### Fluid Mechanics

# U-tube Manometer

A U-tube manometer filled with mercury is connected between two points in a pipeline. If the manometer reading is 26 mm of Hg, calculate the pressure difference between the points when (a) water is flowing through the pipe (b) air at atmospheric pressure and 20^{o}C is flowing in the pipe.

Density of mercury = 13.6 gm/cc Density of water = 1 gm/cc Molecular weight of air = 28.8

Data:

Manometer reading(h) = 26 mm Hg = 0.026 m Hg

Density of mercury(r_{m}) = 13.6 gm/cc

Density of water = 1 gm/cc

Molecular weight of air(MW) = 28.8

Temperature of air = 20^{ o }C = 293 K

R = 8314 J/(kmol.K)

Formulae:

For simple U - tube manometer,

P_{1} - P_{2} = Dp = (r_{m }- r)gh.

Ideal Gas law

PV = n RT

Molal density = n/V = P/(RT)

Mass density(r) = Molecular weight x molal density

Calculations:

(a) Water is flowing through the pipe:

Dp =
(r_{m }-
r)gh = (13600 -
1000) x 9.812 x 0.026 = **3214.4
N/m ^{2}**

(b) Air at atmospheric pressure and 20^{o}C is flowing in the pipe:

r = 28.8 x 101325/(8314 x 293) = 1.2 kg/m^{3}

Dp =
(r_{m }-
r)gh = (13600 - 1.2)
x 9.812 x 0.026 = **3469.2 N/m ^{2}**