Crane-Fluid-Flow-Problems.xls

Example Flow Problems

IntroductionI received my first copy of Crane's Technical Paper No. 410, titled " Flow of Fluids through Valves,fittings, and pipe", in October 1962. It was given to me free of charge by the Crane salesman that took care ofthe business account at Liquid Carbonic Division of General Dynamics in Chicago, where I worked.I had just completed my first year practicing engineering at Liquid Carbonic's affiliated companies in Jamaica,Jamaica Oxygen and Acetylene Ltd. and Jamaica Carbonics. I had spent a year in Jamaica as ProductionManager, replacing Alf Newton who had gone to Barbados and Trinidad to erect a small CO2 plant inBarbados and an industrial gas facility (Oxygen and Acetylene) at Biljah Road in Trinidad.My original copy was the 1957 copyrighted version, sixth printing. It had a stated price of $10.00.This was my first experience in dealing with fluid flow problems using the Darcy equation together with thecorresponding Moody Chart. At Texas A&M we were taught the Fanning equation and its correspondingfriction factor (the Darcy friction factor = 4 x the Fanning friction factor).We had never been exposed to such practical and detailed fluid flow problems at Texas A&M. This bookletwas not only interesting, but it also taught the young engineer how to cope with and resolve practicalplant fluid problems. I went through all 27 example problems which were given in Section 4 of the booklet.Later, during my tenure at Quaker Oats Chemical Division in Chicago (1968 - 1973), I would receive a copyof the 1965 Crane version (9th printing). The example problems were basically the same and resolved inthe same manner as in the 1957 version. The 1965 version had a stated price of $2.00.When I worked for Allstates Engineering on DuPont projects (1989 -1994) I obtained the 1979 version (18thprinting) and it had a stated price of $8.00. This is the version that this Workbook's examples are based on.I still retain the original 1957 version copy, although the original hard, orange carboard front and back coverhave cracked and disintegrated from the stainless steel spiral hinge.I have transcribed the Example problems given in the 1979 (18th printing) Edition into this workbook and alsoadded those problems that were given in the 1957 Edition but were not included in the 1979 Edition. Additionally,I have included in each of the 1979 Example problem solutions those solutions that were given in the 1957 Editionand that were resolved in a different manner. This enables the reader to see the difference in the technology ofsolving these problems and how the methods have increased the accuracy of the answer.My reason for transcribing these Example problems into the Spreadsheet format is to achieve a rapid and efficientmethod by which an engineer can quickly detect the methodology and follow the mathematical computations.Emphasis is put on the logic and reasoning employed rather than worrying about the mathematical mechanics.The spreadsheet allows the reader to insert a variety of different input values and thereby facilitates the engineerin absorbing the manner in which the ultimate answer is affected.Art Montemayor

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Example 4-1Example 4-1 (18th printing)Given:Water at 80 oF is flowing through 70 feet of 2-inch standard wall plastic pipe (smooth wall) at a rateof 50 gallons per minute.Find:The Reynolds Number and the friction factor.Solution:The Reynolds Number is defined as:Where,Q =50gallons/minr =62.22lb/ft3d =2.067inchesm =0.85733cPRe =88,830f =0.0182(from the Moody Chart, for smooth flow)


Example 4-2Example 4-2 (18th printing)Given:A 6-inch Class 125 iron Y-pattern globe valve has a flow coefficient, Cv , of 600.Find:Resistance coefficent, K, the the equivalent lengths L/D and L for flow in the zone of complete turbulence.Solution:K, L/D, and L should be given in terms of 6-inch Schedule 40 pipe;When the resistance coefficient K is used in flow equations, the velocity and internal diameterdimensions used in the equation must be based on the dimensions of the basis Schedule numbersregardless of the pipe with which the valve may be installed.The values in the "K" Factor Table are associated with the internal diameter of the followingpipe schedule numbers for the various ANSI Classes of valves and fittings.Class 300 and lowerSchedule 40Class 400 and 600Schedule 80Class 900Schedule 120Class 1500Schedule 160Class 2500 (sizes 1/2 to 6")XXSClass 2500 (sizes 8" & up)Schedule 160where,d =6.065inches =0.5054ftK =3.36(based on 6", Schedule 40 pipe)f =0.015(from Moody Chart; for 6.065" ID pipe in fully turbulent flow range)L / D =224L = (L / D) (D) =113feetIn the 1957 6th printing edition, an alternate solution is offered:L =113feet


Example 4-3Example 4-3 (18th printing)Given:A 4-inch Class 600 steel conventional angle valve with full area seat.Find:Resistance coefficient K, flow coefficient CV, and equivalent lengths L / D and L for flowin the zone of complete turbulence.Solution:K, L / D, and L should be given in terms of 4-inch Schedule 80 pipe;When the resistance coefficient K is used in flow equations, the velocity and internal diameterdimensions used in the equation must be based on the dimensions of the basis Schedule numbersregardless of the pipe with which the valve may be installed.The values in the "K" Factor Table are associated with the internal diameter of the followingpipe schedule numbers for the various ANSI Classes of valves and fittings.Class 300 and lowerSchedule 40Class 400 and 600Schedule 80Class 900Schedule 120Class 1500Schedule 160Class 2500 (sizes 1/2 to 6")XXSClass 2500 (sizes 8" & up)Schedule 160From the "K" Factor tables,d =3.826inchesfT =0.017(from table on page A-26)K =2.55CV =274L / D =150L =47.8feetIn the 1957 6th Printing edition, the problem is worded and resolved differently:Given:A 4-inch 600-pound conventional angle valve with no obstruction in flat seat.Find:The resistance coefficient K, flow coefficient Cv, and the equivalent lengths L / D and Lfor fully turbulent flow.Solution:K, L / D, and L should be given in terms of 4-inch Schedule 80 pipe;L/D =145(from L/D tables for valves)d =3.826inchesL =46K =2.4(from Nomograph for equivalent lengths and K)Cv =283


Example 4-4Example 4-4 (18th printing)Given:A 6 x 4-inch Class 600 steel gate valve with inlet and outlet ports conically tapered from back of bodyrings to valve ends. Face-to-face dimensions is 22" and back of seat ring to back of seat ring isabout 6".Find:K2 for any flow condition, and L / D and L for flow in the zone of complete turbulence.Solution:K, L/D, and L should be given in terms of 6-inch Schedule 80 pipe;When the resistance coefficient K is used in flow equations, the velocity and internal diameterdimensions used in the equation must be based on the dimensions of the basis Schedule numbersregardless of the pipe with which the valve may be installed.The values in the "K" Factor Table are associated with the internal diameter of the followingpipe schedule numbers for the various ANSI Classes of valves and fittings.Class 300 and lowerSchedule 40Class 400 and 600Schedule 80Class 900Schedule 120Class 1500Schedule 160Class 2500 (sizes 1/2 to 6")XXSClass 2500 (sizes 8" & up)Schedule 160K1 = 8 fT(from K Factor Table)d1 =3.826inchesd2 =5.761inchesfT =0.015b =0.66tan (q / 2) =0.1209= sin (q / 2) --approximatelyK2 =1.40L / D =93diameters of 6" Schedule 80 pipeL =45feet of 6" Schedule 80 pipeIn the 1957 6th Printing edition, the problem is worded differently:Given:A 6 x 4-inch 600-pound steel gate valve.Find:The valve resistance coefficient K, and the equivalent lengths L / D and L, for fully turbulent flowof Reynolds numbers indicated on the Moody Friction Factor diagram.Solution:K, L / D, and L should be given in terms of 6-inch Schedule 80 pipe;For venturi port gate valves:For 6-inch Schedule 80 pipe:d =5.761inchesD =0.4801feetd4 =1,101.5in4For 4-inch Schedule 80 pipe:d =3.826inchesd4 =214.28in4L/D =13This value is for a 4" constant diameter port gate valve(L/D)a =66.8This value is for 6" Schedule 80 pipefT =0.0151This is the fully turbulent friction factor for 6" Schedule 80 pipeas seen in the Moody chartThis is the definition of the resistance coefficient, KK =1.01This is based on the 6" Schedule 80 pipeL = (L/D) D =32.1feetThis equivalent pipe length is based on the 6" Schedule 80 pipe

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A22"5.761"6"3.826"

Example 4-5Example 4-5 (18th printing)Given:A globe type, lift check valve with a wing-guided disc is required in a 3-inch Schedule 40 horizontalpipe carrying 70 oF water at the rate of 80 gallons per minute.Find:The proper size check valve and the pressure drop. The valve should be sized so that the disc isfully lifted at the specified flow.Solution:For all practical purposes, it can be assumed that the pressure drop or head loss due to the flow offluids in the turbulent range through valves and fittings varies as the square of the velocity (DP = k v2 ).The minimum velocity required to lift a check valve's disc to the full-open and stable position has beendetermined by tests for numerous types of check and foot valves, and is given in the "K" Factor Table.It is expressed in terms of a constant times the square root of the specific volume of the fluid beinghandled, making it applicable for use with any fluid.(from K factor table)(the "continuity" equation)(From K Factor Table)(From K Factor Table)(Definition of the "Beta" ratio)d1 =2.469inches(for 2-1/2" Schedule 40 pipe)d2 =3.068inches(for 3" Schedule 40 pipe)0.01605ft3/lb(the specific volume of water at 70 oF)r =62.305lb/ft3(the density of water at 70 oF)fT =0.018(for fully turbulent flow in 2-1/2" or 3" pipe)Q =80gpmvmin =5.1ft/secv =3.5ft/sec(for the 3" check valve)Note that the mean flow velocity of the 3" check valve is less than the recommended.Try a smaller, 2-1/2" check valve instead.v =5.4ft/sec(for the 2-1/2" check valve)Based on the above, a 2-1/2" check valve is recommended to be installed in the 3" pipeusing concentric reducers.b =0.80(this is the Beta ratio between the check valve and the pipe)K2 is the value of the resistance coefficient in terms of the larger pipe size and is determined bybasically dividing K1 by b4.K2 =26DP =2.0psi(pressure drop of 80 gpm through the 2-1/2" check valve)In the 1957 6th Printing edition, the problem is worded differently:Given:A globe type, lift check valve with a wing-guided disc is required in a 3-inch Schedule 40 horizontalpipe carrying 70 oF water at the rate of 100 gallons per minute.Find:The proper size check valve and the pressure drop. The valve should be sized so that the disc isfully lifted under normal flow conditions; see page 2-7 for discussion and page A-30 for minimum flow.Solution:Solve the Darcy equation for the value of d4 :Calculate the Reynolds Number to determine the friction factor based on flow in the 3-inch pipe.Q =100gpmDP =2.0psiThis is the minimum pressure drop required across the globe lift check valve inorder to provide sufficient flow to lift the disc fully. This is given in page A-30.L/D =450This is the same as for a globe valve; also given in page A-30.r =62.305lb/ft3This is the density of water at 70 oF.d =3.068inchesThis is the ID of the 3-inch Schedule 40 pipe.m =0.975cPThis is the viscosity of the 70 oF water.Re =105,396This places the flow in the Transition Zone within the Moody Chart.f =0.021The friction factor taken from the Moody Chartd4 =53.0From the pipe tables, it is seen that the value of the d4 parameter for the 3-inch pipe is88.597while thatfor a 2-1/2 inch size similar check valve is37.161It is evident that for this flow condition the pressure drop through a wide-open valve is more than 2.0 psi for the2-1/2 inch size and less than 2.0 psi for the 3-inch size. Therefore, the 3-inch valve would not be fully lifted anda 2-1/2 inch size check valve should be used in this flow application.(L/D)b =450(da)4 =88.597(db)4 =37.161(L/D)a =1,073DP =2.85psi


