Answer to Question #191226 in Mechanics | Relativity for Vince

Question

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.

Answer 1

Given,

Local atmospheric pressure $(P)=101.3kPa$

Absolute pressure at the point A=?

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

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

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

$P_{gas}-P_{o}=\rho gh$

$P_{gas}=P_o+\rho gh$

$P_{gas}=P_o+g(\rho_{oil} h_{oil}+\rho_{hg}h_{}-\rho_{air}h_{air})$

Now, substituting the values,

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

$=27126kP$