer I came up with looks reasonable, but I am unsure if I used the correct height (.12m) for fluid B. Also, I know the image shows 10kN/m^{3}for the SG of fluid A but the problem statement uses 100kN/m^{3}which is what I'm basing my calculations on.

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# Pressure in a manometer - Absolute pressure

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