Example 4-6Example 4-6 (18th printing)Given:Water at 60 oF is discharged from a tank with 22-feet of average head to the atmosphere through:QuantityItem200feet3" Schedule 40 pipe63" standard 90o threaded elbows13" flanged ball valve having a 2-3/8" diameter seat, 16oconical inlet, and 30o conical outlet end. Sharp-edgedentrance is flush with the inside of the tankFind:The water velocity in the pipe and the rate of discharge in gallons per minute.Solution:K =0.5(for pipe entrance at the tank)K =1.0(for pipe exit at the end)fT =0.018(for fully turbulent flow in 3" pipe)d1 =2.375inches(bore of the reduced port ball valve)d2 =3.068inches(inside diameter of the 3" pipe)For the K of a ball valve, the normal formula must be expanded in order to compensate for the differentinlet and outlet angles:b =0.77(Beta ratio of the valve's bore to the pipe ID)Sin q/2 =sin(16/2)=0.14(this sine value is for the valve's inlet half angle)Sin q/2 =sin(30/2)=0.26(this sine value is for the valve's outlet half angle)K1 =3 fT =0.054K2 =0.58(This is the K for the ball valve)K =30 fT =0.54(This is the K for one screwed elbow)K =3.24(This is the K for the 6 elbows)K =f (L./ D) =14.08(This is the K for the 200 feet of 3" straight pipe)The K for the system is composed of the Ks for the entrance, pipe, elbows, ball valve, and exit.K (total) =19.4v =8.5ft/sec(This is the mean velocity of the water in the 3" pipe)Q =197gpm(This is the water flowrate exiting the system)In order to verify that the assumption that the flow is in the fully turbulent zone,Reynolds Number =123.9 d v r / m =180,742(Reynolds number in the 3" pipe)From the Moody Chart, the corresponding f = 0.0195 and this is not in the fully turbulent zone.Although this flow is in the transition zone, the difference is small enough to forego any correctionof K for the pipe.The solution is valid from a practical point.

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Example 4-7Example 4-7 (18th printing)Given:S.A.E. 10 Lube Oil at 60 oF flows through the system described in Example 4-6 at the same differentialhead.Find:The oil velocity in the pipe and the rate of flow in gallons per minute.Solution:(Friction factor for laminar flow)K =0.5(for pipe entrance at the tank)K =1.0(for pipe exit at the end)K2 =0.58(This is the K for the ball valve as developed in Example 4-6)K =3.24(This is the K for the 6 elbows as developed in Example 4-6)r =54.64lb/ft3(oil density @ 60 oF)m =100cP(oil absolute viscosity @ 60 oF)hL =22ft of oil(static pressure head developed by oil)Note that the resistance coefficient K is considered as being independent of the Friction Factor or the ReynoldsNumber, and is treated as a constant for any valve or fitting under all condtions of flow (including laminar flow)regardless of the fluid handled.It is left to calculate the K for the 200 feet of 3" pipe and a velocity must be assumed in order to generate thepipe K. The velocity can be checked through trial-and-error methods until convergence is reached.Assumev =5.26ft/secRe =1,093(Flow is laminar)f =0.059(Friction factor for the 3" pipe)K =45.8(K for 3" pipe)K (total) =51.1(K for the entire system)v =5.26ft/sec(Oil mean velocity in 3" pipe -- this should equal the assumed value)Q =121gpm(Oil flowrate in the 3" pipe)

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A22'

Example 4-8Example 4-8 (18th printing)Given:S.A.E. 70 Lube Oil at 100 oF is flowing at the rate of 600 barrels per hour through 200 feet of 8-inchSchedule 40 pipe in which an 9-inch conventional globe valve with full bore is installed.Find:The pressure drop due to flow through the pipe and valve.Solution:S =0.916at 60 oF(Specific Gravity of the oil relative to water at 60 oF)S =0.900at 100 oF(Specific Gravity of the oil relative to water at 60 oF)B =600barrels/hrd =7.981inches(8" Schedule 40 pipe inside diameter)m =470cP(Oil viscosity at 100 oF)fT =0.014(Friction factor for fully turbulent flow in 8" pipe)r =56.13lb/ft3(Oil density at 100 oF)Re =318(Oil flow is very Laminar)f =0.20(Friction factor for the laminar flow in the 8" pipe)K1 =4.76(K factor for the full-bore 8" globe valve)K =60.55(K factor for the 200 feet of 8" pipe)K (Total) =65.31(Total K for the system)DP =2.87psi


Example 4-9Example 4-9 (18th printing)Given:S.A.E. 20 Lube Oil at 100 oF is flowing through 5-inch Schedule 40 pipe at a rate of 600 gallons perminute, as shown in the following sketch.Find:The velocity in feet per second and the pressure difference between gauges P1 and P2.Solution:(This is the pressure loss in the system due to flow)(This is the pressure loss in the system due to elevation change)d =5.047inchesS =0.916(Oil Specific Gravity @ 60 oF referenced to water @ 60 oF)S =0.900(Oil Specific Gravity @ 100 oF referenced to water @ 60 oF)m =470cP(Oil absolute viscosity @ 100 oF)r =56.1lb/ft3(Oil density @ 100 oF)fT =0.016(Friction factor for oil in fully turbulent flow)Q =600gpm(Oil flow rate)First, establish if the flow is laminar or turbulent.Re =723(This flow is Laminar)f = 64/Re =0.089(This is the fricition factor for the oil in laminar flow)This K is for the 5" gate valve and =0.13This K is for the 5" angle valve and =2.40This K is for the 5" elbow and is =0.32This K is for the 5" pipe and is =63.17The K for the entire system is the sum of the Ks =66.01v =9.6This is the oil mean velocity in the pipe.DP =37.0psi(This is Pressure drop due to flow)DP =19.5psi(This is Pressure drop due to elevation increase)DP (Total) =56.5psiThis is the total pressure drop between the gauges

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &AP2P1Flow75'50'175'5" Class 150 steel gate valve with full area seat - wide open.5" Class 150, steel angle valve with full area seat - wide open5" R5" weld elbow

Example 4-10Example 4-10 (18th printing)Given:600 psig steam at 850 oF flows through 400 feet of horizontal 6-inch Schedule 80 pipe at a rate of90,000 lb/hr.The system contains three 90o weld elbows having a relative radius of 1.5, one fully-open 6x4-inchClass 600 venturi gate valve as described in example 4-4, and one 6-inch Class 600 y-pattern globe .valve. The latter has a seat diameter equal to 0.9 of the inside diameter of Schedule 80 pipe, discfully liftedFind:The pressure drop through the system.Solution:(This is the K2 for the 6" globe valve)(This is the K1 for the 6" globe valve)b =0.90(This is the given Beta ratio for the 6" globe valve)(This is the K for each 6" welded elbow)(This is the K for the 6" pipe)W =90,000lb/hrd =5.761inches(This is the 6" Schedule 80 pipe ID)1.22ft3/lb(This is the Specific Volume of the superheated steam)m =0.026727cP(This is the viscosity of the superheated steam)fT =0.015(This the friction factor for the 6" pipe in fully turbulent flow)K1 =0.825(for Globe valve)K2 =1.41(for Globe valve)K2 =1.40(for Gate valve, as calculated in example 4-4)Re =3,688,279f =0.015(The pipe friction factor as found in the Moody Chart)K =12.5(for the 6" Schedule 80 pipe)K =0.63(for the 3 - 6" welded elbows)K (Total) =15.94(The total K for globe & gate valves, pipe, and elbows)DP =39.9psiThis is the pressure drop for the system


Comparison 4-10

Example 4-11Example 4-11 (18th printing)Given:Water at 180 oF is flowing through a flat heating coil, shown in the sketch below, at a rate of 15 gpm.Find:The pressure drop from Point A to Point B.Solution:(This is the radius of the pipe bends(This is the K for each of the two 90o bends(K for each 180o bend)r =60.569lb/ft3(Water density at 180 oF)m =0.34cP(Water viscosity at 180 oF)d =1.049inches(1" Schedule 40 pipe ID)fT =0.023(Friction factor for 1" pipe in fully turbulent flow)Q =15gpm(Hot water flow rate)Re =127,131This reveals that the water is in the transition zonef =0.024This is the pipe friction factor at the flowing conditionsK =4.94This is the K for the 18 feet of straight 1" pipeK =0.64This is the K for the 2 -90o bendsKB =3.89This is the K for the 7-180o bendsK(Total) =9.47This is the total K for the entire systemDP =1.92psiThis is the total system pressure dropArt's Note:This example problem doesn't mention whether the flat coil is in a horizontal or a vertical orientation.For practical purposes, it is very important to know the orientation, although the pressure drop willbe the same --- as long as the entire 1" pipe is 100% water filled.If the coil is vertically oriented, then air will initially be trapped at the top of the 4 - 180o returns.This air will create a 2-phase flow region at these sites and the pressure drop will increase. It isvery important in an actual, industrial application that the top of each of the 4 top 180o returns beinitially vented to the atmosphere and all air be expelled from there in order to ensure that thesystem is started up with 100% water-filled condtions. It is in this manner that the system can"recover" the energy spent in going vertically up 2 feet four times in the coil run. If the system is not100% water-filled, then total recovery of this energy cannot be done because of the air'scompressibility.

