Discharge Coefficient Calculator

Discharge Coefficient Diagram and Conceptual Flow Lines for an Orifice in a Pipe

Discharge Coefficient Equation

Valid for 0.4 ≤ C ≤ 0.8   and   0.2 ≤ β ≤ 0.7

Derivation of Discharge Coefficient Equation

Steady flow of an incompressible fluid through an orifice based on a discharge coefficient:

Pressure loss from location 1 to 3 in the pipe written in terms of discharge coefficient:

Pressure loss from 1 to 3 in the pipe due to the orifice written in terms of minor loss coefficient:

Also:

The goal is to solve the above equations for K. Begin by equating discharge coefficient equation (2) to (3):

Solve for K in terms of discharge coefficient:

Many pipe flow analysis programs do not readily implement orifice discharge coefficients because they use K's instead. Hence, having a value for K based on the orifice discharge coefficient is useful for flow calculators.

Symbols and units for discharge coefficient equations: A_o=orifice area (m²), A_p=pipe area (m²), d=orifice diameter (m), D=pipe inside diameter (m), P₁-P₂=differential pressure (N/m²), P₁-P₃=non-recoverable pressure difference (N/m²), Q=flow rate (m³/s), V_o=velocity through orifice (m/s), V_p=velocity in pipe (m/s), ρ=fluid mass density (kg/m³).

Reference: LMNO Engineering - Large diameter orifice flow meter calculation for liquids

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