Answer to Question #130095 in Mechanics | Relativity for Ariyo Emmanuel

Question #130095
The water in a tank is pressurized by air,
and the pressure is measured by a multifluid manometer as shown in the Fig. The
tank is located on a mountain at an
altitude of 1400 m where the atmospheric
pressure is 85.6 kPa. Determine the air
pressure in the tank if ℎ1 = 0.1 m, ℎ2 =
0.2 m, and ℎ3 = 0.35 m. Take the
densities of water, oil, and mercury to be
1000 kg/m3
, 850 kg/m3
, and 13,600
, respectively?
Expert's answer


given data:-

atmospheric pressure( Patm)=85.6kPa

Patm =85600Pa

density of water"(\\rho_w)=1000kg\/m^3"

density of oil"(\\rho_o)=850kg\/m^3"

density of mercury"(\\rho_m)=13600kg\/m^3"

height of water column(h1)= 0.1m

height of oil column from water level(h2)=0.2m

height of mercury column (h3)=0.35m

figure can be drawn like this using data of question

pressure at point B from left side of figure can be written

"P_B =P_{air}+\\rho_ogh_1+\\rho_wgh_2" ........(eq.1)

pressure at point B from right side of figure can be written

"P_B =P_{atm}+\\rho_mgh_3" ................(eq.2)

from equation 1 and 2


"P_{air}=P_{atm}+\\rho_mgh_3-\\rho_ogh_1-\\rho_wgh_2" ...(eq.3)




by putting the value in eq.3




therefore pressure of air in the tank is 129.45KPa.

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