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &AAB1" Schedule 40 pipe1'1'2'4" Radius4" Radius4" Radius

Comparison 4-11

Example 4-12Example 4-12 (18th printing)Given:A 12-inch Schedule 40 steel pipe 60 feet long, containing a standard gate valve 10 feet from theentrance, discharges 60 oF water to atmosphere from a reservoir. The entrance projects inward intothe reservoir and its center line is 12 feet below the water level in the reservoir.Find:The diameter of a thin-plate orifice that must be centrally installed in the pipe to restrict the velocityof flow to 10 feet per second when the gate valve is wide open.Solution:K =0.78(K for pipe entrance)K =1.00(K for pipe exit)K1 =8 fT(K for the 12" gate valve)(K for the 12" pipe)(this is the relationship between an orifice K and its b ratio)v =10ft/secd =11.938inchesr =62.371lb/ft3m =1.12cPfT =0.013(This the friction factor for the 12" pipe in fully turbulent flow)hL =12.0ft(This is the system head; assume the reservoir's level to remain constant)Re =822,889flow is in the transition zonef =0.014The pipe's friction factor, using the Moody ChartK =7.73This is the system's K required for the desired velocity of 10 ft/sec.K1 =0.104This is gate valve's KK =0.84This is the 12" pipe's KK(Total) =2.728+ the orifice's KK(orifice)=5.00(This is the K of the orifice that satisfies the system's needs)From the graph on page A-20 showing C versus Reynolds Number at varying Beta values, an assumed Betayields a C with which the K(orifice) can be calculated. Trial-and-Error method is used as follows:At the Reynolds Number of 822,889, different values of Beta ratio are assumed.Assumed b valueC valueK0.700.704.33The assumed b is too large; use a smaller one0.650.677.21The assumed b is too small; use an intermediate0.670.6825.88This is close enough; use b = 0.68d1 =8.12inches(This is the bore diameter of the required orifice)

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &ARO12'60'30'10'

Example 4-13Example 4-13 (18th printing)Given:Fuel oil with a density of 0.815 grams per cubic centimeter and a kinematic viscosity of 2.7centistokes is flowing through 50 millimeter I.D. steel pipe, 30 meters long at a rate of 7.0 litersper second.Find:Head loss in meters of fluid and pressure drop in kg/cm2, bar, and megapascal (MPa)Solution:Define the symbols in SI units as follows:A =Pipe cross-sectional flow area, in meters2 =0.001963D =Pipe internal diameter, in meters =0.0500g =Acceleration of gravity =9.80665meters/sec2hL =head loss, in meters of fluidL =Pipe length, in meters =30q =flow rate, in meters3/sec =0.007v =mean fluid velocity =3.565meter/sec(mean velocity by the continuity equation)r =fluid density, in grams/centimeter3 =0.815DP(kpc) =fluid pressure drop, in kilograms/centimeter2DP(bar) =fluid pressure drop, in barsDP(MPa)=fluid pressure drop, in megapascals1.0meter =3.28feet =39.37inches1.0kg/cm2 =0.98067bar =14.22334psi1.0kg/cm3 =0.098067Mpascal =14.22334psiA column of fluid one square centimeter in cross-sectional area and one meter high is equal to a pressure of0.1 r kg/cm2; therefore:Re =7740 d v/ nwhere,d =1.9685inchesRe =65,986v =11.6934ft/secn =2.7centistokes (Kinematic viscosity)f =0.023(This is the friction factor from the Moody Chart)=8.94meters(This is the head loss through the 50 mm pipe)DP(kpc) =0.729kg/cm2DP(bar) =0.715barDP(MPa) =0.071MegaPascal


Example 4-14Example 4-14 (18th printing)Given:Water at 60 oF is flowing through the piping system, shown in the sketch below, at a rate of 400 gpm.Find:The velocity in both the 4 and 5-inch pipe sizes and the pressure differential between the pressuregauges P1 and P2.Solution:Use Daniel Bernoulli's theorem, which states:Assume that the hydraulic head of 75 feet has negligible effect on the water's density; therefore, r1 = r2 :(This is the K for the 4" pipe, in terms of the 5" pipe)(This is the K for the 5" 90o elbowThis is the K for the 4" x 5" expanding elbow & is thesum of a straight-sized elbow + a sudden enlargementr =62.371lb/ft3m =1.121cPd1 =4.026inchesd2 =5.047inchesQ =400gpmfT =0.016b =0.80(Z1 - Z2) =75feetv1 =10.08ft/sec(This is the mean velocity in the 4" pipe by the continuity equation)v2 =6.41ft/sec(This is the mean velocity in the 5" pipe by the continuity equation)(v22 - v21)/2g =-0.94feetRe =279,689(This is the Reynolds Number for the 4" pipe; it falls within the Transition Zone)Re =223,108(This is the Reynolds Number for the 5" pipe; it falls within the Transition Zone)f =0.018(This is the friction factor for both 4" and 5" pipe)K =9.6(This is the K for the 225 feet of 5" pipe)K =5.9(This is the K for the 110 feet of 4" pipe)K2 =14.6(This is the K for the 4" pipe in terms of the 5" pipe)K =0.22(This is the K for the 5" common elbow)K =0.55(This is the K for the 4" x 5" expander elbow)K (Total) =24.98This is the total K for the entire system of pipe & elbowshL =16.0feet of fluidDP =(P1 - P2) =39.0psi

&LArt Montemayor&RAugust 21, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &AP1P2Flow110'150'75'4" Schedule 40 pipe5" Schedule 40 pipe5" Schedule 40 pipe5"x4" Reducing weld elbowwith 7-1/2" radius5" weld elbow with 7-1/2" radius

Example 4-15Example 4-15 (18th printing)Given:Water at 70 oF is pumped through the piping system shown in the sketch at the rate of 100 gpm.Find:The total discharge head (H) at flowing conditions and the brake horsepower (bhp) required for a pumphaving an efficiency (eP) of 70 per cent.Solution:Use Daniel Bernoulli's theorem, which states:Assume that the hydraulic head of 400 feet has negligible effect on the water's density; therefore, r1 = r2.Since the mean velocity at the pump discharge is the same as at the outlet (v1 = v2), the equation is:The head loss through the 3" discharge pipe system due to flowThe Reynolds Number through the 3" pipe systemThe mean water velocity through the 3" pipe systemThe Brake Horsepower required to pump the water throughthe 3" pipe system and up to the 400 feet of elevation.K =30 fTThe K for 90o elbowsK1 =8 fTThe K for the gate valveK =f (L/D)The K for the 3" pipeK =1.00This is the K for the 3" pipe fluid exit lossd =3.068inchesThis is the ID of the 3" Schedule 40 piper =62.305lb/ft3This is the density of the 70 oF waterm =0.97cPThis is the absolute viscosity of 70 oF waterfT =0.018This is the friction factor for water in fully turbulent flow in the 3" pipeQ =100gpmv =4.33ft/secRe =105,294This Reynolds Number identifies the flow as in the Transition zone.f =0.021This is the 3" pipe's friction factor from the Moody ChartK =2.16This is the K for the four 90o elbowsK1 =0.14This is the K for the gate valveK =26.33This is the K for the Check Valve with reducers as per Example 4-5K =41.07This is the K for the 500 feet of 3" Schedule 40 pipeK (Total) =70.70This is the Total K for the system, including the exit KhL =21ft of waterThis is the head loss for the 3" pipe system due to flowH =421ft of waterThis is the head loss for the 3" pipe system including static headbhp =15.2This is the Pump's Brake Horsepower, assuming 70% efficiency.

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A30'70'100'3" Std. Gate Valve3" Schedule 40 pipeFour 3" Std. 90o threadedelbows300'2-1/2" Globe lift check valve with wing-guided disc & concentric reducers for 3" pipe.

Example 4-16Example 4-16 (18th printing)Given:Air at 65 psig and 110 oF is flowing through 75 feet of 1-inch Schedule 40 pipe at a rate of 100standard cubic feet per minute (scfm).(Standard Conditions are defined here as: 60 oF and 14.7 psia)Find:The pressure drop in psi and the velocity in ft/min at both upstream and downstream gauges.Solution:Refer to the Table for the Flow of Air through Schedule 40 steel pipe.DP =2.21psifor 100 psi, 60 oF air at a flow rate of 100 scfm through 100 ftof 1", Schedule 40 pipe.DP =2.61psiThis is the DP corrected for length, pressure, & temperature.q'm =100scfmThe air flow measured at Std. conditionsqm(1) =20.2acfmThe air flow measured at 65 psig & 110 oF (Upstream)qm(2) =20.9acfmThe air flow measured at (65 - 2.61) psig & 110 oF (Downstream)V =3,369ft/minMean air velocity at upstream conditionsV =3,483ft/minMean air velocity at downstream conditionsArt's Note:1.)Standard Conditions were not defined for this problem. This should be mandatory.2.)The 65 psig pressure is not defined as to location; it was assumed that this is the initial pressure.3.)Note that it is not mentioned that it is assumed that the temperature stays constant (Isothermal).4.)Since the pressure drop is less than 10% of the initial pressure, the conventional Darcy equationcould have been used to calculate the pressure drop:where,f =the friction factor for flow in the 1" pipeL =the 100 feet of 1" piper =the density of the air, lb/ft3, at the initial conditionsV =the mean air velocity at the initial conditionsd =the internal diameter of the 1" pipe.Note that the Reynolds Number would also have to be calculated to obtain f; this means that theviscosity of the air at the initial conditions would also have to be known.The density of air at standard conditions would have to be known in order to find the mass of airflowing. This mass air flow is constant, so the volumetric flow can be calculated using the densityvalues at the initial as well as at the final points.The air tables have already taken the air density into consideration and this is the reason they areuseful for calculating this type of problem.

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A

Example 4-17Example 4-17 (18th printing)Given:Crude oil with 30 degrees API at 15.6 oC with a viscosity of 75 Universal Saybolt seconds is beingpumped through a 12-inch Schedule 30 steel pipe at a rate of 1,900 barrels per hour. The pipe line is50 miles long with discharge at an elevation of 2,000 feet above the pump inlet. Assume the pumphas an efficiency of 67%.Find:The brake horsepower of the pump.Solution:t =15.6oC =60.1oFTemperature of the crude oil; it remains constantL =50miles =264,050ftr =54.65lb/ft3This is the degrees API converted to densityS =0.8762This is the density converted to Specific GravityB =1,900bbls/hr =1,330gpmd =12.090inchesm =14.2cPThis is the kinematic viscosity converted to absolute viscosityh =2,000feetThis is the height that the crude is elevated by the pumpRe =21,442This Reynolds Number identifies the flow as in the Transition Zone.f =0.025This is the friction factor as read from the Moody ChartDP =533psiThis is the oil's pressure drop over 50 miles of pipelinehL =1,406ftThis is the pressure drop converted to head lossH =3,406ftThis is the total head developed by the pump to pump the oil for50 miles and raise it to an elevation of 2,000 feet.The pump's Brake Horsepower =1,496


