Basic Calculations for Process Engineer

7/29/2019 Basic Calculations for Process Engineer

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BASIC CALCULATION FOR PROCESS ENGINEER

One of the most basic calculations performed by any process engineer, whether in designor in the plant, is line sizing and pipeline pressure loss. Typically known are the flowrate, temperature and corresponding viscosity and specific gravity of the fluid that will

flow through the pipe. These properties are entered into a computer program orspreadsheet along with some pipe physical data (pipe schedule and roughness factor) andout pops a series of line sizes with associated Reynolds Number, velocity, friction factorand pressure drop per linear dimension. The pipe size is then selected based on acompromise between the velocity and the pressure drop. With the line now sized and thepressure drop per linear dimension determined, the pressure loss from the inlet to theoutlet 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 pressuredrop 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 byengineers 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 Equation2.

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) Determinethe number of valves and fittings in the pipe. For example, there may be two gate valves,a 90o elbow and a flow thru tee. (3) Determine the means of incorporating the valves andfittings into the Darcy equation. To accomplish this, most engineers use a table of


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equivalent lengths. This table lists the valve and fitting and an associated length ofstraight pipe of the same diameter, which will incur the same pressure loss as that valveor fitting. For example, if a 2 90o elbow were to produce a pressure drop of 1 psi, theequivalent length would be a length of 2 straight pipe that would also give a pressuredrop 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 equivalentlength is usually added to the total straight pipe length obtained in step one to give a totalpipe equivalent length. (5) This total pipe equivalent length is then substituted for L inEquation 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 CRANETechnical Paper No. 410. It is the authors opinion that this manual is the closest thing

the industry has to a standard on performing various piping calculations. If the readercurrently 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 ofhead loss. This can be expressed by another form of the Darcy equation similar toEquation 1:

When comparing Equations 1 and 3, it becomes apparent that:

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


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Pipe friction in the inlet and outlet straight portions of the valve or fitting is very smallwhen compared to the other three. Since friction factor and Reynolds Number are mainlyrelated to pipe friction, K can be considered to be independent of both friction factor andReynolds Number.Therefore, K is treated as a constant for any given valve or fittingunder 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 fittingsize. Note that this is also true for the friction factor in straight clean commercial steelpipeas long as flow conditions are in the fully developed turbulent zone. It was alsofound that the ratio L/D tends towards a constant for all sizesof a given valve or fittingtypeat the same flow conditions. The ratio L/D is defined as the equivalent length of thevalve or fitting in pipe diametersandL is the equivalent length itself.

In Equation 4, therefore varies only with valve and fitting size and is independent ofReynolds Number. This only occurs if the fluid flow is in the zone ofcompleteturbulence (see the Moody Chart in reference 1 or in any textbook on fluid

flow). Consequently, in Equation 4 isnot the same as in the Darcy equation for

straight pipe, which isa function of Reynolds Number. For valves and fittings, is thefriction factor in the zone ofcomplete turbulenceand is designatedt, and the equivalentlength of the valve or fitting is designated Leq. Equation 4 should now read (with D beingthe diameter of the valve or fitting):

The equivalent length, Leq, is related to t, not, the friction factor of the flowing fluidin the pipe. Going back to step four in our five step procedure for calculating the totalpressure drop in the pipe, adding the equivalent length to the straight pipe length for usein 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 substitutet for and Leq 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 thestraight pipe to give the total pipe pressure drop.


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

Notice that use of equivalent length and friction factor in the pressure drop equation iseliminated, although both are still required to calculate the values of K1. As a matter offact, there is nothing stopping the engineer from converting the straight pipe length into aK 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, itdepends. Below is a real world example showing the difference between the EquivalentLength method (as applied by most engineers) and the K value method to calculatepressure drop.

An Example

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

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 P/100 ft. 1.308

Friction Factor at Full Turbulence (t): 0.018

Straight Pipe, ft: 31.5


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Fittings Leq/D1 Leq2, 3 K1, 2 =t(L/D)

Quantity Total Leq Total K

90o Long Radius

Elbow

20 5.1 0.36 2 10.23 0.72

Branch Tee 60 15.3 1.08 1 15.34 1.08Swing Check Valve 50 12.8 0.9 1 12.78 0.9Plug Valve 18 4.6 0.324 1 4.6 0.324

3 x 1 Reducer4 None5

822.685 57.92 1 822.68 57.92

TOTAL 865.633 60.944

Notes:

1. K values and Leq/D are obtained from reference 1.2. K values and Leqare given in terms of the larger sized pipe.

3. Leq 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, justreducers. It is standard to specify the reducer with the larger size shownfirst. The K value for the expansion is calculated as a gradual enlargement with a30o angle.

