Orifice plate pressure drop calculator

This free orifice plate pressure drop calculator finds the irreversible loss coefficient K of a thin sharp-edged orifice plate from the pipe bore and the orifice bore, then the head loss and pressure drop it adds at your 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. It works in metric or imperial units, and any liquid can be set through the Custom density field.

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's GFSSP turbulent orifice option to within 3% in the turbulent regime (it is one of the element-reference cases on the verification page, where the numbers are solved live). 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 and orifice bore diameter d.
• Flow rate Q and the fluid (for the pressure drop).

Outputs

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

Loss coefficient K by diameter ratio

Computed from the same sharp-orifice correlation the calculator uses, on the upstream pipe velocity head, cross-checked against NASA GFSSP within 3% (an element-reference case on the verification page: K = 29.7 here against GFSSP's 30.49 at beta = 0.5). The pressure-drop column is K x rho V^2 / 2 for water at 998.2 kg/m3 and 2 m/s. Values apply to a thin sharp-edged plate: a thick bore (length up to about five bore diameters) loses less, falling toward 0.58 of the thin value as the jet reattaches. Handbook values (Idelchik's Handbook of Hydraulic Resistance, and Crane TP-410) can differ by a few per cent.

Permanent pressure loss of a metering orifice

A common approximation associated with ISO 5167-2, the orifice-plate part of the differential-pressure flow-measurement standard, gives the permanent (irreversible) loss as about (1 - beta^1.9) of the differential pressure measured between the standard tappings, with the remainder recovered downstream of the vena contracta. Use it to judge the true energy cost of a metering orifice. This calculator reports the permanent loss directly from K, not the tapping differential.

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 9.80665) = 2.45 m
dp   = 998.2 x 9.80665 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 pipe velocity head, for sizing a restriction or a pipe run. It is not the metering discharge coefficient C_d (about 0.6 for a sharp orifice) used to infer flow from a differential-pressure tapping.

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, where there is no restriction at all.

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

K is Reynolds-independent in the turbulent regime, so it does not depend on the fluid, and the calculator never asks for a viscosity. The fluid density sets the pressure drop for a given head loss, and any liquid can be entered via the Custom density field. In deep laminar flow a real orifice loses more than this fixed K.

Can I size an orifice bore for a target pressure drop?

Yes, by iteration. The result recalculates as you type, so adjust the orifice bore until the pressure drop row reads your target. There is no inverse mode, but convergence by hand takes a few tries because K moves monotonically with the bore.

How much of a flow meter's differential pressure is permanently lost?

Roughly (1 - beta^1.9) of the differential measured at the standard tappings, so about 73% at beta 0.5 and about 42% at beta 0.75, with the rest recovered downstream. See the permanent pressure loss table above. This calculator reports the permanent loss directly from K rather than the tapping differential.

Does it work in imperial units?

Yes. The unit toggle converts every input and result in place, with bores in inches, flow in gpm, velocity in ft/s and the pressure drop in psi, so the physical problem is unchanged when you switch.

References

• ISO 5167-2, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full - Part 2: Orifice plates, for the metering geometry and the permanent-loss approximation. iso.org
• Idelchik, I. E., Handbook of Hydraulic Resistance, the standard compilation of loss coefficients for restrictions and fittings.
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe. tp410.com
• NASA/TP-2016-218218, Generalized Fluid System Simulation Program (GFSSP), the independent reference the orifice element is cross-checked against. NASA NTRS

Related

• Pipe pressure drop calculator
• Pipe velocity calculator
• Rectangular duct pressure drop calculator
• Minor losses in a real line, and how the elements are verified against NASA GFSSP.
• Open the Studio to place an orifice in a full network and solve it.