Orifice Meters: The velocity through an orifice can be computed knowing the value of orifice coefficient C_V, which is a function or Reynolds number. The expansion factor for liquids is 1.0, whereas for gases it is found from the following equation.

Example 4.6: Air is flowing through an orifice meter and water manometer reads 1 in. What is the expansion factor of this meter? The density of air under the operating conditions is 0.075 lb/ft³. Nominal diameters of orifice are 3 in and 2 in. Use the following information:

Heat capacity ratio, k = 1.4, density of water = 62.43 lb/ft³, density of air = 0.075 lb/ft³

Inlet pressure of air, P₁ = 14.7 psi.

Solution

C Pressure drop, ΔP (Equation 4.1)

C Final pressure, P₂:

P₂ = P₁ - ΔP = 2116.2 - 5.2 = 2111 lb_f/ft²

C Pressure ratio, r (Equation 4.8):

r = P₂/P₁ = 2111/2116.2 = 0.998

C Diameter ratio, β (Equation 4.6)

d₂ = 0.622 in, d₁ = 3.068 in

β = d₂/d₁ = 0.622/3.068 = 0.203.

C Expansion factor, Y (Equation 4.10).