Question #290845

The pressure in the pressurized water tank is measured by a multi-fluid manometer

with one end open to the atmosphere. Determine the absolute pressure of air in the

tank (pressure at point 1) assuming that the air pressure is uniform. The densities of

mercury, water and oil are 13,600 kgm/m3, 1000 kgm/m3, 850 kgm/m3, respectively. h1

= 20 cm, h2 = 30 cm and h3 = 46 cm


1
Expert's answer
2022-01-27T13:25:51-0500

Now We know that



At point B

PB=Pair+ρgh1+ρwgh2P_B=P_{air}+\rho gh1+\rho_wgh_2

PB=Patm+ρmgh3P_B=P_{atm}+\rho_m gh_3

Both equation are equal


Pair+ρgh1+ρwgh2=Patm+ρmgh3P_{air}+\rho gh1+\rho_wgh_2=P_{atm}+\rho_m gh_3

Pair=Patm+ρmgh3ρgh1ρwgh2P_{air}=P_{atm}+\rho_m gh_3-\rho g h_1-\rho_wgh_2

ρmgh3=13600×9.8×0.46=61308.8pa\rho_mgh_3=13600\times9.8\times0.46=61308.8pa

ρogh1=800×9.8×0.20=1568pa\rho_ogh_1=800\times9.8\times0.20=1568pa

ρwgh2=1000×9.8×0.30=2940pa\rho_wgh_2=1000\times9.8\times0.30=2940pa

Now put value


Pair=105+61308.815682940P_{air}=10^5+61308.8-1568-2940

Pair=156.8008KpaP_{air}=156.8008Kpa


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