The discharge coefficient - c d - varies considerably with changes in area ratio and the Reynolds number. Pipe location - Pressure tap location 2.5 times nominal pipe diameter upstream and 8 times nominal pipe diameter downstream from face of orifice." Vena Contracta" location - Pressure tap location 1 pipe diameter (actual inside) upstream and 0.3 to 0.8 pipe diameter downstream from face of orifice.Flange location - Pressure tap location 1 inch upstream and 1 inch downstream from face of orifice.The coefficient of a meter depends on the position of the taps. There are in general three methods for placing the taps. There is a pressure tap upstream from the orifice plate and another just downstream. The orifice meter consists of a flat orifice plate with a circular hole drilled in it. The formula above can be used with limitations for applications with relatively small changes in pressure and density. When measuring the mass flow in gases, its necessary to considerate the pressure reduction and change in density of the fluid. Q = c d (π / 4) D 2 2 1/2 (4)ĭ 2 = orifice, venturi or nozzle inside diameter (m, ft)ĭ 1 = upstream and downstream pipe diameter (m, ft)Įquation (4) can be modified to mass flow for fluids by simply multiplying with the density: The pressure recover to a pressure level lower than the pressure before the obstruction and adds a head loss to the flow.Įquation (3) can be modified with diameters to: After the metering device the velocity will decrease to the same level as before the obstruction. The viscous effect is usually expressed in terms of the non-dimensional parameter Reynolds Number - Re.ĭue to the Benoulli and the Continuity Equation the velocity of the fluid will be at it's highest and the pressure at the lowest in " Vena Contracta". " Vena Contracta" is the minimum jet area that appears just downstream of the restriction. The discharge coefficient c d is a function of the jet size - or orifice opening - theĪ vc = area in "vena contracta" (m 2, ft 2) The ideal equation (3) can be modified with a discharge coefficient: The theoretical flow rate q will in practice be smaller ( 2 - 40%) due to geometrical conditions. Q = A 2 1/2 (3)įor a given geometry (A), the flow rate can be determined by measuring the pressure difference p 1 - p 2. Γ = specific weight of fluid (kg/m 3, slugs/ft 3)Īssuming uniform velocity profiles in the upstream and downstream flow - the Continuity Equation can be expressed asĬombining (1) and (2), assuming A 2 < A 1, gives the "ideal" equation: The equation can be adapted to vertical flow by adding elevation heights : The Bernoulli EquationĪssuming a horizontal flow (neglecting the minor elevation difference between the measuring points) the Bernoulli Equation can be modified to: To understand orifice, nozzle and venturi meters it is necessary to explore the Bernoulli Equation. In a flow metering device based on the Bernoulli Equation the downstream pressure after an obstruction will be lower than the upstream pressure before.