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

Typical Equivalent LengthMethod K Value Method

Straight Pipe P, psi Not applicable 0.412Total Pipe Equivalent Length P,psi

11.322 Not Applicable

Valves and Fittings P, psi Not applicable 6.828

Total Pipe P, psi 11.322 7.24

The line pressure drop is greater by about 4.1 psi (about 56%) using the typicalequivalent length method (adding straight pipe length to the equivalent length and usingthe pipe line fiction factor and 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 allcalculations, should be done in a correct and consistent manner. If the engineer gets intothe 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 shownabove.


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Another point to consider is how the engineer treats a reducer when using the typicalequivalent 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 usetand K. Why not usethese 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 andt for valves and fittings). Since then, Hooper2suggested a 2-K method

for calculating the pressure loss contribution for valves and fittings. His argument wasthat the equivalent length in pipe diameters (L/D) and K was indeed a function ofReynolds 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 acombination of two Ks, one being the K found in CRANE Technical Paper No. 410,

designated K, 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/ NRE +K (1 +1/D)

The term (1+1/D) takes into account scaling between different sizes within a givenvalve or fitting group. Values for K1 can be found in the reference article

2 and pressuredrop is then calculated using Equation 7. For flow in the fully turbulent zone and largersize 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 themix. 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 havecaught on as of yet. Some newer commercial computer programs allow for the use ofthe 2-K method, but most engineers inclined to use the K method instead of theEquivalent Length method still use the procedures given in CRANE. The latest 3-Kmethod comes from data reported in the recent CCPS Guidlines4 and appears to bedestined to become the new standard; we shall see.

Conclusion

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


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NOMENCLATURED = Diameter, ftd = 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 feetK = Resistance coefficient or velocity head lossK1 = K for the fitting at NRE =1

K = K value from CRANEL = Straight pipe length, ftLeq = Equivalent length of valve or fitting, ftNRE = Reynolds Number

P = Pressure drop, psi

= Velocity, ft/secW = Flow Rate, lb/hr

= Density, lb/ft3

REFERENCES

1. Crane Co., Flow of Fluids through Valves, Fittings and Pipe, Crane TechnicalPaper No. 410, New York, 1991.

2. Hooper, W. B., The Two-K Method Predicts Head Losses in Pipe Fittings, Chem.Eng., p. 97-100, August 24, 1981.

3. Darby, R., Correlate Pressure Drops through Fittings, Chem. Eng., p. 101-104,July, 1999.

4. AIChE Center for Chemical Process Safety, Guidelines for Pressure Relief andEffluent Handling systems, pp. 265-268, New York, 1998.

Reader / Author Question and Answers

1. "Could you please give me in layman terms a better definition for K values. I knowthat K is defined as "the number of velocity heads lost"...But what exactly does thatmean???"

Well, I'll try to give you the Chemical Engineer's version of the layman answer. Velocityof any fluid increases through pipes, valves and fittings at the expense of pressure. Thispressure loss is referred to as head loss. The greater the head loss, the higher the velocityof the fluid. So, saying a velocity head loss is just another way of saying we loosepressure due to and increase in velocity and this pressure loss is measured in terms of feetof head. Now, each component in the system contributes to the amount of pressure loss indifferent amounts depending upon what it is. Pipes contribute fL/D where L is the pipelength, D is the pipe diameter and f is the friction factor. A fitting or valve contributes K.Each fitting and valve has an associated K.


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2. "It appears that the K values in CRANE TP-410 were established using a liquid (water)flow loop. Is this K value also valid for compressible media systems? (Can a K value beused for both compressible and incompressible service?)"

Crane also tested their system on steam and air. Now, this is where things get sticky. As

per CRANE TP-410, K values are a function of the size and type of valve or fitting onlyand is independent of fluid and Reynolds number. So yes, you can use it in ALL services,including two-phase flow. However, as I point out towards the end of my article, there isnow evidence that shows using a single K value for the valve and fitting is not correctand that K is indeed a function of both Reynolds number and fitting/valvegeometry. I reference an article by Dr. Ron Darby of Texas A&M University which canbe found in Chemical Engineering Magazine, July 1999. Dr. Darby just published asecond article on the subject which can be found in Chemical Engineering Magazine,April 2001.

I don't believe there is any question as to the proper way to use K values in pressure drop

calculations. The only question is whether industry will accept the new data.

3. "When answering my first question, you stated: 'Velocity of any fluid increasesthrough pipes, valves and fittings at the expense of pressure.' When you say this, you aretalking about compressible (gas) flow right? For example, in a pipe of constant area, thevelocity of a gas would increase as the fluid traveled down the pipe (due to the decreasingpressure). However, the velocity of a liquid would remain constant as it traveled downthe same pipe (even with the decreasing pressure). Is this a correct statement?

