Resolving Fisher Gas Valve Sizing Equation Conflicts

Fisher gas valve sizing results diverge when the compared equations use different gas models, flow regimes, unit bases, or valve coefficients. Start by fixing those inputs, then select the equation branch from the pressure ratio and gas compressibility. Treat a quoted flow as comparable only after the vendor confirms the same basis.

Calculation-basis gate

Before anything else, confirm the calculation basis. The constants 520, 59.64, 1.06, and 1.29 belong to particular equation and unit conventions. A numerically correct substitution into the wrong convention still produces the wrong flow.

1. Identify the required result. Record whether Q is standard volumetric flow, actual volumetric flow, or mass flow. The density-form equation explicitly defines Qs as flow in lb/hr; that result cannot be compared directly with an unspecified volumetric Q.
2. Confirm the pressure basis. Record upstream pressure P1 and downstream pressure P2 on the absolute-pressure basis required by the selected catalog equation. Calculate the pressure drop separately as ΔP = P1 - P2. Do not move on until both pressures use the same units and reference.
3. Confirm the temperature basis. The expression Temp + 460 represents an absolute-temperature conversion within the stated equation. Verify the catalog definition of Temp before entering it; do not substitute an already absolute temperature into that expression.
4. Fix the gas state. Record specific gravity SG and, for non-ideal service, compressibility factor Z at the inlet condition used by the equation.
5. Fix the valve data. Use Cg and C1 for the quoted valve, size, trim, and travel. Do not substitute Cv for Cg or infer missing coefficients from another valve.
6. Confirm the service phase. Apply these gas equations only to gas service. Liquid and mixed-phase service require different sizing methods.

Pressure-ratio and sine-term check

The full gas-flow relationship presented for comparison is:

Q = SQRT(520/(SG*(Temp+460))) * Cg * P1 * SIN((59.64/C1) * SQRT((P1-P2)/P1))

The source notation SQRT(P1-P2/P1) is parenthetically ambiguous. Read literally, it combines P1 with the dimensionless ratio P2/P1, which is dimensionally invalid. Resolve the expression against the applicable manufacturer catalog before calculating. The normalized pressure-drop form shown above, SQRT((P1-P2)/P1), is dimensionless and matches the stated use of downstream pressure and pressure drop.

1. Calculate ΔP = P1 - P2. If ΔP is zero or negative, stop: the assumed forward-flow condition is absent or the pressure entries are reversed.
2. Calculate the normalized drop ΔP/P1. A result outside the physical range for positive upstream and downstream absolute pressures signals a pressure-reference or data-entry problem.
3. Calculate the complete sine argument using the catalog’s angle convention. Do not mix degrees and radians. The stated limiting argument is 90 degrees, equivalent to pi/2 radians.
4. If the argument is below its limiting value, retain the calculated sine term and proceed to the gas-model check. If it reaches or exceeds the limit, cap the sine term at 1.0 and follow the critical-flow branch.

The sine term represents the pressure-ratio contribution to gas capacity. Before the limit, downstream pressure affects calculated flow. At the limit, further reduction of P2 no longer increases the equation’s predicted flow.

Ideal-gas and real-gas branch

The form containing SQRT(520/(SG*(Temp+460))) is an ideal-gas form. For a gas whose compressibility differs materially from ideal behavior, use the stated correction:

Q = SQRT(520/(Z*SG*(Temp+460))) * Cg * P1 * SIN((59.64/C1) * SQRT((P1-P2)/P1))

The Z term changes the state correction by a factor of 1/SQRT(Z). For otherwise identical inputs, the ratio between the real-gas and ideal-gas results is therefore:

Q_real / Q_ideal = 1/SQRT(Z)

Obtain Z for the gas composition, inlet pressure, and inlet temperature used in the sizing case. A compressibility factor from a different state point does not correct the calculation being performed.