Example 4-18Example 4-18 (18th printing)Given:A 14-inch, Schedule 20, natural gas pipe line is 100 miles long. The inlet pressure is 1,300 psia, theoutlet pressure is 300 psia, and the average temperature is 40 oF. The gas analysis is 75% CH4,21% C2H6, and 4% C3H8.Find:The flowrate in millions of standard cubic feet per day (MMscfd).Solution:(Art's Note: First and foremost, note that the basis of the gas composition is totally lacking; this is agross error on the part of any engineer. Without a basis, this problem can't be solved. A mole %basis is therefore assumed. This is the same as a volumetric basis.)Three solutions to this example are presented for the purpose of illustrating the variations in resultsobtained by use of:1.the Simplified Compressible Flow forumula;2.the Weymouth formula; and,3.the Panhandle formula.Simplified Compressible Flow forumulad =13.376inches(the pipeline internal diameter)m =0.011cP(absolute viscosity estimated from gas graphs)f =0.0128(assumed friction factor for fully turbulent flow; from the Moody Chart)T =500oR(the absolute gas temperature)P'1 =1,300psia(initial pipeline pressure)P'2 =300psia(final pipeline pressure)Lm =100miles(pipeline length)Componentmolecular weightmole %MW x mole frac.CH4167512.00C2H630216.30C3H84441.76Mixture Molecular Weight =20.06The Specific Gravity of gases is defined as the ratio of the molecular weight of the gas to that of air.MW(air) =28.964Sg =0.693q'h =4,489,682scfh =107.8MMscfdRe =10,186,290This Reynolds Number identifies the flow as fully turbulentf =0.0128This friction factor is equal to that of the assumedSince the assumed friction factor is correct, the correct flow rate is that calculated. Note that if the assumedfriction factor were found to be incorrect, it would have necessary to repeat the exercise with a new assumptionuntil the assumed friction factor was in reasonable agreement with that based upon ithe calculated ReynoldsNumber.Weymouth formulaq'h =4,379,360scfh =105.1MMscfdPanhandle formulaE =0.92Assume a flow efficiency for average operation conditionsq'h =5,575,520scfh =133.8MMscfd


Example 4-19Example 4-19 (18th printing)Given:Water at 60 oF is flowing from a reservoir through the piping system below. The reservoir has aconstant head of 11.5 feet.Find:The flow rate in gallons per minute.Solution:K =0.5K for entrance lossK =60 fTK for the Mitre elbowK1 =8 fTK for the gate valveK =f (L/D)K for straight pipe runsThis is the K for the sudden contraction between the 3" and 2" pipesThis is K for the 2" pipe in terms of the 3" pipeK =1/b4This is the K for the exit from the 2" pipe in terms of the 3" pipehL =11.5ft of waterthe head above the water outletd1 =3.068inchesthe large pipe inside diameterd2 =2.067inchesthe smaller pipe inside diameterm =1.1211cPthe absolute viscosity of water at 60 oFr =62.371lb/ft3the density of water at 60 oFfT =0.018the friction factor for fully turbulent flow in the 3" pipefT =0.019the friction factor for fully turbulent flow in the 2" pipeb =0.67this is the Beta ratio between the two pipesK =0.50This K is for the water entering from the tank into the outletK =1.08This K is for the 3" mitered elbowK1 =0.14This K is for the 3" gate valveK =0.70This K is for the 10' of 3" pipeK =10.71This K is for the 20' of 2" pipe in terms of the 3" pipeK =4.85This K is for the 2" exit in terms of the 3" pipeK2 =1.33This K is for the sudden contraction from 3" to 2"K (Total) =19.31This is the Total K for the systemQ =143gpmThis solution has assumed the pipe flow is in the fully turbulent zoneand has used the corresponding fT to calculate the individual pipe Ks.In order to verify that the pipe flow is verily in the fully turbulent zone, the Reynolds Numbers must be calculatedand the corresponding friction factors found and compared with the fT used.Re =130,953This is the Reynolds Number for the 3" pipef =0.020This is the friction factor for flow in the 3" pipeRe =194,371This is the Reynolds Number for the 2" pipef =0.021This is the friction factor for flow in the 2" pipeThe friction factors used for the straight pipe are not in agreement with the fully turbulent flow values used inobtaining the approximate flow rate. Therefore, the K factors for the two pipes should be corrected accordingly:K =0.78This corrected K is for the 10' of 3" pipeK =11.83This corrected K is for the 20' of 2" pipe in terms of the 3" pipeK (Total) =20.52This is the corrected Total K for the systemQ =138gpmThis the correct solution.

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A10'd120'11.5'Water @ 60o F3" Sch 40 Pipe3" Std. gate valve; wide open2" Sch 40 Pipe

Example 4-20Example 4-20 (18th printing)Given:A header with 170 psia saturated steam is feeding a pulp stock digester through 30 feet of 2-inchSchedule 40 pipe which includes one standard 90 degree elbow and a fully-open conventionalplug type disc globe valve. The initial pressure in the digester is atmospheric.Find:The initial flow rate in pounds per hour, using both the modified Darcy formula and the sonicvelocity and continuity equations.Solution:Using the Modified Darcy FormulaK =0.5K for Entrance from headerK =30 fTK for 2", 90o ElbowK1 =340 fTK for 2" globe valveK =1.0K for exit from 2" pipe into digesterk =Cp/Cv =1.297Ratio of specific heats for saturated steam vapor; from tabular datad =2.067inchesInternal diameter of 2" pipeL =30ftStraight length of 2" pipe2.6748ft3/lbSpecific volume of saturated steam at 170 psiafT =0.019The friction factor for fully turbulent flow in the 2" pipeg =32.20ft/sec2The acceleration of gravityK =0.50This is the K for the header steam entering the 2" pipeK =0.57This is the K for the 2", 90o elbowK1 =6.46This is the K for the 2" globe valve, fully openedK =1.00This is the K for the steam exiting the 2" pipe and entering the digesterK =3.31This is the K for the 2" pipe (assumed @ fully turbulent flow)K (Total) =11.84This is the total K for the system (assuming fully turbulent flow)DP/P1 =0.914This is the ratio of the overall pressure drop to the initial pressureFrom tabular data, it is seen that the maximum DP/P1 for sonic flow to exist is 0.785 when the system K = 11.84.This means that, since this value is less than the calculated DP/P1, sonic ("choked") flow is taking placeat the end of the 2" pipe as it enters the digester. Therefore, the pressure drop for these flow conditions is:DP =133.5psiThis is the pressure drop that is fixed by the steam sonic flowY =0.710Y net expansion factor for adiabatic flow (isenthalpic expansion)and used to compensate for the changes in fluid properties due tofluid expansion.W =11,776lb/hrThis is the steam flow rate occurring at sonic conditions and isthe maximum mass flow rate that can occur under these pressureconditions.Using Sonic Velocity and Continuity EquationsThis is the sonic velocity for an expanded gasThis is the Continuity equationP'1 =170psiaThe initial saturated steam pressureDP =133.5psiThe pressure drop @ sonic conditions as developed abovehg =1,197.2btu/lbThe enthalpy of the saturated steam entering the 2" pipeP'2 =36.6psiaThis is the final (maximum) pressure that will yield sonic flow;constant, sonic flow will continue even though the final pressureis dropped to a lower value - such as 14.7 psia.The steam expansion that takes place across the globe valve is assumed to be adiabatic and, therefore, theenthalpy conditions are equal on both sides of the valve - DH = 0.0. Therefore,hg =1,197.2btu/lbThe enthalpy of the saturated steam exiting the 2" pipe;This is the same as the steam entering the pipe (DH = 0)The enthalpy of the saturated steam exiting the 2" pipe;12.425ft3/lbThis is the steam's specific volume at 36.6 psia and H= 1,197.2 but/lbThe resulting temperature = 317 oF and superheated.vS =1,653ft/secThis is the steam's sonic velocity 36.6 psia and 317 oFW =11,164lb/hrArt's Note:The problem asks for "the initial flow rate"; the DP has been calculated assuming that 36.6 psiais the downstream pressure when the initial downstream pressure will be, by definition, 14.7 psia.

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A20'Spherical Digester @ 14.7 psia10'

Example 4-21Example 4-21 (18th printing)Given:Coke oven gas with a specific gravity of 0.42, a header pressure of 125 psig, and a temperatureof 140 oF is flowing through 20 feet of 3-inch Schedule 40 pipe before discharging to atmosphere.Assume that the gas's ratio of specific heats, k = 1.4.Find:The flow rate in standard cubic feet per hour (scfh).Solution:P'1 =139.7psiaheader absolute pressuref = fT =0.0175The Reynolds Number is not necessary to identify f since the discharged gasto the atmosphere will have a very large Re, and flow will always be in thefully turbulent range, in which the friction factor is a horizontal line on theMoody Chart - and constant.d =3.068inchesthe discharge pipe IDSg =0.42the specific gravity of the gasT1 =600oRthe initial, absolute temperature of the gas in the header.L =20feetlength of 3" discharge pipeK =0.5This is the entrance loss KK =1.369This is the 3" pipe KK =1.0This is the K for the exit loss out of the 3" pipeK (Total) =2.87This is the K for the Total SystemDP/P'1 =0.895This is the ratio of the overall pressure drop to the initial pressureFrom tabular data, it is seen that the maximum DP/P1 for sonic flow to exist is 0.657 when the system K = 2.87.Since the indicated DP/P'1 is less than that calculated above, sonic velocity occurs at the end of the 3" pipeand the DP for the corresponding flow equation is:DP =91.8psiY =0.637Interpolated from the tabulated data for Yq'h =1,027,686scfhgas flow rate measured at 60 oF & 14.7 psiaSource:http://www.cheresources.com/indexzz.shtmlSonic Flow, Crane TP-410 example 4-21Taran BakerMy question concerns sonic gas flow from a pipe. Example 4-21 (pg 4-14) of CraneDec 1 2004TP-410 includes an exit loss when calculating the equivalent length of pipe. However, Istruggle to comprehend why this is required. If we are including an exit loss, aren't wesaying that the flow is choked not at the end of the pipe, but some distance from the pipedischarge? The reason I am asking is that I am trying to calculate the reaction force froma pipeline vent. As such, I require the choked pressure at the end of the vent pipe. Mygut feeling tells me that I shouldn't include an exit loss. Any assistance with this would bemost appreciated.rxnarangIn adibatic flow of gas through a conduit of constant cross section, the sonic velocity isalways reached at the end of the pipe. You are correct.However, there is always energy loss involved due to friction, including entrance andexit losses, which are a form of energy loss. All these energy losses influence the energyprofile of the fluid. Given that sonic velocity occurs at the end of the line, higher thelosses, lesser the amount of fluid flow. Hence, taking the exit losses into account isimportant, as it will influence the amount of fluid which can flow in the pipe.Crane Example 4-21 is correct in computing all the losses which occur.Hope this helps.Regards

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A125 psig

Example 4-22Example 4-22 (18th printing)Given:Air at a pressure of 19.3 psig and a temperature of 100 oF is measured at a point 10 feet fromthe outlet of a 1/2-inch Schedule 80 pipe discharging to atmosphere.Find:The air flow rate in standard cubic feet per minute (scfm).Solution:The modified Darcy flow equation for compensating for the changeof fluid properties due to free, adiabatic expansion of the fluid.P'1 =34.0psiaThe initial, absolute pressure in the 1/2" pipeDP =19.3psiThe pressure difference between the pipe initial pressure and atm.d =0.546inchesThe internal diameter of the 1/2" pipefT =0.0275The friction factor under fully turbulent flowL =10ftThe straight length of the 1/2" pipeT1 =560oRThe initial, absolute temperature of the air in the pipeK =6.04This is the K for the 10 feet of 1/2" pipeK =1.00This is the K for the pipe exit into the atmosphereK (Total) =7.04This is the Total K for the systemDP/P'1 =0.568This is the ratio of the overall pressure drop to the initial pressureY =0.76Y net expansion factor for adiabatic flow (isenthalpic expansion)and used to compensate for the changes in fluid properties due tofluid expansion.q'm =62.7scfmArt's Note:Note that fully turbulent flow is assumed to be occurring while the 1/2" pipe is venting to atmosphere.While this is more than probable, it hasn't been verified.Sub-sonic air flow is also assumed in this problem. This is another item that hasn't been verified.


