Turbulent and laminar flow are flow regimes that characterize the behavior of flow. In laminar flow, all fluid particles move parallel to one another in an orderly fashion and with no mixing of the fluid.
Conversely, in turbulent flow, the velocity direction and magnitude is random. Significant fluid mixing occurs in turbulent flow. There is no distinct line between these two regimes, so a third was developed. The physical quantities that govern this third flow regime are viscous and inertial forces, the ratio of what is known as the Reynolds number. When the viscous forces dominate, the Reynolds number is over and the flow is laminar. If the inertial forces dominate, the Reynolds number is over and the flow is turbulent.
For equivalent flow rates, the pressure differential across a restriction will be different for each of these flow regimes. To compensate for this effect, a correction factor was developed to be incorporated into valve sizing. The required Cv can be determined from the following equation:. The factor Fr is a function of the Reynolds number and can be determined from a nomograph not included in this paper. To predict the flow rate or resulting pressure differential, the required flow coefficient is used in place of the rated flow coefficient in the appropriate equation.
When a valve is installed in the field, it is almost always going to be installed in a piping configuration different than that of the test configuration. Elbows, reducers, couplers, and other fittings may be used in the field. To correct this situation, two correction factors are used. These factors are Fp, which is used in incompressible flow situations, and Flp, which is used in the choked flow range.
In order to determine these values, the loss coefficients of all devices must be known. In the absence of test data or knowledge of loss coefficients, loss coefficients may be estimated from information contained in resources outside the scope of this paper.
In order to use the liquid flow equation for air, it was necessary to make two modifications. The result is the Cv equation revised for the flow of air at 60F. Generalizing this equation to handle any gas at any temperature requires only a simple modification factor based upon Charles Law:.
The term represents the product of the specific gravity and temperature of air at standard conditions. The specific gravity is one or unity. It is essential to be aware of the limitations that result from compressibility effects and critical flow with regard to equation An actual flow curve would show good agreement with the theoretical flow curve at low flow pressure drops.
However, a significant deviation occurs at pressure drop ratios greater than approximately. When the pressure drop ratio exceeds. A much more serious limitation on this equation involves the choked flow condition, which was explained earlier. When critical flow is reached, equation 12 becomes useless for predicting the flow since the flow no longer increases with pressure drop.
In order to compensate for this problem, valve manufacturers modified the Cv equation even further in an attempt to predict the behavior of gases at both critical and subcritical flow conditions. This was economically beneficial to valve manufacturers as they could continue to test their valves on water only. The modified equation would then predict the gas flow. As it turned out, three equations were developed, all of which did a decent job predicting the gas flow through a standard globe valve at pressure drop ratios of less than 0.
For globe valves, critical flow is reached at a pressure drop ratio of about 0. In the low-pressure drop region, the slope of the flow curve established by any of these equations is equal to that established by the original Cv equation.
When the pressure drop ratio is equal to 0. This indicates that once critical flow is reached, the flow will change only as a function of the inlet pressure.
Low recovery valves work rather well in equations such as this. High recovery valves introduce new problems altogether. Unlike the flow through low-recovery valves, the flow through high recovery valves is quite streamlined and efficient. If two valves have equal flow areas and are passing the same flow, the high recovery valve will exhibit much less pressure drop than the low recovery valve. High and low recovery refers to the valves ability to convert velocity at the vena contracta back to pressure downstream of the valve.
As we learned earlier, the low recovery valves generally exhibit critical flow at a pressure drop ratio of. The high recovery valves generally reach critical flow at pressure drop ratios of. Since the flow predicted by the critical flow equation depends directly upon Cv, and the high recovery valve exhibits critical flow at pressure drop ratios as low as. It should be realized that in order for both valves to have the same Cv , the high recovery valve would be much smaller than the low recovery valve.
The geometry of the valve greatly influences liquid flow, whereas the critical flow of gas depends essentially on the flow area of the valve.
Thus, a smaller high recovery valve will pass less critical gas flow, but its greater streamlines flow geometry allows it to pass as much liquid flow as the larger low recovery valve. Because of the problems in using the Cv equation to predict gas flow in both high and low recovery valves, valves were finally tested using air as well as liquid.
From these tests, a gas sizing coefficient Cg was defined in to relate critical flow to the absolute inlet pressure. Since Cg is experimentally determined for each style and size of valve, it can be used to accurately predict the critical flow for both high and low recovery valves. The following equation is the defining equation for Cg :.
The Cg value is determined by testing the valve with 60 F air under critical flow conditions. To make the equation applicable for any gas at any temperature, the same correction factor can be used that was applied previously to the to the original Cv equation:. Now, there were two equations for gas sizing. One was applied to low pressure drops, while the other was good for predicting critical flow.
This equation is universal in the sense that it accurately predicts the flow for either high or low recovery valves for any gas and under any service conditions. Sense Line Protectors. Solenoid Valves. Supply Gas Regulators. Other Accessories. Float Operated Controllers. Temperature Controllers.
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