Sorry for the confusion. Yes to both of your questions. If you look at the Bernoulliequation, you will see that velocity cancels out for a liquid as long as there is no change

in pipe size along the way and pressure drop is only a function of frictional losses and achange in elevation.

However, the K value of a fitting is still a quantifier of the head loss (frictional loss) inthat fitting and this head loss is still calculated as the velocity head of the liquid (V 2/2g).So in essence, you still achieve aliquid velocity at the expense of pressure loss; the velocity head just happens to beconstant. Read section 2-8 in CRANE TP-410. They define the velocity head as adecrease in static head due to velocity.

The big thing is not to get too hung up on the definitions and just remember you can'thave flow unless you have a driving force and that force is differential pressure. Also, ina piping system there is frictional losses which comes from the pipe and all fittings andvalves. The use of K is just a way of quantifying the frictional component of the fittingsand valves. You can even put the piping friction in terms of K by using fL/D for the pipeand multiplying that by V 2/2g.

I hope this helps. If you are still confused, let me know and I'll just explain it again but I'll


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try to do it in a different way. Sometimes, a concept just needs to be re-worded and I'mwilling to spend as much time on this as you need.

4. I'm reading the Crane Technical Paper #410 and I have the followingquestions/comments:

Page 2-8 of TP 410 states that:"Velocity in a pipe is obtained at the expense of static head". This makes sense andEquation 2-1 shows this relationship where the static head is converted to velocityhead. However, there is no diameter associated with this. So is it correct to say based onequation 2-1 that if you had a barrel of water with a short length of pipe attached to thebottom that discharged to atmosphere, and in this barrel you had 5 feet of water (5' ofstatic head), the resulting water velocity would be 17.94 ft/sec (regardlessof the pipe diameter).

Maybe the real question is how do you use equation 2-1. Do you have to know the

velocity and then you can calculate the headloss? And why does equation 2-1 andequation 2-3 seem to show headloss equaling two different things?

Also, why does it say that a diameter is always associtated with the K value, when as Imentioned above there is no diameter associated with equation 2-1?

Maybe I'm trying to read into all of this too deeply, but I still do not feel that I fully graspwhat page 2-8 is trying to reveal.

You need a diameter to get velocity. Velocity is lenght/time (for example, feet/sec). Flowis usually given in either mass units (weight/time or lb/hr for example) or in volumetric

units (cubic feet per minute for example). To get velocity, you need to divide thevolumetric flow by a cross sectional area (square feet). To get an area, you need adiameter. So the velocity is always based on some diameter.

As I show in my paper, equation 2-1 is just the basis of the velocity head. To get thefrictional loss, you need to know the contribution of each component in the system; pipe,fitting and valve. To get that contribution, you use 'K' (equation 2-2). Each componenthas an associated 'K' value. You multiply the velocity head by the appropriate 'K' value.Equation 2-3 is just another way of expressing the same thing. As you can see, this meansyou can calculate a 'K' for a component such as a pipe using the formula fL/D as shownin Equation 2-3. Again, I explain this in my paper so I would suggest you re-read it.

I would also suggest you look at the examples in CRANE. There are many of them inChapter 4.

'K' is associated with the velocity and therefore the diameter. Look at the values for 'K' inCRANE (starting on page A-26). You will see that for the most part, K is a function of aconstant times the friction factor at fully turbulent flow. This friction factor changes with


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pipe diameter as shown on page A-26. Again, re-read my paper and look at the examplesin Chapter 4.

Table of Minor Loss Coefficients (Km is unit-less): References Back toCalculation

Fitting K m Fitting K m

Valves: Elbows:

Globe, fully open 10 Regular 90, flanged 0.3

Angle, fully open 2 Regular 90, threaded 1.5

Gate, fully open 0.15 Long radius 90, flanged 0.2

Gate 1/4 closed 0.26 Long radius 90, threaded 0.7

Gate, 1/2 closed 2.1 Long radius 45, threaded 0.2

Gate, 3/4 closed 17 Regular 45, threaded 0.4

Swing check, forward flow 2

Swing check, backward flow infinity Tees:

Line flow, flanged 0.2

180 return bends: Line flow, threaded 0.9

Flanged 0.2 Branch flow, flanged 1.0Threaded 1.5 Branch flow, threaded 2.0

Pipe Entrance (Reservoir to Pipe): Pipe Exit (Pipe to Reservoir)

Square Connection 0.5 Square Connection 1.0

Rounded Connection 0.2 Rounded Connection 1.0

Re-entrant (pipe juts into tank) 1.0 Re-entrant (pipe juts into tank) 1.0
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Basic Calculations for Process Engineer