Valve Sizing

Sizing flow valves is a science with many rules of thumb that few people agree on. In this article I'll try to define a more standard procedure for sizing a valve as well as helping to select the appropriate type of valve. **Please note that the correlation within this article are for turbulent flow

STEP #1: Define the system

The system is pumping water from one tank to another through a piping system with a total pressure drop of 150 psi. The fluid is water at 70 ⁰F. Design (maximum) flowrate of 150 gpm, operating flowrate of 110 gpm, and a minimum flowrate of 25 gpm. The pipe diameter is 3 inches. At 70⁰F, water has a specific gravity of 1.0.

Key Variables: Total pressure drop, design flow, operating flow, minimum flow, pipe diameter, specific gravity

STEP #2: Define a maximum allowable pressure drop for the valve

When defining the allowable pressure drop across the valve, you should first investigate the pump. What is its maximum available head? Remember that the system pressure drop is limited by the pump. Essentially the Net Positive Suction Head Available (NPSHA) minus the Net Positive Suction Head Required (NPSHR) is the maximum available pressure drop for the valve to use and this must not be exceeded or another pump will be needed. It's important to remember the trade off, larger pressure drops increase the pumping cost (operating) and smaller pressure drops increase the valve cost because a larger valve is required (capital cost).The usual rule of thumb is that a valve should be designed to use 10-15% of the total pressure drop or 10 psi, whichever is greater. For our system, 10% of the total pressure drop is 15 psi which is what we'll use as our allowable pressure drop when the valve is wide open (the pump is our system is easily capable of the additional pressure drop).

STEP #3: Calculate the valve characteristic

For our system,

At this point, some people would be tempted to go to the valve charts or characteristic curves and select a valve. Don't make this mistake, instead, proceed to Step #4!

STEP #4: Preliminary valve selection

Don't make the mistake of trying to match a valve with your calculated Cv value. The Cv value should be used as a guide in the valve selection, not a hard and fast rule. Some other considerations are:

a. Never use a valve that is less than half the pipe size

b. Avoid using the lower 10% and upper 20% of the valve stroke. The valve is much easier to control in the 10-80% stroke range.

Before a valve can be selected, you have to decide what type of valve will be used (See the list of valve types later in this article). For our case, we'll assume we're using an equal percentage, globe valve (equal percentage will be explained later). The valve chart for this type of valve is shown below. This is a typical chart that will be supplied by the manufacturer (as a matter of fact, it was!)

For our case, it appears the 2 inch valve will work well for our Cv value at about 80-85% of the stroke range. Notice that we're not trying to squeeze our Cv into the 1 1/2 valve which wouldneed to be at 100% stroke to handle our maximum flow. If this valve were used, two consequences would be experienced: the pressure drop would be a little higher than 15 psi at our design (max) flow and the valve would be difficult to control at maximum flow. Also, there would be no room for error with this valve, but the valve we've chosen will allow for flow surges beyond the 150 gpm range with severe headaches!

So we've selected a valve...but are we ready to order? Not yet, there are still some characteristics to consider.

STEP #5: Check the Cv and stroke percentage at the minimum flow

If the stroke percentage falls below 10% at our minimum flow, a smaller valve may have to be used in some cases. Judgements plays role in many cases. For example, is your system more likely to operate closer to the maximum flowrates more often than the minimum flowrates? Or is it more likely to operate near the minimum flowrate for extended periods of time. It's difficult to find the perfect valve, but you should find one that operates well most of the time. Let's check the valve we've selected for our system:

Referring back to our valve chart, we see that a Cv of 6.5 would correspond to a stroke percentage of around 35-40% which is certainly acceptable. Notice that we used the maximum pressure drop of 15 psi once again in our calculation. Although the pressure drop across the valve will be lower at smaller flowrates, using the maximum value gives us a "worst case" scenario. If our Cv at the minimum flow would have been around 1.5, there would not really be a problem because the valve has a Cv of 1.66 at 10% stroke and since we use the maximum pressure drop, our estimate is conservative. Essentially, at lower pressure drops, Cv would only increase which in this case would be advantageous.

STEP #6: Check the gain across applicable flowrates

Gain is defined as:

Now, at our three flowrates:

Qmin = 25 gpm

Qop = 110 gpm

Qdes = 150 gpm

we have corresponding Cv values of 6.5, 28, and 39. The corresponding stroke percentages are 35%, 73%, and 85% respectively. Now we construct the following table:

Flow (gpm)	Stroke (%)	Change in flow (gpm)	Change in Stroke (%)
25	35	110-25 = 85	73-35 = 38
110	73
150	85	150-110 = 40	85-73 = 12

Gain #1 = 85/38 = 2.2

Gain #2 = 40/12 = 3.3

The difference between these values should be less than 50% of the higher value.

