### Fluid Mechanics

# Manometer Connected Between Two Pipes

A U - tube differential mercury manometer is connected between two pipes X and Y. Pipe X contains carbon tetra chloride (Sp.gr. 1.59) under a pressure of 103 kN/m^{2} and pipe Y contains oil (Sp.gr. 0.8) under a pressure of 172 kN/m^{2}. Pipe X is 2.5 m above pipe Y. Mercury level in the limb connected to pipe X is 1.5 m below the centerline of pipe Y. Find the manometer reading as shown by a centimeter scale attached to it.

Data:

Fluid in pipe X = carbon tetra chloride

Density of Carbon tetra chloride = 1.59 x 1000 kg/m^{3}

P_{x} = 103 kN/m^{2 }

Fluid in pipe Y= oil

Density of Carbon tetra chloride = 0.8 x 1000 kg/m^{3}

P_{y} = 172 kN/m^{2 }

Formula:

P = rgh

Principle: Pressure at the same level in a continuous body of static fluid is equal.

Calculations:

Equating the pressure at the two legs of the manometer at OO':

For the left hand leg pressure at O = P_{o} = P_{x} + (2.5 + 1.5) x 1590 x 9.812 + a x 13600 x 9.812 N/m^{2}

For the right hand leg pressure at O' = P_{o'} = P_{y} + (1.5 + a) x 800 x 9.812 N/m^{2}

P_{x} + (2.5 + 1.5) x 1590 x 9.812 + a x 13600 x 9.812 = P_{y} + (1.5 + a) x 800 x 9.812

Substituting for P_{x} and P_{y},

103000 + 62404.32 + 133443.2 x a = 172000 + 7849.6 x a + 11774.4

-18370.08 = - 125593.6 x a

a = 0.146 m = 14.6 cm

Manometer Reading = **14.6 cm of
Hg**