ISA-75.01.01-2007 includes equations for predicting the flow coefficient of compressible and

incompressible fluids through control valves.

The equations for incompressible flow are based on standard hydrodynamic equations for Newtonian incompressible fluids. They are not intended for use when non-Newtonian fluids, fluid mixtures, slurries, or liquid-solid conveyance systems are encountered.

**1.**** ****Valve Style Modifier ***F*_{d}

The ratio of the hydraulic diameter of a single flow passage to the diameter of a circular orifice, the area of which is equivalent to the sum of areas of all identical flow passages at a given travel

**2.1 ****Non-Choked Turbulent Flow Without Attached Fittings**

The flow coefficient shall be determined by-

**2.2 Non-Choked Turbulent Flow With Attached Fittings**

**3. Choked Turbulent Flow**

**3.1 ****Choked Turbulent Flow without Attached Fittings**

**3.2 Choked Turbulent Flow with Attached Fittings**

**4.1 Flow Co-efficient for Non-Choked Turbulent Flow**

**4.2 Non-Choked Turbulent Flow with Attached Fittings**

**5.1 Choked Turbulent Flow without Attached Fittings**

**5.2 Choked Turbulent Flow with Attached Fittings**

**6. ****Piping Geometry Factor F**_{p}

The piping geometry factor *F*_{P} is necessary to account for fittings attached upstream and/or downstream to a control valve body. The *F*_{P }factor is the ratio of the flow rate through a control valve installed with attached fittings to the flow rate that would result if the control valve was installed without attached fittings and tested under identical conditions which will not produce choked flow in either installation.

When estimated values are permissible, the following equation shall be used:

In this equation, the factor Σζ is the algebraic sum of all of the effective velocity head loss coefficients of all fittings attached to the control valve. The velocity head loss coefficient of the control valve itself is not included.

In cases where the piping diameters approaching and leaving the control valve are different, the ζ B

coefficients are calculated as follows:

If the inlet and outlet fittings are short-length, commercially available, concentric reducers, the ζ 1 and ζ 2 coefficients may be approximated as follows:

**7. ****Reynold’s Number**

**8. ****Liquid Pressure Recovery Factor without Attached Fittings ***F*_{L}

It is defined as the ratio of the actual maximum flow rate under choked flow conditions to a theoretical, non-choked flow rate which would be calculated if the pressure differential used was the difference between the valve inlet pressure and the apparent *vena contracta *pressure at choked flow conditions.

**9. ****Combined Liquid Pressure Recovery Factor and Piping Geometry Factor with Attached Fittings ***F*_{LP}

Here Σζ 1is the velocity head loss coefficient, ζ 1 + ζ B1, of the fitting attached upstream of the valve as measured between the upstream pressure tap and the control valve body inlet.

**10. ****Liquid Critical Pressure Ratio Factor ***F*_{F}

*F*_{F} is the ratio of the apparent *vena contracta *pressure at choked flow conditions to the vapor pressure of the liquid at inlet temperature. At vapour pressures near zero, this factor is 0.96. Values of *F*_{F} may be approximated from the following equation:

**11. ****Expansion Factor Y**

The expansion factor *Y *accounts for the change in density as the fluid passes from the valve inlet to the *vena contracta *(the location just downstream of the orifice where the jet stream area is a minimum). It also accounts for the change in the *vena contracta *area as the pressure differential is varied.

**12. ****Pressure Differential Ratio Factor with Attached Fittings**

**13. ****Specific Heat Ratio Factor**

#### References

ISA 75.01.01-2007 FLOW EQUATIONS FOR SIZING CONTROL VALVES

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