# Valve sizing based on flow calculations

01 April 2010

### Valve size often is described by the nominal size of the end connections but a more important measure is the flow that the valve can provide. Using the principles of flow calculations, some basic formulas, and the effects of specific gravity and temperature, flow can be estimated well enough to select a valve size - easily, and without complicated calculations

The principles of flow calculations are illustrated by the common orifice flow meter (Figure 1). We need to know only the size and shape of the orifice, the diameter of the pipe, and the fluid density. With that information, we can calculate the flow rate for any value of pressure drop across the orifice (the difference between inlet and outlet pressures).

For a valve, we also need to know the pressure drop and the fluid density, plus all valve passage dimensions and all the changes in size and direction of flow through the valve. However, rather than doing complex calculations, we use the valve flow coefficient, which combines the effects of all the flow restrictions in the valve into a single number (Figure 2).

Valve manufacturers determine the valve flow coefficient by testing the valve with water at several flow rates, using a standard test method developed by the Instrument Society of America for control valves and now used widely for all valves. Flow tests are done in a straight piping system of the same size as the valve, so that the effects of fittings and piping size changes are not included (Figure 3).

Liquid and gas flows
Because liquids are incompressible fluids, their flow rate depends only on the difference between the inlet and outlet pressures (p, 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. (Equation 1 shows the relationship.)

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. Equation 2 applies when there is low-pressure drop flow—outlet pressure (p2) is greater than one half of 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 (Equation 3) is simpler because it depends only on inlet pressure and temperature, valve flow coefficient, and the specific gravity of the gas.

Specific gravity and temperature
The flow equations include the variables liquid specific gravity (Gf) and gas specific gravity (Gg), which are the density of the fluid compared with the density of water (for liquids) or air (for gases).

However, specific gravity is not accounted for in the graphs, so a correction factor must be applied, which includes the square root of G. Taking the square root reduces the effect and brings the value much closer to that of water or air, ie1.0. Figure 4 shows that only if the specific gravity of the liquid is very low or very high will the flow change by more than 10 percent from that of water. The effect of specific gravity on gases is similar. Only gases with very low or very high specific gravity change the flow by more than 10 percent from that of air (Figure 5).

Temperature is usually ignored in liquid flow calculations because its effect is too small. Temperature has a greater effect on gas flow calculations, because gas volume expands with higher temperature and contracts with lower temperature. As with specific gravity, temperature affects flow by only a square-root factor. For systems that operate between –40°C and +100°C, the correction factor is only +12 to -11 percent.

Figure 6 shows the effect of temperature on volumetric flow over a broad range of temperatures. The plus-or-minus 10 percent range covers the usual operating temperatures of most common applications.

DPA is grateful to John Baxter at the Swagelok Company and retired Swagelok senior engineer, Ulrich Koch for this item. It is a summarised version of a more detailed article that can be accessed here

NOTE: For figure references and equations, please see the digital issue, which can be accessed from the home page. Alternatively, a fuller version of this article with figures and equations can be accessed by clicking the link in the previous paragraph.