0.5 (3.3) = 1.65

and 3.3 - 2.2 = 1.10. Since 1.10 is less than 1.65, there should be no problem in controlling the valve. Also note that the gain should never be less than 0.50. So for our case, I believe our selected valve will do nicely!

OTHER NOTES:

Another valve characteristic that can be examined is called the choked flow. The relation uses the F_L value found on the valve chart. I recommend checking the choked flow for vastly different maximum and minimum flowrates. For example if the difference between the maximum and minimum flows is above 90% of the maximum flow, you may want to check the choked flow. Usually, the rule of thumb for determining the maximum pressure drop across the valve also helps to avoid choking flow.

SELECTING A VALVE TYPE

When speaking of valves, it's easy to get lost in the terminology. Valve types are used to describe the mechanical characteristics and geometry (Ex/ gate, ball, globe valves). We'll usevalve controlto refer to how the valve travel or stroke (openness) relates to the flow:

1. Equal Percentage: equal increments of valve travel produce an equal percentage in flow change

2. Linear: valve travel is directly proportional to the valve stoke

3. Quick opening: large increase in flow with a small change in valve stroke

So how do you decide which valve control to use? Here are some rules of thumb for each one:

1. Equal Percentage (most commonly used valve control)

a. Used in processes where large changes in pressure drop are expected

b. Used in processes where a small percentage of the total pressure drop is permitted by the valve

c. Used in temperature and pressure control loops

2. Linear

a. Used in liquid level or flow loops

b. Used in systems where the pressure drop across the valve is expected to remain fairly constant (ie. steady state systems)

3. Quick Opening

a. Used for frequent on-off service

b. Used for processes where "instantly" large flow is needed (ie. safety systems or cooling water systems)

Now that we've covered the various types of valve control, we'll take a look at the most common valve types.

Gate Valves

Best Suited Control: Quick Opening

Recommended Uses:

1. Fully open/closed, non-throttling

2. Infrequent operation

3. Minimal fluid trapping in line

Applications: Oil, gas, air, slurries, heavy liquids, steam, noncondensing gases, and corrosive liquids

Advantages: Disadvantages:

1. High capacity 1. Poor control

2. Tight shutoff 2. Cavitate at low pressure drops

3. Low cost 3. Cannot be used for throttling

4. Little resistance to flow

Globe Valves

Best Suited Control: Linear and Equal percentage

Recommended Uses:

1. Throttling service/flow regulation

2. Frequent operation

Applications: Liquids, vapors, gases, corrosive substances, slurries

Advantages: Disadvantages:

1. Efficient throttling 1. High pressure drop

2. Accurate flow control 2. More expensive than other valves

3. Available in multiple ports

Ball Valves

Recommended Uses:

1. Fully open/closed, limited-throttling

2. Higher temperature fluids

Applications: Most liquids, high temperatures, slurries

Advantages: Disadvantages:

1. Low cost 1. Poor throttling characteristics

2. High capacity 2. Prone to cavitation

3. Low leakage and maint.

4. Tight sealing with low torque

Butterfly Valves

Best Suited Control: Linear, Equal percentage

Recommended Uses:

1. Fully open/closed or throttling services

2. Frequent operation

3. Minimal fluid trapping in line

Applications: Liquids, gases, slurries, liquids with suspended solids

Advantages: Disadvantages:

1. Low cost and maint. 1. High torque required for control

2. High capacity 2. Prone to cavitation at lower flows

3. Good flow control

4. Low pressure drop

Other Valves

Another type of valve commonly used in conjunction with other valves is called a check valve. Check valves are designed to restrict the flow to one direction. If the flow reverses direction, the check valve closes. Relief valves are used to regulate the operating pressure of incompressible flow. Safety valves are used to release excess pressure in gases or compressible fluids.

Equivalent Lengths of Valves and Fittings in Pipeline Pressure Drop Calculations

One of the most basic calculations performed by any process engineer, whether in design or in the plant, is line sizing and pipeline pressure loss. Typically known are the flow rate, temperature and corresponding viscosity and

specific gravity of the fluid that will flow through the pipe. These properties are entered into a computer program or spreadsheet along with some pipe physical data (pipe schedule and roughness factor) and out pops a series of line sizes with associated Reynolds Number, velocity, friction factor and pressure drop per linear dimension. The pipe size is then selected based on a compromise between the velocity and the pressure drop. With the line now sized and the pressure drop per linear dimension determined, the pressure loss from the inlet to the outlet of the pipe can be calculated.

