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FIGURE 20-2
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Double-seated
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valve.
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the effort needed to open the valve with the result that a smaller, less expensive actuator is needed. In a double-seated valve, it is difficult to have tight shut-off. If one plug has tight closure, there is usually a small gap between the other plug and its seat. For this reason, single-seated valves are recommended if the valve is requited to be shut tight. In many processes, the valve is used for throttling flow and is never expected to operate near its shut-off position. For these conditions, the fact that the valve has a small leakage at shut-off position does not create a problem.
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In order to specify the size of a valve in terms of its capacity to provide flow when fully open, the following equation is used:
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where
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q = flow rate, gpm
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Ap, = pressure drop across the wide-open valve, psi G = specific gravity of fluid at stream temperature relative to water; for water G = 1. C, = factor associated with capacity of valve Equation (20.1) applies to the flow of an incompressible fluid through a fully open valve. Manufacturers rate the size of a valve in terms of the factor C,. Sometimes the C, is defined as the flow (gpm) of a fluid of unit specific gravity through a fully open valve, across which a pressure drop of 1 .O lbf/in2 exists. This verbal definition is, of course, obtained directly from Eq. (20.1) by letting q = 1, Ap, = 1, and G = 1. Equation (20.1) is based on the well-known Bernoulli equation for determining the pressure drop across valves and resistances. It is important to emphasize that C, must be determined from Eq. (20.1) using the units listed. Since so many valves in use are rated in terms of C,, Eq. (20.1) is of practical importance; however, some industries now are defining a valve coefficient K, that is defined by the equation
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where
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4 = flow rate, m3/hr Ap, = pressure drop across valve, Kg&m2 G = specific gravity relative to water The relation between K, and C, is:
K, = 0.856C,
For gases and steam, modified versions of Eq. (20.1) are used in which C, is still used as a factor. Manufacturers of valves provide brochures, nomographs, and special slide rules for sizing valves for use with gases and steam. In general, as the physical size of a valve body (i.e., size of pipe connectors) increases, the value of C, increases. For a sliding stem and plug type of control valve, the value of C, is roughly equal to the square of the pipe size multiplied by ten. Using this rule, a three-inch control valve should have a C, of about 90, with units corresponding to those of Eq. (20.1). Example 20.1. A valve with a C, rating of 4.0 is used to throttle the flow of glycerine for which G = 1.26. Determine the maximum flow through the valve for a pressure drop of 100 psi.
The coefficient C, varies with the design of the valve (shape, size, roughness) and the Reynolds number for the flow through the valve. This relationship is analogous to the relationship between friction factor and roughness and Reynolds number for flow through a pipe. For relatively nonviscous fluids, C, in Eq. (20.1) can be taken as a constant for a valve of given size and type. The reason for this is that at high Reynolds numbers, the friction factor changes very little with flow rate. Except for very viscous fluids, the flow through a valve, which involves sudden contraction and expansion, is in the turbulent regime of fluid flow; turbulence in the valve exists even if the flow in the supply pipe is near the critical Reynolds number of 2 100. Consequently, for relatively nonviscous fluids, Eq. (20.1) is satisfactory for sizing a valve for any fluid. For the control of flow of very viscous fluids, such as tar or molasses, the value of C, found from Eq. (20.1) must be multiplied by a correction factor that depends on viscosity, density, flow rate, and valve size (i.e., on the Reynolds number). Methods for determining the viscosity correction factor are provided by manufacturers for their valves. If one does not apply the correction factor for a very viscous fluid, the value of C, will be too low and the valve will be undersized. VALVE CHARACTERISTICS
The function of a control valve is to vary the flow of fluid through the valve by means of a change of pressure to the valve top. The relation between the flow through the valve and the valve stem position (or lift) is called the valve characteristic, which can be conveniently described by means of a graph as shown in Fig. 20.3 where three types of characteristics are illustrated.
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