Both ends of the U-tube mercury manometer of Fig. P2.52 are initially open to th

Question

Both ends of the U-tube mercury manometer of Fig. P2.52 are initially open to the atmosphere and under standard atmospheric pressure. When the valve at the top of the right leg is open, the level of mercury below the valve is h_1. After the valve is closed, air pressure is applied to the left leg. Determine the relationship between the differential reading on the manometer and the applied gage pressure, p_g. Show on a plot how the differential reading varies with p_g for h_1 = 25, 50, 75, and 100 mm over the range 0 lessthanorequalto p_g lessthanorequalto 300 kPa. Assume that the temperature of the trapped air remains constant.

Explanation / Answer

intially Patm = h1

now valve is closed and pressure is applied Pg

and after applying that differential reading is h

so new height is =h1-h

patm (Ax h1)= Pnewx(A x(h1-h))

Pnew =patm x h1/(h1-h)

in gauge pressure

Pnew=patm x [h1/(h1-h)-1]

Pnew=patm.h/(h1-h)

for new pressure pg is equal to pressure imparted by gas plus pressure due to mercury height

pg = rho gh +pnew

pg=rhogh +patm h/(h1-h)

this is realtion ship, where rho is density of mercury

for h=100mm =0.1

from this realtionship you can draw charts but careful for units.

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