Calculating Pressure Drop

The most commonly used equation for determining pressure drop in a straight pipe is the Darcy Weisbach equation. One common form of the equation which gives pressure drop in terms of feet of head is given below:

The term

is commonly referred to as the Velocity Head.

Another common form of the Darcy Weisbach equation that is most often used by engineers because it gives pressure drop in units of pounds per square inch (psi) is:

To obtain pressure drop in units of psi/100 ft, the value of 100 replaces L in Equation 2.

The total pressure drop in the pipe is typically calculated using these five steps. (1) Determine the total length of all horizontal and vertical straight pipe runs. (2) Determine the number of valves and fittings in the pipe. For example, there may be two gate valves, a 90^o elbow and a flow thru tee. (3) Determine the means of incorporating the valves and fittings into the Darcy equation. To accomplish this, most engineers use a table of equivalent lengths. This table lists the valve and fitting and an associated length of straight pipe of the same diameter, which will incur the same pressure loss as that valve or fitting. For example, if a 2” 90^o elbow were to produce a pressure drop of 1 psi, the equivalent length would be a length of 2” straight pipe that would also give a pressure drop of 1 psi. The engineer then multiplies the quantity of each type of valve and fitting by its respective equivalent length and adds them together. (4) The total equivalent length is usually added to the total straight pipe length obtained in step one to give a total pipe equivalent length. (5) This total pipe equivalent length is then substituted for L in Equation 2 to obtain the pressure drop in the pipe.

See any problems with this method?

Relationship Between K, Equivalent Length and Friction Factor

The following discussion is based on concepts found in reference 1, the CRANE Technical Paper No. 410. It is the author’s opinion that this manual is the closest thing the industry has to a standard on performing various piping calculations. If the reader currently does not own this manual, it is highly recommended that it be obtained.

As in straight pipe, velocity increases through valves and fittings at the expense of head loss. This can be expressed by another form of the Darcy equation similar to Equation 1:

K is called the resistance coefficient and is defined as the number of velocity heads lost due to the valve or fitting. It is a measure of the following pressure losses in a valve or fitting:

• Pipe friction in the inlet and outlet straight portions of the valve or fitting
• Changes in direction of flow path
• Obstructions in the flow path
• Sudden or gradual changes in the cross-section and shape of the flow path

Pipe friction in the inlet and outlet straight portions of the valve or fitting is very small when compared to the other three. Since friction factor and Reynolds Number are mainly related to pipe friction, K can be considered to be independent of both friction factor and Reynolds Number. Therefore, K is treated as a constant for any given valve or fitting under all flow conditions, including laminar flow. Indeed, experiments showed¹ that for a given valve or fitting type, the tendency is for K to vary only with valve or fitting size. Note that this is also true for the friction factor in straight clean commercial steel pipe as long as flow conditions are in the fully developed turbulent zone. It was also found that the ratio L/D tends towards a constant for all sizes of a given valve or fitting type at the same flow conditions. The ratio L/D is defined as the equivalent length of the valve or fitting in pipe diameters andL is the equivalent length itself.

In Equation 4, ¦ therefore varies only with valve and fitting size and is independent of Reynolds Number. This only occurs if the fluid flow is in the zone of complete turbulence (see the Moody Chart in reference 1 or in any textbook on fluid flow). Consequently, ¦ in Equation 4 is not the same ¦ as in the Darcy equation for straight pipe, which is a function of Reynolds Number. For valves and fittings, ¦ is the friction factor in the zone of complete turbulence and is designated ¦_t, and the equivalent length of the valve or fitting is designated L_eq. Equation 4 should now read (with D being the diameter of the valve or fitting):

The equivalent length, L_eq, is related to ¦_t, not ¦, the friction factor of the flowing fluid in the pipe. Going back to step four in our five step procedure for calculating the total pressure drop in the pipe, adding the equivalent length to the straight pipe length for use in Equation 1 is fundamentally wrong.

Calculating Pressure Drop, The Correct Way

So how should we use equivalent lengths to get the pressure drop contribution of the valve or fitting? A form of Equation 1 can be used if we substitute ¦_t for ¦ and L_eq for L (with d being the diameter of the valve or fitting):

The pressure drop for the valves and fittings is then added to the pressure drop for the straight pipe to give the total pipe pressure drop.

