# Valve Flow and Sizing

## Flow

A valve can be used to stop and start as well as throttle or regulate the flow or movement of media through a system. The given and desired properties of the flow can be used when selecting a valve.

### Flow Coefficient

The valve flow coefficient is the number of U.S. gallons per minute of 60°F water that will flow through a valve at a specified opening with a pressure drop of 1 psi across the valve. The coefficient is used to determine the size that will best allow the valve to pass the desired flow rate, while providing stable control of the process fluid. It can be used to compare flow capacities of valves of different sizes, types, and manufacturers. The flow coefficient is different for gases, liquids, and steam and is also dependent on the pressure drop across the valve. The Cv can apply to either the opening or closing action depending on the function.

The simple equation is defined as:

Cv = flow x m (Specific gravity at flowing temperature/pressure drop)1/2

The flow coefficient varies based on the media type in the system. The chart below defines the appropriate formula and variables needed to calculate Cv for each system type.

Variable and formulas for calculating flow coefficient. Image Credit: Siemens

For air and gases: Compressible media - The density of the gas changes with a change in pressure and therefore the flow rate changes. Low pressure is defined as P2 > P1/2 and high pressure is defined as P1 > P2/2

For liquids: Incompressible media- The flow rate only depends on the difference between the inlet and outlet pressures so the rate stays the same as long as the change in pressure remains the same.

For steam: Compressible media- The density of the steam changes with a change in pressure. There is a critical (choked1) and non-critical pressure drop. Critical is defined as the pressure dropping by 58% or more from the inlet to the outlet.

If the calculated Cv is too small the valve will be undersized and the process system may be starved for fluid. This also causes a higher pressure drop across the valve causing cavitation or flashing. If Cv is too high the valve will be too big leading to monetary waste and difficult machine maneuverability. A larger Cv can also be a problem for throttling because the flow cannot be effectively controlled at the openings. The location of the closure element leads to the possibility of creating a high pressure drop and faster velocities causing cavitation, flushing, or erosion.

### Flow Characteristic

The flow characteristic describes the relationship between the flow coefficient and the valve stroke. It is inherent to the design of the selected valve. For example, as the valve is opened, the flow characteristic allows a certain amount of flow through the valve at a particular percentage of the stroke. This is especially important for throttle control because it controls the flow in a predictable manner. The flow rate is affected by the flow characteristic as well as the pressure drop. Inherent flow characteristic is when the valve is operating with a constant pressure drop without taking into account the effects of piping. Installed flow characteristics consider both the valve and piping effects. This is also considered an ideal curve and takes the entire system into account.

### Inherent Flow Characteristics

The three common types of inherent flow can be plotted as curves on a graph; however the characteristics of these curves can only be affected by the body style and design, and the piping factors.

Variables for flow characteristics
Variable Symbol Unit
TemperatureTdegree
Inlet pressurepipsia
Valve travelL
Minimum controllable flowQ0

The curves are based on constant pressure drop across the valve and graphs are usually available through the manufacturer. For control valves, as shown below, there are six inherent characteristics. The chart is plotted as stem opening % vs. flow %. The stem opening describes how much the valve is open. In this context, valve opening refers to the position of the disc relative to the closed seat position. The three most common flow characteristics are linear, equal-percentage and modified flow.

• Linear - The flow rate is directly proportional to the amount the disc travels. Linear flow characteristics produce equal change in flow per unit of valve stroke. If the disc is open 50%, the flow rate is at 50% of maximum flow. This provides better flow capacity throughout the entire stroke. Linear valves are best used for water systems.

The equation for linear flow is as follows:

Q = kL, dQ/dL = k

Where: k = constant of proportionality

• Equal percentage - The flow rate is related to the percent the valve opening changed in an incremental manner. For example, if the valve changed from 20% open to 30% open and produced a 70% change in flow rate, changing the valve from 30% to 40% open would increase the flow rate another 70%. Equal percentage valves are best used for throttling applications since the flow rate is small at the beginning of the stroke and increases at the end of the stroke. This provides exact control of the closure element in the first part of the stroke where the closure element is more easily affected by the process forces. The equal percentage characteristic also provides increased capacity in the second half of the stroke so the valve can pass the required flow.

Q = Q0enL, dQ/dL = nQ

Where: e = 2.718, n = constant

Advantage- Increase in rangeability, better repeatability and resolution in first half of stroke.

• Quick-opening - Quick opening flow is characterized by the maximum flow produced immediately as the valve begins to open. It is only used for on-off applications and due to the extreme nature of the flow, the inherent and installed characteristics are similar.

When choosing a flow characteristic, consider the direct relationship between valve opening and flow over the distance the valve stem travels.

### Installed Flow Characteristics

Valves have installed flow characteristics when the valve is installed into a system with pumps, piping, and fittings, causing the pressure drop to vary. The system components alter the flow rate so it is no longer determined by the geometry of the valve body and disc. The flow rate is altered by resistances resulting from pipelines, orifices, or other equipment in series with the valve. For a linear valve, the effect may be described by the following equation.

