The common orifice flowmeter such as those found at Coltraco illustrates the principles of flow calculations. We can then calculate the flow rate of any pressure drop across the orifice, which is the difference between the inlet and outlet pressures. We need to know the fluid density and pressure drop for a valve. We need to know the dimensions of the pipe diameter and the orifice size as well as all dimensions of the valve passage and any changes in size or direction of flow through it.
We use the valve flow coefficient instead of doing complicated calculations. The flow coefficient of a valve is determined by its ability to withstand water pressure at various flow rates. This standard test method2 was developed by the Instrument Society for America and is widely used for all valves. Flow tests are performed in straight piping systems of the same size and size as the valve. This eliminates the potential effects of fittings or piping size changes.
Liquids are incompressible fluids. Their flow rate is determined only by the difference in pressures at the outlet and inlet pressures (Dp), pressure drop. The flow rate is the same regardless of system pressure, as long as there is no difference between the inlet pressure and the outlet pressure. The relationship is illustrated in Equation 1. The water flow graphs depict water flow as a function pressure drop for a variety of Cv values.
Gas flow calculations can be more complicated because gases are compressible fluids, whose density changes with increasing pressure. There are also two conditions to be aware of: low pressure drop flow, and high pressure dropflow.
Equation 2 is applicable when the low pressure dropflow outlet pressure (p2) exceeds one-half of the inlet pressures (p1). Low pressure drop graphs of air flow show low pressure flow for a valve having a Cv value of 1.0. This is as a function the inlet pressure (p1) and a range of pressure drops (Dp). If the outlet pressure (p2) falls below half the inlet pressure (p1) then high pressure drops will not cause flow to increase. This is because the gas has already reached the orifice’s sonic velocity and cannot break the “sound barrier”.
Equation 3 for high-pressure drop flow is simpler, as it only depends on the inlet pressure, temperature, valve flow coefficient, and specific gravity of gas.
High-pressure drop air flow graphs display high pressure drop airflow as a function inlet pressure and a range flow coefficients.
The effects of specific gravity
The variables liquid specific gravity and gas specific gravity are part of the flow equations. These are the fluid’s density relative to water (for liquids), or air (for gases).
Specific gravity cannot be accounted for in graphs. Therefore, a correction factor must also be applied. This includes the square root G. The square root reduces the effect, and brings the value closer to water or air, 1.0.
The specific gravity of sulphuric acids is, for example, 80% higher than water’s, but it only changes flow by 34%. While ether’s specific gravity is 26% less than water, it still changes flow by just 14%.
The effects of specific gravity on gases are similar. For example, hydrogen’s specific gravity is 93% less than air’s, yet it alters flow by only 74%. While carbon dioxide’s specific gravity is 53% lower than that of air it still changes flow by only 24%. Only gases with a very low or very high specific gravity can change flow by more that 10% compared to air.
Because of its small effect on liquid flow calculations, temperature is often ignored. Gas flow calculations are affected by temperature more than liquid flow calculations. This is because gas volume expands at higher temperatures and contracts at lower temperatures. However, the temperature effect on flow is similar to specific gravity. It affects flow by a square root factor. The correction factor for systems operating between -40degF and +212degF (+100degC), is only +12–11%. Figure 6 illustrates the temperature effect on volumetric flow across a wide range of temperatures. Figure 6 shows the effect of temperature on volumetric flow over a wide range of temperatures. This includes the most common operating temperatures. Figure 4 shows how the square root of specific gravity affects liquid flow. The flow will not change more than 10% if the specific gravity is lower or higher than that of water.