Another approach would be to use the K values of the individual valves and fittings. The quantity of each type of valve and fitting is multiplied by its respective K value and added together to obtain a total K. This total K is then substituted into the following equation:

Notice that use of equivalent length and friction factor in the pressure drop equation is eliminated, although both are still required to calculate the values of K¹. As a matter of fact, there is nothing stopping the engineer from converting the straight pipe length into a K value and adding this to the K values for the valves and fittings before using Equation 7. This is accomplished by using Equation 4, where D is the pipe diameter and ¦ is the pipeline friction factor.

How significant is the error caused by mismatching friction factors? The answer is, it depends. Below is a real world example showing the difference between the Equivalent Length method (as applied by most engineers) and the K value method to calculate pressure drop.

An Example

The fluid being pumped is 94% Sulfuric Acid through a 3”, Schedule 40, Carbon Steel pipe:

Mass Flow Rate, lb/hr:	63,143
Volumetric Flow Rate, gpm:	70
Density, lb/ft3:	112.47
S.G.	1.802
Viscosity, cp:	10
Temperature, oF:	127
Pipe ID, in:	3.068
Velocity, fps:	3.04
Reynold's No:	12,998
Darcy Friction Factor, (f) Pipe:	0.02985
Pipe Line DP/100 ft.	1.308
Friction Factor at Full Turbulence (¦t):	0.018
Straight Pipe, ft:	31.5

Notes:

1. K values and L_eq/D are obtained from reference 1.

2. K values and L_eq are given in terms of the larger sized pipe.

3. L_eq is calculated using Equation 5 above.

4. The reducer is really an expansion; the pump discharge nozzle is 1” (Schedule 80) but the connecting pipe is 3”. In piping terms, there are no expanders, just reducers. It is standard to specify the reducer with the larger size shown first. The K value for the expansion is calculated as a gradual enlargement with a 30^o angle.

5. There is no L/D associated with an expansion or contraction. The equivalent length must be back calculated from the K value using Equation 5 above.

	Typical Equivalent Length Method	K Value Method
Straight Pipe DP, psi	Not applicable	0.412
Total Pipe Equivalent Length DP, psi	11.734	Not Applicable
Valves and Fittings DP, psi	Not applicable	6.828
Total Pipe DP, psi	11.734	7.24

The line pressure drop is greater by about 4.5 psi (about 62%) using the typical equivalent length method (adding straight pipe length to the equivalent length of the fittings and valves and using the pipe line fiction factor in Equation 1).

One can argue that if the fluid is water or a hydrocarbon, the pipeline friction factor would be closer to the friction factor at full turbulence and the error would not be so great, if at all significant; and they would be correct. However hydraulic calculations, like all calculations, should be done in a correct and consistent manner. If the engineer gets into the habit of performing hydraulic calculations using fundamentally incorrect equations, he takes the risk of falling into the trap when confronted by a pumping situation as shown above.

Another point to consider is how the engineer treats a reducer when using the typical equivalent length method. As we saw above, the equivalent length of the reducer had to be back-calculated using equation 5. To do this, we had to use ¦_t and K. Why not use these for the rest of the fittings and apply the calculation correctly in the first place?

Final Thoughts - K Values

The 1976 edition of the Crane Technical Paper No. 410 first discussed and used the two-friction factor method for calculating the total pressure drop in a piping system (¦ for straight pipe and ¦_t for valves and fittings). Since then, Hooper² suggested a 2-K method for calculating the pressure loss contribution for valves and fittings. His argument was that the equivalent length in pipe diameters (L/D) and K was indeed a function of Reynolds Number (at flow rates less than that obtained at fully developed turbulent flow) and the exact geometries of smaller valves and fittings. K for a given valve or fitting is a combination of two Ks, one being the K found in CRANE Technical Paper No. 410, designated K_Y, and the other being defined as the K of the valve or fitting at a Reynolds Number equal to 1, designated K₁. The two are related by the following equation:

K = K₁ / N_RE + K_Y (1 + 1/D)

The term (1+1/D) takes into account scaling between different sizes within a given valve or fitting group. Values for K₁ can be found in the reference article² and pressure drop is then calculated using Equation 7. For flow in the fully turbulent zone and larger size valves and fittings, K becomes consistent with that given in CRANE.

Darby³ expanded on the 2-K method. He suggests adding a third K term to the mix. Darby states that the 2-K method does not accurately represent the effect of scaling the sizes of valves and fittings. The reader is encouraged to get a copy of this article.

