Control valve sizing involves determining the correct valve to
install from the many valves commercially available. The procedure is
based on information provided by valve manufacturers, who specify the capacity
of their valves using the valve coefficient, C_{v}. The valve
coefficient is defined as the flow of water that will pass through the valve
when fully open with a pressure drop of 1 psi. In these tables, the units
of C_{v} are gallons of water per minute per psi^{1/2}.
The engineer must calculate the desired C_{v} for the process fluid
and conditions by applying appropriate correction factors and select the valve
using tables of C_{v} versus valve stem position and line size provided
by the manufacturers
The required flow and pressure drop information used to size a valve is based on the process operations and equipment, and ISA Form S20.50 (ISA, 1992) provides a helpful method for recording the data. The size of the valve depends on the pressure drop across the valve. A general guideline for pumped systems is that the valve pressure drop should be 2533% of the total pressure drop from supply to the end of the pipe (Moore, 1970). To provide appropriate rangeability, the C_{v} (flow rate) should be determined for the extremes of expected operation. Typically, a valve should be selected that has the maximum C_{v} value at about 90% of the stem position; this guideline allows for some extra capacity. The valve should have the minimum C_{v} at no less than 1015% stem position, which will give a reasonable rangeability, especially since the accuracy of the characteristic is poor below 10% stem position..
For liquids in turbulent flow, the defining
equation is the equation for flow through an orifice, which can be rearranged
and supplemented with correction factors.
relationship for liquids in turbulent flow through an orifice 


C_{v}  =  flow coefficient (gallons/min/psi^{1/2}) 
F_{liq}  =  flow rate (gallons/min) 
F_{P}  =  dimensionless factor accounting for difference in piping due to fittings for piping changes at inlet and outlet; values range from 0.80 to 0.98 and are typically about 0.95 (see Driskell 1983 for details) 
F_{R}  =  dimensionless factor accounting for viscosity effects for liquids; the value is 1.0 for Reynolds numbers greater than 4x10^{4} (see Hutchison 1976 for the calculation of the valve Reynolds number and FR) 
G_{liq}  =  specific gravity of process fluid at 60 °F (15 °C) 
DP  =  pressure drop across the valve (psi) 
When the process conditions, including the valve (C_{v}),
are known, equation (9) can be used to calculate the flow. When designing
the process, the desired flow is known but the valve is not; equation (9) can
be rearranged to calculate the valve coefficient required for the specified
conditions.
The pressure decreases as the liquid flows through the valve. The possibility
exists for the liquid to partially vaporize due the pressure drop, and this
vaporization can have serious consequences for the control valve. Two
situations can occur: cavitation where the vapor forms and is condensed
due to the pressure recovery and flashing where vapor remains after the
pressure recovery. The effect of vaporization on the flow is shown in
Figure 9. Importantly, cavitation involves the collapsing of bubbles
that can generate significant forces that will damage the valve components,
so that cavitation should be avoided when designing a flow system. This
can be achieved by raising the pressure (e.g., higher supply pressure), lowering
the stream temperature (e.g., locating upstream of a heater) or using a valve
with little pressure recovery.
Flashing occurs
when vapor remains downstream of the valve after the pressure recovery.
This situation will not result in damage to the valve and is an acceptable design.
Special flow models are required for valve sizing when vaporization occurs and
can be found is standard references, e.g., Driskell (1983).
For gases and vapors with subsonic flow, the development of the equation is
similar but must consider the change in density with an expansion factor and
the lack of ideal behavior with the compressibility.
relationship for gases and
vapors with subsonic flow through an orifice



F_{g}  =  gas flow rate (std. ft^{3}/h) 
G_{g}  =  specific gravity of the process fluid relative to air at standard conditions 
N  =  unit conversion factor (equal to 1380 for English units) 
P_{1}  =  upstream pressure (psia) 
T_{1}  =  upstream temperature (°R) 
Y  =  dimensionless expansion factor which depends on P1/P2 and the specific heat ratio; ranges from 0.67 to 1.0 (see Driskell 1983) 
z  =  compressibility factor 
Figure
9. Typical effect of vaporization on flow rate.
Figure 10.
The effect of sonic velocity on flow.
When the pressure drop across the valve is large, sonic flow can occur which will require special calculations for valve sizing (Hutchison, 1976). The general behavior of flow versus pressure drop is shown in Figure 10. When choked flow occurs, the downstream pressure does not influence the flow rate. A rough guideline is that sonic flow does not occur when the pressure drop is less than 42% of the supply pressure. Sonic flow through valves occurs often and does not represent difficulties when the proper valve trim design and materials are used.
Special models are available for unique situations like sonic flow, mixed phase flow, slurries, excessive vibration and noise, and condensation in the valve. See Hutchison (1976) and Driskell (1983) for details.
A good simple introduction to valve sizing with a
worked example is
available by clicking on the figure.
The table used in the example is typical of the tables provided by valve manufacturers. 

A comprehensive explanation of control valve sizing is available by clicking on this figure and selecting Chapter 5 