Q = L / [a + ( 1 - a) L2]1/2

Where: a= ratio of valve head differential at max flow to zero flow
Design Tip: The best choice is usually a linear valve and because they tend to be used most often, the installed and inherent characteristics are similar and linear. Therefore, there will be limited gain in the control loop. Equal percentage valves will also provide good results and are tolerant of over-sizing.

The following graphs show the flow curves for linear, equal-percentage, and quick-opening flow characteristics for both the inherent and installed characteristics of the valve. The addition of the piping factors in the installed characteristics generally moves the flow characteristic away from the ideal characteristic and toward the inherent linear characteristic.

### Pressure Drop

The pressure drop is the pressure change between the inlet and outlet of the system. The pressure drop must exist for flow to occur. The formula is as follows:

ΔP = G (q/FpCv)2

Disc position will generally determine the pressure drop. For example if the valve is closed the pressure drop will be minimal or zero and if the valve is open the pressure drop is 100%. If the pressure drop is too high, a larger valve or a valve with a higher Cv can be used to lower the pressure.

Image Credit: ITT

The actual pressure drop is the difference between the upstream (inlet) and downstream (outlet) pressures.

The pressure drop affects the flow characteristic of the valve.

• Quick- opening valves show little change in fluid flow until the valve actually closes. This is because the pressure drop across the valve is not a large enough percentage of the total system drop when the valve is fully opened.
• For linear valves, the percentage of the lift improves as the pressure drops at full flow. However, this characteristic is only applicable if the pressure drop remains nearly constant across the valve for full stem travel. For control valves a good rule of thumb is “at maximum flow, 25-50% of the total system pressure drop should be absorbed.” Pressure drops of 15 – 30% of the total system pressure provide good control if the variation in flow is small.

### Rangeability

Rangeability is a very important factor when selecting a valve type. It is defined as the maximum to minimum flow rate that can be controlled by a given valve type. The characteristic is affected by three factors: the geometry of the valve, the seat leakage, and the actuator's accuracy or stiffness at near closure of the valve. Geometry is inherent due to the design of the seat and closure and excessive seat leakage can cause instability in the valve as it lifts off the seat.

Rangeability is easily calculated based on the valve’s geometry and actuator. If the valve is not accurate at 5 percent of stroke, then the rangeability is 20:1 (100 percent divided by 5%). As the rangeability increases, a wider range of flow rates can be controlled by the valve. It is not imperative that the valve has the highest rangeability because most systems do not have an excessively wide flow rate range. V-notched ball valves have the highest rangeability at 200:1, while globe valves have a high rangeability of 100:1. Higher rangeability usually indicates the sensitivity is lower when the closing element is near closed and increases as the valve opens.

### Flow Rate

Flow rate is affected by the flow characteristic and the pressure drop across the valve.

## Valve Sizing

Valves are used in many industrial, commercial, and residential applications and therefore must be available in a wide variety of sizes and shapes. Valves can be as large as 10 tons and as small as 1 pound; however most valves used in process systems are installed in piping that is equal to or less than 4 inches in size. The variables to consider when sizing a valve include:

• Media: specific gravity and viscosity
• Inlet temperature and pressure: under maximum load
• Pressure drop: under maximum load
• Maximum capacity
• Maximum pressure differential the valve will need to close again.

The science behind valve sizing is determining the flow through the diameter of the valve. Since throttling valves may contain two different sized openings designed to accommodate a pressure drop, proper sizing is critical for an efficient system.

• Open/Close valves are expected to pass 100% of the flow without a significant drop in pressure. They do not throttle the flow so the openings are generally the same size. If the valve is too small, the flow will be restricted, defeating the purpose of the on/off valve. A large valve will cost more because increasers will need to be installed.
• Throttle valves are expected to produce a certain amount of flow at certain positions of opening to create a pressure drop. Throttle valves work best when the valve uses the full range of stroke while producing desired flow characteristics and maximum flow output.

Oversizing a valve happens more frequently than undersizing because the manufacturer adds safety factors to the specifications they receive from the user, which are generally the maximum specifications of the system. Having an oversized valve is more manageable and safer than undersized valves.

The use of increasers or reducers to create nonstandard piping configurations can be corrected in the Cv equation. In order to determine the piping geometry factor, Fp, the inside diameter of the pipe is required. In the table below, "d" is the inside diameter and "D" is the outside diameter.

Piping- geometry factor for valves with reducers and increasers on both ends. Table Credit: Valtek International

### Resources

Valve and Valve Actuator Selection Guide
Skousen, Philip L. Valve Handbook. New York: McGraw-Hill, 1998. Print.
The Engineering ToolBox- Flow Coefficient
Control Valve Selection and Sizing
Control Valves and Flow Characteristics