Example 4-23Example 4-23 (18th printing)Given:A square-edged orifice with 2.0-inch diameter is installed in a 4-inch Schedule 40 pipe having amercury manometer connected between taps located 1 diameter upstream and 0.5 diameterdownstream.Find:a)The theoretical calibration constant for the meter when used on 60 oF water and forthe flow range where the orifice flow coefficient C is constant.b)The flow rate of 60 oF water when the mercury manometer difference is 4.4 inches.Solution:The flow equation for an orificeThe Reynolds numberThe differential pressure across the orifice tapsDhm =the differential head in inches of Mercury (Hg)The weight density of mercury under water =rW (SHg - SW)rW =62.371lb/ft3Density of water at 60 oFSHg =13.568Specific Gravity of Mercury at 60 oF, referred to Water at 60 oFSW =1.000Specific Gravity of Water at 60 oF, referred to Water at 60 oFrHg =783.88lb/ft3Density of Mercury underwaterDP =0.454Dhmthe differential pressure across the orifice tapsd1 =2.000inchesthe orifice diameterd2 =4.026inchesthe pipe's I.D.b =0.497The ratio of the orifice diameter to the I.D. of the pipeC =0.625Q =50.32(Dhm)^0.5This is the calibration constant and solution "a)".Q =106gpmm =1.1211cPthis is the viscosity of the 60 oF waterRe =73,800The calculated value of C = 0.625 corresponds to the calculated Reynolds Number of 73,800; therefore, theflow rate106gpm through the 4" pipe is verified as correct.(this is solution "b)" )Should the C factor prove to be incorrect for the Reynolds number based on the calculated flow, it must beadjusted by trial-and-error methodology until reasonable agreement is reached.

&LArt Montemayor&RSeptember 30, 2006Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &AFlow

Example 4-24Example 4-24 (18th printing)Given:SAE 10 Lube Oil at 90 oF is flowing through a 3-inch Schedule 40 pipe and produces 0.4 psipressure differential between the pipe taps of a 2.15-inch I.D. square-edged orifice.Find:The oil flow rate in gallons per minute (gpm).Solution:

Example 4-25Example 4-25 (18th printing)Given:A rectangular concrete overflow aqueduct, 25 feet high and 16.5 feet wide, has an absoluteroughness (e) of 0.01 foot. Refer to the sketch below.Find:The discharge rate in cubic feet per second when the liquid in the reservoir has reached themaximum height indicated in the sketch below. Assume the average water temperature is 60 oF.Solution:

Example 4-26Example 4-26 (18th printing)Given:A cast iron pipe is two-thirds full of steady, uniform flowing water at 60 oF. The pipe has an insidediameter of 24 inches and a slope of 3/4-inch per foot. Note the sketch below.Find:The water flow rate in gallons per minute (gpm).Solution:

Example 4-27Example 4-27 (18th printing)Given:A steam boiler operating at 300 psia has a maximum capacity of 100,000 pounds per hour ofsaturated steam.Find:The boiler capacity in both kilo Btu per hour and in boiler horsepower.Solution:

Example 4-28Example 4-6 in the 1957 (6th printing) versionGiven:A 600-pound steel in-line ball check valve is required in a 2-inch pipe line carrying 48 degree APIcrude oil at 150 oF and a rate of 37 gallons per minute.Find:The proper size check valve and the pressure drop with the valve installed in both vertical andhorizontal positions. The valve should be sized so that the disc is fully lifted under normal flowconditions.Solution:

Example 4-29Example 4-7 in the 1957 (6th printing) versionGiven:Bunker C fuel oil at 90 oF is flowing through a wide open 5-inch, 150-pound steel gate valve at arate of 400 gallons per minute; the face-to-face dimension of the valve is 10 inches.Find:The pressure drop through the valve.Solution:

Example 4-30Example 4-12 in the 1957 (6th printing) versionGiven:Saturated steam at 150 psig is flowing through a cylindrical pipe coil, as shown in the sketchbelow, at a rate of 2,000 pounds per hour. The coil is made of 2-inch Schedule 40 steel pipe.Find:The pressure drop from Point A to Point B.Solution:

