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 20oC 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 (ρm) = 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,

P1 - P2 = Δp = (ρm - 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 = (ρm - ρ)gh = (13600 - 1000) x 9.812 x 0.026 = 3214.4 N/m2

(b) Air at atmospheric pressure and 20oC is flowing in the pipe:

ρ = 28.8 x 101325/(8314 x 293) = 1.2 kg/m3

Δp = (ρm - ρ)gh = (13600 - 1.2) x 9.812 x 0.026 = 3469.2 N/m2