Answer to Question #290845 in Molecular Physics | Thermodynamics for eysiii

Question

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

Answer 1

Now We know that

At point B

$P_B=P_{air}+\rho gh1+\rho_wgh_2$

$P_B=P_{atm}+\rho_m gh_3$

Both equation are equal

$$P_{air}+\rho gh1+\rho_wgh_2=P_{atm}+\rho_m gh_3$$

$$P_{air}=P_{atm}+\rho_m gh_3-\rho g h_1-\rho_wgh_2$$

$$\rho_mgh_3=13600\times9.8\times0.46=61308.8pa$$

$$\rho_ogh_1=800\times9.8\times0.20=1568pa$$

$$\rho_wgh_2=1000\times9.8\times0.30=2940pa$$

Now put value

$$P_{air}=10^5+61308.8-1568-2940$$

$$P_{air}=156.8008Kpa$$