3'30"AB

Moody Chart

Pipe TablesNominal Pipe Size InchesOutside DiameterWall ThicknessPipe Inside DiameterInside Diameter FunctionsTransverse Internal ("Flow") Area(in Inches)InchesInchesInchesFeetd2d3d4d5in2ft2May 8, 2003Commercial Wrought Steel Pipe DataAlthough pipe classification is common knowledge that is taken for granted among a lot of us old engineers, I haveSchedule Wall Thickness - Per ASA B36.10 - 1950found that young engineers are lacking this information because both academic professors and we experiencedengineers are both guilty of not passing on the information which used to be common and available when piping andSchedule 1014140.25013.5001.1250182.252,460.433,215.1448,403.3143.140.994fitting catalogs like Vogt, Tube Turns, Walworth, etc. used to be freely available to us. Now, these valuable free16160.25015.5001.2917240.253,723.957,720.1894,661.0188.691.310catalogs have become a thing of the past18180.25017.5001.4583306.255,359.493,789.11,641,308.6240.531.67020200.25019.5001.6250380.257,414.9144,590.12,819,506.2298.652.074Because I regard this subject as very basic and important for all engineers to dominate, some years back I prepared24240.25023.5001.9583552.2512,977.9304,980.17,167,031.5433.743.012the following explanation for young engineers working under me and with me in plant projects. I would like to share30300.31229.3762.4480862.9525,350.0744,681.621,875,767.4677.764.707it with any one else who hasn't had the opportunity to find out this logical explanation of how pipe is classified.Schedule 2088.6250.2508.1250.677166.02536.44,358.135,409.351.850.360Industrial pipe thicknesses follow a set formula, expressed as the schedule number as established by the1010.7500.25010.2500.8542105.061,076.911,038.1113,140.882.520.573American Standards Association (ASA) now re-organized as ANSI - the American National Standards Institute.1212.7500.25012.2501.0208150.061,838.322,518.8275,854.7117.860.818Eleven schedule numbers are available for use: 5, 10, 20, 30, 40, 60, 80, 100, 120, 140, & 160. The most popular14140.31213.3761.1147178.922,393.232,011.4428,184.9140.520.976schedule, by far, is 40. Sch 5, 60, 100, 120, & 140 have rarely, if ever been employed by myself in over 40 years16160.31215.3761.2813236.423,635.255,895.1859,442.6185.681.289as a practicing engineer. The schedule number is defined as the approximate value of the expression:18180.31217.3761.4480301.935,246.391,158.91,583,977.6237.131.64720200.37519.2501.6042370.567,133.3137,316.62,643,343.9291.042.021Schedule Number = (1,000)(P/S)24240.37523.2501.9375540.5612,568.1292,207.86,793,831.7424.562.948Where,30300.50029.0002.4167841.0024,389.0707,281.020,511,149.0660.524.587P = the internal working pressure, psigS = the allowable stress (psi) for the material of construction at the conditions of use.Schedule 3088.6250.2778.0710.672665.14525.84,243.434,248.151.160.3551010.7500.30710.1360.8447102.741,041.410,555.2106,987.580.690.560For example, the schedule number of ordinary steel pipe having an allowable stress of 10,000 psi for use at a1212.7500.33012.0901.0075146.171,767.221,365.1258,304.2114.800.797working pressure of 350 psig would be:14140.37513.2501.1042175.562,326.230,822.2408,394.0137.890.95816160.37515.2501.2708232.563,546.654,085.3824,801.1182.651.268Schedule Number = (1,000)(350/10,000) = 35 (approx. 40)18180.43817.1241.4270293.235,021.385,984.61,472,401.0230.301.59920200.50019.0001.5833361.006,859.0130,321.02,476,099.0283.531.969This would be the proper schedule for welded joints and steel fittings but not for threaded connections and cast-iron24240.56222.8761.9063523.3111,971.3273,854.86,264,702.3411.012.854or malleable-iron fittings. In practice, schedule 40 would be used for welded construction and Sch 80 (about 2x the30300.62528.7502.3958826.5623,763.7683,205.619,642,160.0649.184.508computed value) for iron fittings. The higher schedule is required because of weaknesses in the iron fittings and themetal lost in cutting the threads.Schedule 401/80.4050.0680.2690.02240.070.00.00.00.060.0001/40.5400.0880.3640.03030.130.00.00.00.100.001For all pipe sizes below 10", Sch 40 pipe is identical with what was once called standard pipe, and Sch 80 is3/80.6750.0910.4930.04110.240.10.10.00.190.001identical with the former extra-strong pipe. There is no equivalent schedule number for double-extra-strong1/20.8400.1090.6220.05180.390.20.10.10.300.002pipe, and Sch 160 is the only other weight in which pipe smaller than 4" is available.3/41.0500.1130.8240.06870.680.60.50.40.530.00411.3150.1331.0490.08741.101.21.21.30.860.006Temperature has no direct bearing on the schedule, except as it either weakens (or strengthens) the material's1 1/41.6600.1401.3800.11501.902.63.65.01.500.010allowable stress. Stainless steels (304ELC & 316ELC), for example, yield a stronger allowable stress at the low1 1/21.9000.1451.6100.13422.594.26.710.82.040.014temperatures near the cryogenic zone (-50 to -150 oF). Copper and Brass also exhibit the same behavior.22.3750.1542.0670.17234.278.818.337.73.360.023I've used the rule of thumb that the softer the metal, the stronger it is at the lower temperatures.2 1/22.8750.2032.4690.20586.1015.137.291.74.790.03333.5000.2163.0680.25579.4128.988.6271.87.390.051I hope this has helped you in explaining how pipe is classified.3 1/24.0000.2263.5480.295712.5944.7158.5562.29.890.06944.5000.2374.0260.335516.2165.3262.71,057.712.730.088Art Montemayor55.5630.2585.0470.420625.47128.6648.83,274.720.010.13966.6250.2806.0650.505436.78223.11,353.18,206.428.890.20188.6250.3227.9810.665163.70508.44,057.232,380.750.030.3471010.7500.36510.0200.8350100.401,006.010,080.2101,004.078.850.5481212.7500.40611.9380.9948142.521,701.420,310.8242,469.9111.930.77714140.43813.1241.0937172.242,260.529,666.4389,341.9135.280.93916160.50015.0001.2500225.003,375.050,625.0759,375.0176.711.22718180.56216.8761.4063284.804,806.381,110.71,368,823.9223.681.55320200.59318.8141.5678353.976,659.5125,292.42,357,250.3278.001.93124240.68722.6261.8855511.9411,583.1262,078.35,929,784.5402.072.792Schedule 6088.6250.4067.8130.651161.04476.93,726.229,113.147.940.3331010.7500.5009.7500.812595.06926.99,036.988,109.674.660.5181212.7500.56211.6260.9688135.161,571.418,269.3212,398.6106.160.73714140.59312.8141.0678164.202,104.026,961.2345,480.5128.960.89616160.65614.6881.2240215.743,168.846,542.6683,617.7169.441.17718180.75016.5001.3750272.254,492.174,120.11,222,981.0213.821.48520200.81218.3761.5313337.686,205.2114,026.02,095,342.0265.211.84224240.96822.0641.8387486.8210,741.2236,993.85,229,031.3382.352.655Schedule 801/80.4050.0950.2150.01790.04620.00990.00210.00050.0360.00031/40.5400.1190.3020.02520.09120.02750.00830.00250.0720.00053/80.6750.1260.4230.03530.17890.07570.03200.01350.1410.00101/20.8400.1470.5460.04550.29810.16280.08890.04850.2340.00163/41.0500.1540.7420.06180.55060.40850.30310.22490.4320.003011.3150.1790.9570.07980.91580.87650.83880.80270.7190.00501 1/41.6600.1911.2780.10651.63332.08732.66763.40921.2830.00891 1/21.9000.2001.5000.12502.25003.37505.06257.59381.7670.012322.3750.2181.9390.16163.75977.290114.135527.40872.9530.02052 1/22.8750.2762.3230.19365.396312.535729.120467.64664.2380.029433.5000.3002.9000.24178.410024.389070.7281205.11156.6050.04593 1/24.0000.3183.3640.280311.3238.069128.1430.88.8880.061744.5000.3373.8260.318814.6456.0214.3819.811.4970.079855.5630.3754.8130.401123.16111.5536.62,582.718.1940.126366.6250.4325.7610.480133.19191.21,101.56,345.826.070.181088.6250.5007.6250.635458.14443.33,380.325,775.045.660.31711010.7500.5939.5640.797091.47874.88,366.880,019.971.840.49891212.7500.68711.3760.9480129.411,472.216,747.8190,523.2101.640.705814140.75012.5001.0417156.251,953.124,414.1305,175.8122.720.852216160.84314.3141.1928204.892,932.841,980.2600,904.0160.921.11818180.93716.1261.3438260.054,193.567,624.91,090,519.1204.241.41820201.03117.9381.4948321.775,771.9103,537.11,857,248.9252.721.75524241.21821.5641.7970465.0110,027.4216,230.74,662,798.2365.212.536Schedule 