An alternative density-based relationship is:

Qs = 1.06 * SQRT(d1*P1) * Cg * SIN(same pressure-ratio term)

Here, Qs is in lb/hr and inlet density d1 is in lb/ft3. This form can represent gases across pressure and temperature conditions when d1 describes the actual inlet state and every other variable follows the catalog’s unit convention. Compare it with the corrected specific-gravity form only after converting both answers to the same mass- or standard-volume basis.

Critical-flow branch

For critical flow, set the sine term to 1.0. The full relationship then reduces to the stated Fisher simplified form:

Q = Cg * P1 * SQRT(520/(SG*(Temp+460)))

For non-ideal gas behavior, retain the compressibility correction:

Q = Cg * P1 * SQRT(520/(Z*SG*(Temp+460)))

Do not use either critical-flow expression merely because it is shorter. First calculate the full sine argument and confirm that it reaches the limiting value. If the argument remains below the limit, setting the sine term to one overstates capacity because the calculation discards the remaining dependence on P2.

Mixed-phase flow does not become valid gas sizing merely because the gas branch predicts critical flow. Flashing, condensation, or entrained liquid changes the governing model and requires phase-appropriate property data and a suitable sizing method.

Equation-selection matrix

Fixed-multiplier screening

The alternate simplified expression is:

Q = P1 * Cg * 1.29

Because it contains no explicit SG, temperature, Z, P2, or C1, the multiplier 1.29 must embed a particular state and flow-regime basis. It is not interchangeable with the general equation for arbitrary gases and conditions.

Use it only when its originating documentation defines assumptions matching the current service. Otherwise, treat it as a screening relationship. For critical ideal-gas flow, its implied state factor can be inspected by setting:

1.29 = SQRT(520/(SG*(Temp+460)))

That equality identifies combinations of SG and temperature represented by the multiplier, but it does not identify a unique gas or temperature. With real-gas behavior included, Z adds another unknown. The fixed multiplier therefore cannot select the correct process-design case by itself.

Vendor-quote reconciliation

A vendor capacity is the controlling comparison only after both calculations describe the same physical case and the same valve configuration. Send one calculation sheet rather than only a requested flow.

1. List gas composition, SG, inlet-state Z, and inlet density d1 when the density form is used. Ask which property representation the vendor applied.
2. List inlet temperature, absolute P1, absolute P2, and ΔP. Ask whether the vendor classified the case as critical or subcritical and request the calculated limiting term.
3. State the requested flow basis and units. Record the reference pressure and temperature for any standard-volume result.
4. Identify the proposed valve, size, trim, travel, and the exact Cg and C1 used. Ask the vendor to return those same fields with the quote.
5. Compare intermediate terms: state factor, normalized pressure drop, sine argument, capped or uncapped sine value, and final flow. The first divergent term locates the disagreement.
6. Check the selected method against the manufacturer’s current sizing documentation and the ISA Handbook of Control Valves. Treat the handbook as a method reference to verify, not as approval of a particular valve or overload.

Process design should use the applicable manufacturer method with documented valve coefficients and real-gas properties where required. Preserve the input sheet, equation form, unit convention, property source, critical-flow decision, and vendor-returned calculation as the design record.

Final sizing and verification procedure

1. Enter one set of absolute inlet and outlet pressures and confirm P1 > P2.
2. Calculate ΔP/P1 and the complete sine argument using the verified parentheses and angle convention. Record whether the sine is calculated or capped at 1.0.
3. Select the state model: use the explicit Z correction for a real-gas calculation or use the inlet-density equation with d1 in lb/ft3 for a mass-flow result in lb/hr.
4. Insert the quoted valve’s Cg and C1. Recalculate at the actual proposed travel rather than silently using coefficients for another configuration.
5. Convert the result and vendor capacity to the same flow units and reference conditions.
6. Match every intermediate term with the vendor calculation. Do not release the selection until the flow regime, gas-property basis, coefficients, and converted capacity agree or each remaining difference has a documented cause.

Frequently asked questions