The use of the 2-K method has been around since 1981 and does not appear to have “caught” on as of yet. Some newer commercial computer programs allow for the use of the 2-K method, but most engineers inclined to use the K method instead of the Equivalent Length method still use the procedures given in CRANE. The latest 3-K method comes from data reported in the recent CCPS Guidlines⁴ and appears to be destined to become the new standard; we shall see.

Conclusion

Consistency, accuracy and correctness should be what the Process Design Engineer strives for. We all add our “fat” or safety factors to theoretical calculations to account for real-world situations. It would be comforting to know that the “fat” was added to a basis using sound and fundamentally correct methods for calculations.

NOMENCLATURE
D	=	Diameter, ft
d	=	Diameter, inches
¦	=	Darcy friction factor
¦t	=	Darcy friction factor in the zone of complete turbulence
g	=	Acceleration of gravity, ft/sec2
hL	=	Head loss in feet
K	=	Resistance coefficient or velocity head loss
K1	=	K for the fitting at NRE = 1
KY	=	K value from CRANE
L	=	Straight pipe length, ft
Leq	=	Equivalent length of valve or fitting, ft
NRE	=	Reynolds Number
DP	=	Pressure drop, psi
n	=	Velocity, ft/sec
W	=	Flow Rate, lb/hr
r	=	Density, lb/ft3

Cooling Towers: Design and Operation Considerations

Cooling towers are a very important part of many chemical plants. They represent a relatively inexpensive and dependable means of removing low grade heat from cooling water.

Figure 1: Closed Loop Cooling Tower System

The make-up water source is used to replenish water lost to evaporation. Hot water from heat exchangers is sent to the cooling tower. The water exits the cooling tower and is sent back to the exchangers or to other units for further cooling.

Types of Cooling Towers

Cooling towers fall into two main sub-divisions: natural draft and mechanical draft. Natural

draft designs use very large concrete chimneys to introduce air

through the media. Due to the tremendous size of these towers (500

ft high and 400 ft in diameter at the base) they are gen

erally used for water f

lowrates above 200,000 gal/min. Usually these types of towers are only used by utility power stations in the United States. Mechanical draft cooling towers a

re much more widely used. These towers utilize large fans to for

ce air through circulated water. The water falls downward over fill surfaces which help increas

e the contact time between the water and the air. This helps maximize heat transfer between the two.

Types of Mechanical Draft Towers

Figure 2: Mechanical Draft Counterflow Tower Figure 3: Mechanical Draft Crossflow Tower

Mechanical draft towers offer control of cooling rates in t

heir fan dia

meter and speed of operation. These towers often contain several areas (eac

h

with their own fan) called cells.

Cooling Tower Theory

Heat is transferred from water drops to the surrounding air by the transfer of sensible and latent heat.

Figure 4: Water Drop with Interfacial Film

where:

KaV/L = tower characteristic

K = mass transfer coefficient (lb water/h ft²)

a = contact area/tower volume

V = active cooling volume/plan area

L = water rate (lb/h ft²)

T₁ = hot water temperature (⁰F or ⁰C)

T₂ = cold water temperature (⁰F or ⁰C)

T = bulk water temperature (⁰F or ⁰C)

(J/kg dry air or Btu/lb dry air)

h_a = enthalpy of air-water vapor mixture at wet bulb temperature

(J/kg dry air or Btu/lb dry air)

Thermodynamics also dictate that the heat removed from the water must be equal to the heat absorbed by the su

rrounding air:

The tower characteristic value can be calculated by solving Equation 1 with the Chebyshev numberical method:

Figure 5: Graphical Representation of Tower Characteristic

The following represents a key to Figure 5:

C' = Entering air enthalpy at wet-bulb temperature, T_wbBC = Initial enthalpy driving force

CD = Air operating line with slope L/G

DEF = Projecting the exiting air point onto the water operating line and then onto the

temperature axis shows the outlet air web-bulb temperature

As shown by Equation 1, by finding the area between ABCD in Figure 5, one can find the tower characteristic. An increase in heat load would have the following effects on the diagram in Figure 5:

1. Increase in the length of line CD, and a CD line shift to the right

2. Increases in hot and cold water temperatures

3. Increases in range and approach areas

The increased heat load causes the hot water temperature to increase considerably faster than does the cold water temperature. Although the area AB

CD should remain constant, it actually decreases about 2% for every 10 ⁰F increase in hot water temperature above 100 ⁰F. To account for this de

crease, an "adjusted hot water temperature" is usd in cooling tower de

sign.

Figure 6: Graph of Adjusted Hot Water Temperatures