10088.6250.5937.4390.619955.34411.73,062.422,781.043.460.3021010.7500.7189.3140.776166666786.750596807.9950511447525.665906355270094.052251792568.1337587720.47315110261212.7500.84311.0640.922122.4120961354.36743014414984.7212471132165790.95587806196.1422353760.667654412314140.93712.1261.0105147.0398761783.00553637621620.7251340954262172.912976041115.48484855660.80197811516161.03113.9381.1615194.2678442707.70520967237739.9952124083526020.053270548152.57760788481.059566721418181.15615.6881.3073333333246.1133443861.02614067260571.7780948623950250.0547522193.29696836521.342340058120201.28117.4381.4531666667304.0838445302.61407167292466.98418181631612439.27016251238.82689259641.658520087524241.53120.9381.7448333333438.3998449179.215933672192194.4232192244024166.83336412344.31843231132.3911002244Schedule 12044.5000.4383.6240.302013.1347.6172.5625.110.310.07255.5630.5004.5630.380320.8295.0433.51,978.116.350.11466.6250.5625.5010.458430.26166.5915.75,037.423.770.16588.6250.7187.1890.599151.68371.52,671.019,201.840.590.2821010.7500.8439.0640.755382.16744.76,749.661,178.664.530.4481212.7501.00010.7500.8958115.561,242.313,354.7143,562.990.760.63014141.09311.8140.9845139.571,648.919,480.0230,136.1109.620.76116161.21813.5641.1303183.982,495.533,849.4459,133.4144.501.00318181.37515.2501.2708232.563,546.654,085.3824,801.1182.651.26820201.50017.0001.4167289.004,913.083,521.01,419,857.0226.981.57624241.81220.3761.6980415.188,459.7172,375.63,512,324.7326.082.264Schedule 14088.6250.8127.0010.583449.01343.12,402.416,819.038.500.2671010.7501.0008.7500.729276.56669.95,861.851,290.960.130.4181212.7501.12510.5000.8750110.251,157.612,155.1127,628.286.590.60114141.25011.5000.9583132.251,520.917,490.1201,135.7103.870.72116161.43813.1241.0937172.242,260.529,666.4389,341.9135.280.93918181.56214.8761.2397221.303,292.048,971.6728,502.2173.801.20720201.75016.5001.3750272.254,492.174,120.11,222,981.0213.821.48524242.06219.8761.6563395.067,852.1156,068.83,102,022.5310.282.155Schedule 1601/20.8400.1870.4660.03880.220.10.00.00.170.0013/41.0500.2180.6140.05120.380.20.10.10.300.00211.3150.2500.8150.06790.660.50.40.40.520.0041 1/41.6600.2501.1600.09671.351.61.82.11.060.0071 1/21.9000.2811.3380.11151.792.43.24.31.410.01022.3750.3431.6890.14082.854.88.113.72.240.0162 1/22.8750.3752.1250.17714.529.620.443.33.550.02533.5000.4382.6240.21876.8918.147.4124.45.410.03844.5000.5313.4380.286511.8240.6139.7480.39.280.06455.5630.6254.3130.359418.6080.2346.01,492.414.610.10166.6250.7185.1890.432426.93139.7725.03,762.021.150.14788.6250.9066.8130.567846.42316.22,154.514,678.836.460.2531010.7501.1258.5000.708372.25614.15,220.144,370.556.750.3941212.7501.31210.1260.8438102.541,038.310,513.6106,460.880.530.55914141.40611.1880.9323125.171,400.415,667.9175,292.198.310.68316161.59312.8141.0678164.202,104.026,961.2345,480.5128.960.89618181.78114.4381.2032208.463,009.743,453.8627,386.5163.721.13720201.96816.0641.3387258.054,145.366,590.91,069,716.0202.671.40724242.34319.3141.6095373.037,204.7139,151.82,687,578.4292.982.035Standard Wall Pipe (Similar to Schedule 40)1/80.4050.0680.2690.02240.07240.01950.00520.00140.05680.00041/40.5400.0880.3640.03030.13250.04820.01760.00640.10410.00073/80.6750.0910.4930.04110.24300.11980.05910.02910.19090.00131/20.8400.1090.6220.05180.38690.24060.14970.09310.30390.00213/41.0500.1130.8240.06870.67900.55950.46100.37990.53330.003711.3150.1331.0490.08741.1001.1541.2111.2700.8640.00601 1/41.6600.1401.3800.11501.9042.6283.6275.0051.4960.01041 1/21.9000.1451.6100.13422.5924.1736.71910.8182.0360.014122.3750.1542.0670.17234.2728.83118.25437.7313.3560.02332 1/22.8750.2032.4690.20586.09615.05137.16191.7504.7880.033233.5000.2163.0680.25579.4128.988.6271.87.3930.05133 1/24.0000.2263.5480.295712.5944.7158.5562.29.8870.068744.5000.2374.0260.335516.2165.3262.71,057.712.7300.088455.5630.2585.0470.420625.47128.6648.83,274.720.0060.138966.6250.2806.0650.505436.78223.11,353.18,206.428.8900.200688.6250.2778.0710.672665.14525.84,243.434,248.151.1620.35538.625S0.3227.9810.665163.70508.44,057.232,380.750.0270.34741010.750.27910.1920.8493103.881,058.710,790.4109,975.881.5850.566610.750.30710.1360.8447102.741,041.410,555.2106,987.580.6910.560410.75S0.36510.0200.8350100.401,006.010,080.2101,004.078.8540.54761212.750.33012.0901.0075146.171,767.221,365.1258,304.2114.800.797212.75S0.37512.0001.0000144.001,728.020,736.0248,832.0113.100.7854Extra Strong Wall Pipe (Similar to Schedule 80)1/80.4050.0950.2150.01790.04620.00990.00210.00050.03630.00031/40.5400.1190.3020.02520.09120.02750.00830.00250.07160.00053/80.6750.1260.4230.03530.17890.07570.03200.01350.14050.00101/20.8400.1470.5460.04550.29810.16280.08890.04850.23410.00163/41.0500.1540.7420.06180.55060.40850.30310.22490.43240.003011.3150.1790.9570.07980.9160.8760.8390.8030.7190.00501 1/41.6600.1911.2780.10651.6332.0872.6683.4091.2830.00891 1/21.9000.2001.5000.12502.2503.3755.0637.5941.7670.012322.3750.2181.9390.16163.7607.29014.13627.4092.9530.02052 1/22.8750.2762.3230.19365.39612.53629.12067.6474.2380.029433.5000.3002.9000.24178.4124.470.7205.16.6050.04593 1/24.0000.3183.3640.280311.3238.1128.1430.88.8880.061744.5000.3373.8260.318814.6456.0214.3819.811.4970.079855.5630.3754.8130.401123.16111.5536.62,582.718.1940.126366.6250.4325.7610.480133.19191.21,101.56,345.826.0670.181088.6250.5007.6250.635458.14443.33,380.325,775.045.6640.31711010.750.5009.7500.812595.06926.99,036.988,109.674.6620.51851212.750.50011.7500.9792138.061,622.219,061.3223,969.7108.430.7530Double Extra Strong Wall Pipe (Similar to Schedules > 80)1/20.8400.2940.2520.02100.06350.01600.00400.00100.04990.00033/41.0500.3080.4340.03620.18840.08170.03550.01540.14790.001011.3150.3580.5990.04990.3590.2150.1290.0770.2820.00201 1/41.6600.3820.8960.07470.8030.7190.6450.5770.6310.00441 1/21.9000.4001.1000.09171.2101.3311.4641.6110.9500.006622.3750.4361.5030.12532.2593.3955.1037.6701.7740.01232 1/22.8750.5521.7710.14763.1365.5559.83717.4222.4630.017133.5000.6002.3000.19175.2912.228.064.44.1550.02893 1/24.0000.6362.7280.22737.4420.355.4151.15.8450.040644.5000.6743.1520.26279.9431.398.7311.17.8030.054255.5630.7504.0630.338616.5167.1272.51,107.212.9650.090066.6250.8644.8970.408123.98117.4575.12,816.118.8340.130888.6250.8756.8750.572947.27325.02,234.015,359.037.1220.2578Stainless Steel Pipe (Schedule 5S)1/20.8400.0650.7100.05920.50410.35790.25410.18040.39590.00273/41.0500.0650.9200.07670.84640.77870.71640.65910.66480.004611.3150.0651.1850.09881.4041.6641.9722.3371.1030.00771 1/41.6600.0651.5300.12752.3413.5825.4808.3841.8390.01281 1/21.9000.0651.7700.14753.1335.5459.81517.3732.4610.017122.3750.0652.2450.18715.04011.31525.40257.0273.9580.02752 1/22.8750.0832.7090.22587.33919.88053.856145.8975.7640.040033.5000.0833.3340.277811.1237.1123.6411.98.7300.06063 1/24.0000.0833.8340.319514.7056.4216.1828.411.5450.080244.5000.0834.3340.361218.7881.4352.81,529.114.7530.102455.5630.1095.3450.445428.57152.7816.24,362.522.4380.155866.6250.1096.4070.533941.05263.01,685.110,796.332.2400.223988.6250.1098.4070.700670.68594.24,995.341,995.755.5100.38551010.750.13410.4820.8735109.871,151.712,071.9126,537.986.2940.59931212.750.15612.4381.0365154.701,924.223,933.3297,682.1121.500.8438Stainless Steel Pipe (Schedule 10S)1/80.4050.0490.3070.02560.09420.02890.00890.00270.07400.00051/40.5400.0650.4100.03420.16810.06890.02830.01160.13200.00093/80.6750.0650.5450.04540.29700.16190.08820.04810.23330.00161/20.8400.0830.6740.05620.45430.30620.20640.13910.35680.00253/41.0500.0830.8840.07370.78150.69080.61070.53980.61380.004311.3150.1091.0970.09141.2031.3201.4481.5890.9450.00661 1/41.6600.1091.4420.12022.0792.9984.3246.2351.6330.01131 1/21.9000.1091.6820.14022.8294.7598.00413.4632.2220.015422.3750.1092.1570.17984.65310.03621.64746.6933.6540.02542 1/22.8750.1202.6350.21966.94318.29548.208127.0295.4530.037933.5000.1203.2600.271710.6334.6112.9368.28.3470.05803 1/24.0000.1203.7600.313314.1453.2199.9751.511.1040.077144.5000.1204.2600.355018.1577.3329.31,403.014.2530.099055.5630.1345.2950.441328.04148.5786.14,162.322.0200.152966.6250.1346.3570.529840.41256.91,633.110,381.531.7390.220488.6250.1488.3290.694169.37577.84,812.540,083.454.4850.37841010.750.16510.4200.8683108.581,131.411,788.8122,839.785.2760.59221212.750.18012.3901.0325153.511,902.023,566.0291,982.3120.570.8373Note:Stainless Steel Pipe Schedule 40S values are the same, size for size, as those shown above on theStandard Wall Pipe Table (heaviest weight on 8, 10, and 12-inch sizes).Stainless Steel Pipe Schedule 80S values are the same, size for size, as those shown above on theExtra Strong Pipe Table.

