GATE MT 2020 Q45. Figure shows schematic of a venturi meter. The cross sectional area is 100 mm^2 at A and is 50 mm^2 at B. If air is flowing through the venturi meter at a flow rate of 10^-3 m^3. S^-1, the height H in the air over-water manometer is _____________ mm (round off to the nearest integer). A. Incompressible flow with no friction losses.B. Density of air is 1 kg m^-3. C. Density water is 1000 kg m^-3. D. Acceleration due to gravity is 9.8 m s^-2.

According to Bernoulli's Principle at A and B points,

P(A)/ρ*g + v(1)^2/2*g + Z(1) = P(B)/ρ*g + v(2)^2/2*g + Z(2) ----> Eq(1)

Z(1) = Z(2) = 0 (since.. datum line is axial line of the pipe)
ρ = 1 kg/m^3

Given Q(volumetric flowrate) = 10^(-3) m^3/s.
v(1) = Q/A(1) = 10^(-3)/(100*(10^-3)^2) = 10 m/s
v(2) = Q/A(2) = 10^(-3)/(50*(10^-3)^2) = 20 m/s

Substituting above values in Eq - 1;

P(A) - P(B) = 150 ---> Eq(2)

Air-over-Water Manometer;

P(A) + ρ(air)*g*(H+h) = ρ(water)*g*H + ρ(water)*g*h + P(B) ---> Eq(3)

cancelling like terms and Equating Eq(2) & Eq(3)

150 = ρ(water)*g*H
H = 150 / (1000 * 9.8) = 0.0153m = 15.3mm