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U-tube Manometer for Measuring Pressure Difference in Pipe Flow

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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 (ρ_{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} = Δp = (ρ_{m }- ρ)gh.

Ideal Gas law

PV = n RT

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

Mass density (ρ) = Molecular weight x molal density

Calculations:

(a) Water is flowing through the pipe:

Δp =
(ρ_{m }-
ρ)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:

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

Δp =
(ρ_{m }-
ρ)gh = (13600 - 1.2)
x 9.812 x 0.026 = **3469.2 N/m**^{2}

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Last Modified on: 01-May-2024

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