Orifice plate loss coefficient calculator

Find the irreversible loss coefficient K of a thin, sharp-edged orifice plate from the pipe bore and the orifice bore, and the pressure drop it adds at a given flow. This is the loss coefficient you use to size a pipe or a restriction, not the metering discharge coefficient C_d used to infer flow from a differential-pressure tapping.

Method

The orifice is treated as a fixed minor loss on the upstream pipe velocity head. The loss coefficient depends only on the diameter ratio beta = d / D, where d is the orifice bore and D is the pipe internal diameter:

K = [1 + 0.707 sqrt(1 - beta^2) - beta^2]^2 / beta^4

The head loss is then hf = K V^2 / (2 g) on the upstream mean velocity V, and the pressure drop is dp = rho g hf. This is the same sharp-orifice correlation the Studio uses for its orifice element, cross-checked against NASA GFSSP (Verification Part N) to within 3% in the turbulent regime. K is Reynolds-independent here (the fully turbulent value); in deep laminar flow a real orifice loses more, and the Studio raises a laminar advisory.

K, not C_d. This is the irreversible pressure loss across the plate, referenced to the pipe velocity. It is not the metering discharge coefficient (about 0.6 for a sharp orifice) that a flow-measurement standard uses to work flow back out of a measured differential pressure.

Inputs

• Pipe internal diameter D (mm) and orifice bore diameter d (mm).
• Flow rate Q (L/s) and the fluid (for the pressure drop).

Outputs

• Loss coefficient K and the diameter ratio beta.
• Upstream pipe velocity, head loss and pressure drop.

Worked example

A 50 mm orifice in a 100 mm water line carrying 10 L/s:

beta = 50 / 100 = 0.5
K    = [1 + 0.707 sqrt(0.75) - 0.25]^2 / 0.25^2 = 29.7
V    = 0.010 / (pi (0.1)^2 / 4) = 1.27 m/s
hf   = 29.7 (1.27)^2 / (2 x 9.81) = 2.45 m
dp   = 998.2 x 9.81 x 2.45 = 24.0 kPa

so a half-bore orifice adds about 24 kPa at this flow.

Frequently asked questions

Is this K or the discharge coefficient C_d?

It is K, the irreversible loss coefficient on the upstream velocity head, for sizing a restriction or a pipe. It is not the metering discharge coefficient C_d (about 0.6 for a sharp orifice) used to infer flow from a differential-pressure measurement.

What diameter is beta based on?

beta = d / D, the orifice bore divided by the pipe internal diameter. K rises steeply as beta falls (a smaller hole is a bigger restriction) and is exactly zero at beta = 1 (no restriction).

Does the loss depend on the fluid or the Reynolds number?

The coefficient K is Reynolds-independent in the turbulent regime, so it does not depend on the fluid. The fluid density sets the pressure drop for a given head loss. In deep laminar flow the real loss is higher.

Related

• Pipe flow and pressure drop calculator
• Rectangular duct pressure drop calculator
• How the elements are verified against NASA GFSSP.
• Open the Studio to place an orifice in a full network and solve it.