Engineering Resources • Calculator

Orifice Beta Ratio Calculator

Merobix Engineering •

Flow and instrument engineers use this when sizing or checking an orifice-plate flow element. Enter the orifice bore and the pipe internal diameter, and it returns the beta ratio and the velocity-of-approach factor, and flags a beta outside the range most sizing keeps to.

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The beta ratio is the ratio of the orifice bore to the pipe inside diameter, and it sets much of a differential-pressure flow element's behavior. This calculator computes beta and the velocity-of-approach factor E, and notes when beta falls outside the 0.2 to 0.75 band that common sizing practice tends to stay within.

The Calculator

Any length unit, as long as D uses the same one.
Same unit as the bore.

Result

Beta ratio (d / D)-
Velocity of approach, E-

Common practice keeps beta between 0.2 and 0.75.

The Formula

Beta is the diameter ratio; the velocity-of-approach factor E corrects for the fluid already moving as it reaches the orifice:

beta = d / D
E = 1 / sqrt(1 - beta4)

Worked example. A 2 inch bore in a 4 inch pipe gives beta = 2 / 4 = 0.5. Then beta4 = 0.0625, so E = 1 / sqrt(1 - 0.0625) = 1 / sqrt(0.9375) = 1 / 0.9682 = 1.0328. A beta of 0.5 sits comfortably inside common practice.

Assumptions and Limits

FAQ

Why keep beta between 0.2 and 0.75?

Very low beta wastes permanent pressure and can be hard to manufacture accurately; very high beta makes the reading sensitive to upstream disturbance and can push the discharge coefficient outside well-characterized ranges. The 0.2 to 0.75 band is where common practice keeps the measurement predictable.

What does the velocity-of-approach factor do?

The fluid is already moving in the pipe before it reaches the orifice. E corrects the ideal equation for that approach velocity; it grows as beta grows because the approach velocity becomes a larger share of the throat velocity.

Does a larger beta mean more flow for the same differential?

Broadly yes, a larger bore passes more flow at a given differential pressure, but the relationship is not linear and depends on the discharge coefficient and fluid properties. Use a full sizing calculation rather than beta alone to set flow.