Answer to Question #191226 in Mechanics | Relativity for Vince

Question #191226
The pressure in a water pipeline is measured by the manometer with one of the arms open to the atmosphere where the local atmospheric pressure is 101.3 kPa. Determine the absolute pressure at point A. The densities of air and mercury are 1.2 kg/m3 and 13 600 kg/m3 respectively. The specific gravity of oil is 0.85.
1
Expert's answer
2021-05-10T09:19:27-0400

Given,

Local atmospheric pressure (P)=101.3kPa(P)=101.3kPa

Absolute pressure at the point A=?

The density of the air (ρair)=1.2kg/m3(\rho_{air})=1.2 kg/m^3

The density of the mercury (ρhg)=13600kg/m3(\rho_{hg})=13600 kg/m^3

Specific gravity of oil (goil)=0.85(g_{oil})=0.85

PgasPo=ρghP_{gas}-P_{o}=\rho gh

Pgas=Po+ρghP_{gas}=P_o+\rho gh

Pgas=Po+g(ρoilhoil+ρhghρairhair)P_{gas}=P_o+g(\rho_{oil} h_{oil}+\rho_{hg}h_{}-\rho_{air}h_{air})

Now, substituting the values,

Pgas=101.3kPa+9.8(0.0254)(13600×6+1000×271.25×25)P_{gas}=101.3kPa+9.8(0.0254)(13600\times6+1000\times 27 -1.25\times 25)

=27126kP=27126kP


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