&LArt Montemayor&CU.S.A. Pipe Dimensions&RSeptember 30, 2003Rev: 0&CPage &P of &N&RFileName: &FWorkSheet: &A

Water PipesNominal Pipe Size:1/8 Inch1/4 Inch3/8 Inch1/2 Inch3/4 Inch1 Inch1-1/4 Inch1-1/2 Inch2 Inch3 Inch4 Inch6 Inch8 Inch10 Inch12 Inch14 Inch16 Inch18 Inch20 Inch24 Inch30 Inch36 Inch42 Inch48 Inch54 Inch60 Inch72 Inch84 InchSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeSchedule 40 Steel PipeAsphalt-Dipped Cast Iron PipeI. D. =36.0000inchesI. D. =42.0000inchesI. D. =48.0000inchesI. D. =54.0000inchesI. D. =60.0000inchesI. D. =72.0000inchesI. D. =84.0000inchesI. D. =0.2690inchesI. D. =0.3640inchesI. D. =0.4930inchesI. D. =0.6220inchesI. D. =0.8240inchesI. D. =1.0490inchesI. D. =1.3800inchesI. D. =1.6100inchesI. D. =2.0670inchesI. D. =3.0680inchesI. D. =3.0000inchesI. D. =4.0260inchesI. D. =4.0000inchesI. D. =6.0650inchesI. D. =6.0000inchesI. D. =7.9810inchesI. D. =8.0000inchesI. D. =10.0200inchesI. D. =10.0000inchesI. D. =11.9380inchesI. D. =12.0000inchesI. D. =13.1240inchesI. D. =14.0000inchesI. D. =15.0000inchesI. D. =16.0000inchesI. D. =16.8760inchesI. D. =18.0000inchesI. D. =18.8120inchesI. D. =20.0000inchesI. D. =22.6240inchesI. D. =24.0000inchesI. D. =29.0000inchesI. D. =30.0000inchesSteel PipeCast Iron PipeSteel PipeCast Iron PipeSteel PipeCast Iron PipeSteel PipeCast Iron PipeSteel PipeCast Iron PipeSteel PipeCast Iron PipeSteel PipeCast Iron Pipe(e/D) =0.006690(e/D) =0.004950(e/D) =0.003650(e/D) =0.002890(e/D) =0.002180(e/D) =0.001720(e/D) =0.001300(e/D) =0.001120(e/D) =0.000870(e/D) =0.000587(e/D) =0.001600(e/D) =0.000447(e/D) =0.001200(e/D) =0.000293(e/D) =0.000800(e/D) =0.000226(e/D) =0.000600(e/D) =0.000180(e/D) =0.000480(e/D) =0.000151(e/D) =0.000400(e/D) =0.000137(e/D) =0.000343(e/D) =0.000120(e/D) =0.000300(e/D) =0.000107(e/D) =0.000267(e/D) =0.000096(e/D) =0.000240(e/D) =0.000080(e/D) =0.000200(e/D) =0.000621(e/D) =0.000160e/d =0.0000500.000133e/d =0.0000430.000114e/d =0.0000380.000100e/d =0.0000330.000089e/d =0.0000300.000080e/d =0.0000250.000066e/d =0.0000210.000057Water FlowrateV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeV ft/secV2/2g fthf, ft per 100' pipehf, ft per 100' pipeCFSGPM0.00004460.020.1130.000200.2720.0620.000060.0340.000020.00008910.040.2260.000790.5430.1230.000240.0670.000070.00011140.050.2820.001240.1540.000370.2030.0840.000110.00013370.060.3390.001780.8150.1850.000530.1010.000160.00017820.080.4520.003171.0870.2470.000950.1340.000280.00022280.100.5650.004951.3590.3080.001480.4050.1680.000440.00026740.120.6770.007131.6300.3700.002130.2020.000630.00031190.140.7900.009711.9020.4320.002900.2350.000860.00035650.160.9030.012682.1740.4930.003780.2690.001120.00040100.181.0160.016052.4450.5550.004790.3030.001420.00044560.201.1290.019812.7170.6170.005910.8100.3360.00176Transition To Turbulent Flow0.0005570.251.4110.030960.7710.009231.0130.4200.002740.0006680.31.6940.044589.7Transition To Turbulent Flow0.5040.003950.0008910.42.2580.0792516.21.2330.023643.70.6720.007020.001110.52.8230.1238324.21.5420.036930.8400.010980.001340.63.3870.1783233.81.8500.053197.61.010.015811.740.001560.73.9520.2427144.82.1580.072391.180.021510.7390.00850.740.001780.84.5160.3170157.42.4660.0945512.71.340.028102.890.8450.01110.002010.95.0810.4012171.62.7750.119671.510.035560.9500.01400.002231.05.6450.4953387.03.0830.1477419.11.680.043904.301.060.01731.860.6020.005630.2600.3710.002140.1140.002671.26.7740.713271223.7000.2127426.72.020.063221.270.02500.7220.008100.4450.003080.003121.47.9030.970841644.3160.2895735.32.350.086051.480.03400.8420.011030.5200.004200.3000.001400.2210.00076Transition To Turbulent FlowTransition To Turbulent FlowTransition To Turbulent Flow0.003561.69.0321.268042124.9330.3782145.22.690.112401.690.04440.9630.01440.5940.005480.3430.001830.2520.000990.004011.810.1621.604862655.5500.4786756.43.030.142251.900.05611.0830.01820.6680.006940.3860.002320.2840.001250.004462.011.2911.981303246.1660.5909669.03.360.1756215.02.110.06934.781.200.02251.210.7420.008570.3790.4290.002860.1020.3150.001540.04920.1910.000570.01510.005572.57.7080.923371054.200.2744122.62.640.10837.161.500.03521.800.9280.013390.5360.004470.3940.002410.2390.000890.006683.09.2491.329651485.040.3951431.83.170.15610.01.800.05062.501.1140.019280.7720.6440.006440.2070.4730.003470.09880.2870.001280.0302Transition To Turbulent Flow0.00783.510.7911.809802005.880.5378342.63.700.21213.32.110.06893.301.2990.02620.7510.008760.5520.004730.3350.001740.00894.012.3322.363822596.720.7024854.94.220.27717.12.410.09004.211.480.03431.2950.8580.011440.3420.6300.006180.1640.3820.002270.04970.01004.513.8742.991713267.560.8890768.44.750.35121.32.710.1145.211.670.04340.9650.014480.7090.007820.4300.002880.06000.01115.015.4163.693473988.401.0976283.55.280.43325.83.010.1416.321.860.05351.931.0730.017880.5080.7880.009650.2420.4780.003550.07310.2170.000730.01120.2270.000800.01280.1260.000250.003100.1280.0002530.003250.01235.59.241.328121005.810.52430.93.310.1702.040.06481.1800.021630.8670.011680.5260.004300.09000.2390.000890.2500.000970.1390.000300.1400.000310.01346.010.081.580581186.340.62436.53.610.2038.872.230.07712.681.2870.02570.7040.9460.01390.3330.5740.005110.10040.2600.001050.2720.001150.1510.000360.1530.000360.01456.510.921.854981376.860.73242.43.910.2382.410.09051.3940.03021.0240.01630.6210.006000.1200.2820.001240.2950.001350.1640.000420.1660.000430.01567.011.772.151341587.390.84948.74.210.27611.82.600.10503.561.5020.03500.9301.1030.01890.4390.6690.006960.1310.3040.001430.3180.001570.1760.000480.1790.000500.01677.512.612.469651817.920.97555.54.510.3162.780.1201.6090.04021.1820.02170.7170.007990.1500.3250.001650.3400.001800.1890.000560.1910.000570.01788.013.452.809912058.451.10962.74.810.36015.02.970.1374.541.7160.04581.181.260.02470.5580.7650.009090.1660.3470.001870.3630.002050.2020.000630.2040.000650.01898.514.293.172132318.971.2570.35.110.4063.160.1551.8230.05171.340.02790.8130.010270.1900.3690.002120.3860.002310.2140.000710.2170.000730.02019.015.133.556292589.501.4078.35.410.45618.83.340.1735.651.9310.05791.461.420.03130.6890.8610.01150.2050.3910.002370.4080.002590.2270.000800.2300.000820.02129.515.973.9624128610.031.5686.95.720.5083.530.1932.0380.06451.500.03480.9080.01280.2300.4120.002640.4310.002890.2390.000890.2430.000910.02231016.814.3904931610.561.7395.96.020.56323.03.710.2146.862.1450.07151.771.580.03860.8290.9560.01420.2480.4340.002930.03720.4540.003200.04350.2520.000990.010170.2550.001010.010800.1110.0001920.001460.1130.0002000.001570.06410.0000640.0004010.06380.0000630.0003990.04070.0000260.0001380.04080.0000260.0001400.02451111.62.101156.620.68127.64.080.2592.3600.08651.730.04671.0520.01720.2900.4770.003540.4990.003870.2770.001190.2810.001230.1220.000230.1250.0002420.07050.0000770.07020.0000770.04480.0000310.04490.0000310.02671212.72.501367.220.81032.64.450.3089.622.5740.1032.481.890.05561.161.150.02050.3430.5210.004220.5450.004610.3020.001420.3060.001460.1330.000280.1360.0002880.07700.0000920.07660.0000910.04880.0000370.04900.0000370.02901313.72.931597.820.95137.84.830.3622.7890.1212.050.06521.240.02400.4000.5640.004950.5900.005410.3280.001670.3320.001710.1440.000320.1480.0003380.08340.0001080.08300.0001070.05290.0000430.05310.0000440.03121414.83.401838.421.10343.55.200.42012.83.0030.1403.282.210.07571.531.340.02780.4530.6080.005740.6350.006280.3530.001930.3570.001990.1550.000380.1590.0003920.08980.0001250.08940.0001240.05700.0000500.05720.0000510.03341515.83.902099.021.2749.75.570.4823.2180.1612.360.08691.430.03200.5100.6510.006590.07620.6810.007200.09000.3780.002220.3830.002280.1670.000430.1700.0004500.09620.0001440.09570.0001420.06100.0000580.06130.0000580.0356169.631.4456.35.940.54816.53.4320.1834.202.520.09881.961.530.03640.5780.6940.00750.7260.00820.4030.002530.4080.002590.1780.000490.1820.0005120.10260.0001640.10210.0001620.06510.0000660.06540.0000660.03791710.231.6363.16.310.6193.6470.2072.680.1121.630.04110.6400.7380.00850.7720.00930.4280.002850.4340.002930.1890.000550.1930.0005780.10900.0001850.10850.0001830.06920.0000740.06940.0000750.04011810.81.8270.36.680.69420.63.8610.2325.222.840.1252.421.720.04600.7170.7810.00950.8170.01040.4540.003200.4600.003280.2000.000620.2040.0006480.11540.0002070.11490.0002050.07320.0000830.07350.0000840.04231911.42.0378.07.050.7734.0760.2582.990.1391.820.05130.7900.8250.01060.8620.01160.4790.003560.4850.003660.2110.000690.2160.0007220.12190.0002310.12130.0002290.07730.0000930.07760.0000940.04462012.02.2586.17.420.85725.14.2900.2866.343.150.1542.941.910.05680.8680.8680.01170.1260.9080.01280.15100.5040.003950.03440.5110.004050.037000.2220.000770.004870.2270.0008000.005230.12830.0002560.0013200.12770.0002530.0013200.08140.0001030.0004510.08170.0001040.0004600.04902213.22.721048.171.03730.24.7190.3467.583.470.1873.522.100.06881.030.9550.01420.9990.01550.5540.004780.5620.004900.2440.000930.2500.0009690.14110.0003090.14040.0003060.08950.0001250.08990.0001260.05352414.43.241228.911.2335.65.1480.4128.923.780.2224.142.290.08181.201.0420.01691.0890.01840.6050.005690.6130.005840.2670.001100.2720.0011530.15390.0003680.15320.0003650.09760.0001480.09800.0001490.05792615.63.801439.651.4541.65.5770.48310.374.100.2614.812.490.09601.391.130.01981.180.02160.6550.006670.6640.006850.2890.001300.2950.0013530.16670.0004320.16600.0004280.10580.0001740.10620.0001750.06242816.84.4116410.391.6847.96.0060.56113.64.410.3035.512.680.1111.601.220.02301.270.02510.7060.007740.7150.007940.3110.001500.3180.0015690.17960.0005010.17870.0004960.11390.0002020.11440.0002030.06683018.05.0618711.11.9354.66.4350.64413.64.730.3476.262.870.1281.821.300.02630.2621.360.02880.3200.7560.008880.07020.7660.009120.07700.3330.001730.009880.3400.0018010.010700.19240.0005750.002660.19150.0005700.002690.12210.0002320.12250.0002330.07133211.92.1961.86.8640.73215.35.040.3957.073.060.1452.051.390.03001.450.03280.8060.010110.8170.010370.3550.001960.3630.0020490.20520.0006550.20420.0006480.13020.0002630.13070.0002660.07583412.62.4869.47.2930.82717.25.360.4467.923.250.1642.291.480.03381.540.03700.8570.011410.8680.011710.3780.002220.3860.0023130.21800.0007390.21700.0007320.13830.0002970.13890.0003000.08023613.42.7877.47.7220.92719.25.670.5008.823.440.1842.541.560.03791.630.04150.9070.012790.9190.013130.4000.002480.4080.0025940.23090.0008280.22980.0008210.14650.0003330.14710.0003360.08473814.13.0986.08.1511.03321.35.990.5579.783.630.2052.811.650.04231.720.04620.9580.014260.9700.014630.4220.002770.4310.0028900.24370.0009230.24250.0009140.15460.0003720.15520.0003750.08914014.83.4395.08.5801.1423.56.300.61810.793.820.2273.101.740.04680.4431.820.05120.5491.0080.015800.1181.0210.016210.1310.4440.003070.01640.4540.0032020.01790.25650.0010230.004420.25530.0010130.004470.16270.0004120.001490.16340.0004150.001540.09364215.63.78104.59.0091.2625.86.620.68111.84.020.2513.391.820.05161.910.05651.0590.017411.0720.017870.4660.003380.4770.0035300.26940.0011280.26810.0011170.17090.0004540.17160.0004580.09804416.34.151149.4381.3828.26.930.74712.94.210.2753.701.910.05672.000.06201.1090.019111.1230.019610.4890.003710.4990.0038740.28220.0012380.28080.0012260.17900.0004980.17970.0005020.10254617.14.531249.8671.5130.77.250.81714.04.400.3014.022.000.06192.090.06781.1590.020891.1740.021440.5110.004060.5220.0042350.29500.0013530.29360.0013400.18720.0005440.18790.0005490.10694817.84.9313510.2961.6533.37.560.88915.24.590.3274.352.080.06742.180.07381.2100.022751.2250.023340.5330.004420.5450.0046110.30780.0014730.30640.0014590.19530.0005930.19610.0005980.11145018.65.3514610.7251.7936.07.880.96516.44.780.3554.672.170.07320.6622.270.08000.8301.2600.024680.1761.2770.025330.1990.5550.004790.02440.5670.0050030.02680.32070.0015980.006520.31910.0015830.006640.20340.0006430.20420.0006480.1235520.46.4817611.7982.1643.28.671.1719.75.260.4305.592.390.08860.7892.500.09690.9931.3860.029861.4040.030650.6110.005800.6240.0060540.35270.0019340.35110.0019150.22380.0007780.22470.0007850.1346022.37.7120912.8702.5751.09.461.3923.25.740.5116.592.600.1050.9242.720.1151.1701.5120.035540.2451.5320.036470.2780.6660.006900.03370.6810.0072040.03740.38480.0023010.009040.38300.0022800.009200.24410.0009260.003040.24510.0009340.003150.1456524.19.0524513.9433.0259.610.241.6327.16.210.6007.692.820.1241.072.950.1351.361.6380.041711.6600.042800.7220.008100.7380.0084550.41690.0027010.41490.0026750.26450.0010870.26550.0010960.1567026.010.5028315.0153.5068.811.031.8931.36.690.6968.863.040.1431.223.180.1571.561.7640.048370.3251.7870.049640.3700.7770.009390.04450.7940.0098060.04960.44890.0031320.011900.44680.0031030.012100.28480.0012610.28590.0012710.1677527.812.032416.0884.0278.711.82.1735.87.170.79910.13.250.1651.393.400.1801.781.8900.055531.9150.056990.8330.010780.8510.0112570.48100.0035960.47870.0035620.30520.0014470.30640.0014590.1788029.713.736717.1604.5889.212.62.4740.57.650.90911.43.470.1871.573.630.2052.022.0160.063180.4152.0420.064840.4760.8880.012270.05640.9080.0128080.06350.51310.0040910.01510.51060.0040520.01540.32550.001650.005050.32680.0016600.005250.1898531.615.541318.2335.17100.213.42.7945.68.131.0312.83.690.2121.763.860.2312.282.1420.071332.1700.073200.9440.01380.9650.0144590.54510.0046190.54250.0045750.34580.001860.34720.0018740.2019033.417.346219.3055.7911214.23.1351.08.611.1514.23.910.2371.964.080.2592.552.2680.079960.5152.2980.082060.5940.9990.01550.06981.0210.0162100.07890.57720.0051780.01860.57450.0051290.01910.36620.002080.36760.0021010.2129535.319.351320.3786.4512415.03.4856.59.081.2815.84.120.2642.174.310.2892.822.3940.089092.4250.091431.0550.01731.0780.0180610.60930.0057690.60640.0057150.38650.002320.38810.0023410.22310037.121.456721.4507.1513815.83.8662.29.561.4217.44.340.2932.394.540.3203.102.5200.098720.6242.5530.101310.7251.1110.01920.08431.1350.0200120.09580.64130.0063930.02240.63830.0063320.02320.40690.002570.007470.40850.0025940.007830.2870.001280.003250.2840.001250.003200.24511023.5958.6516617.34.6774.510.521.7220.94.770.3542.864.990.3873.732.7720.119450.7442.8080.122590.8691.2220.02321.2480.0242150.70550.0077350.70210.0076620.44760.003110.44930.0031380.3150.001550.3120.001510.26712025.74010.319718.95.5688.311.52.0524.75.210.4223.375.450.4614.403.0240.142160.8773.0640.145891.031.3330.02760.1181.3620.0288180.1300.76960.0092050.03110.76590.0091180.03230.48820.003710.01030.49020.0037350.010580.3440.001840.004480.3400.001800.004450.29013027.88512.123020.56.5210312.42.4028.85.640.4953.925.900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Crane-Fluid-Flow-Problems.xls

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Transcript of Crane-Fluid-Flow-Problems.xls