Introduction

This document discusses how to size a valve for liquid or gas service.
- Equations
- Parameters

This is a nice technical bulletin from Swagelok, for those who are interested in Engineering and Valve Sizing.

Liquid Flow
Because liquids are incompressible fluids, their flow rate depends only on the difference between the inlet and outlet pressures (Dp, pressure drop). The flow is the same whether the system pressure is low or high, so long as the difference
between the inlet and outlet pressures is the same. This equation shows the relationship:

Gas Flow
Gas flow calculations are slightly more complex because gases are compressible fluids whose density changes with pressure. In addition, there are two conditions that must be considered low-pressure drop flow and high-pressure drop flow.

This equation applies when there is a low-pressure drop flow outlet pressure (p2) is greater than one half of the inlet pressure (p1):

When outlet pressure (p2) is less than half of inlet pressure (p1) (high-pressure drop) any further decrease in outlet pressure does not increase the flow because the gas has reached sonic velocity at the orifice, and it cannot break that “sound barrier.”
The equation for high-pressure drop flow is simpler because it depends only on inlet pressure and temperature, valve flow coefficient, and the specific gravity of the gas:

Symbols and Constants

Cited References
1. ISA S75.01, Flow Equations for Sizing Control Valves, Standards and Recommended Practices for Instrumentation and Control, 10th ed., Vol. 2, 1989.
2. ISA S75.02, Control Valve Capacity Test Procedure, Standards and Recommended Practices for Instrumentation and Control, 10th ed., Vol. 2, 1989.