Eat 259 (Chapter 2) Part 2

8/9/2019 Eat 259 (Chapter 2) Part 2

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EAT 259

HYDRAULICSCHAPTER 2 (PART 2)

SEPARATION LOSSES INPIPE FLOW


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2.3.1 Introd !t"on• Apart from head loss due to friction

occurring in pipe ow, head loss also due toow separation.

• The head loss due to this phenomenon is

called separation loss.• The separation losses can occur due to

many reasons, for example whenever thereare pipe ttings in the pipe. Pipe ttingscan include valves, bends junctions,sudden changes in cross section. Also, itcan occur at any pipe entry or pipe exit.


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2.3.1 Introd !t"on

• eparation losses are important insmall, complex pipe networ!s."owever, in a large pipe systems,they are negligible compared tofriction losses.

• Thus, sometimes the losses is alsocalled minor losses.


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E#$%&' o S &$r$t"on Lo** *


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2.3.2 R *"*t$nt Co +!" nt (,)•

#nergy losses are proportional to the velocityhead of the uid as it ows around an elbow,through an enlargement or contraction of theow section, or through a valve.

• #xperimental values for energy losses areusually reported in terms of a resistancecoe$cient K as follows%

• where h & is the minor loss, K is the resistancecoe$cient, and is the average velocity of owin the pipe in the vicinity where the minor loss


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2.3.2 R *"*t$nt Co +!" nt (,)•

The resistance coe$cient is dimensionlessbecause it represents a constant ofproportionality between the energy loss andthe velocity head.

• The magnitude of the resistance coe$cientdepends on the geometry of the device thatcauses the loss and sometimes on the velocityof ow.


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2.3.3 S dd n En'$r- % nt•

As a uid ows from a smaller pipe into a largerpipe through a sudden enlargement, itsvelocity abruptly decreases, causingturbulence, which generates an energy loss.

• 'ig (.)* shows the sudden enlargement.


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2.3.3 S dd n En'$r- % nt• 'ig (.)- shows the resistance coe$cient

sudden enlargement.


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2.3.3 S dd n En'$r- % nt• Table (./ shows the resistance coe$cient

sudden enlargement


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E#$%&' 2.12Determine the energy loss that will occur as 100 L/min ofwater flows through a sudden enlargement from a 1-incopper tube (Type K to a !-in tube (Type K "#i$en%

&or 1-in copper tube (Type KD ' )"! mm

!-in tube (Type KD ' *!"+ mm


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E#$%&' 2 12 (So' t"on),sing the subscript 1 for the section ust ahead of theenlargement and for the section downstream from theenlargement. we get


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E#$%&' 2 12 (So' t"on)To find a $alue for K . the diameter ratio is needed" efind that

&rom &ig" -1 . K ' 0"* " Then we ha$e

This result indicates that 0" 0 2m of energy is dissipatedfrom each newton of water that flows through thesudden enlargement"


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E#$%&' 2.13Determine the difference between the pressure ahead ofa sudden enlargement and the pressure downstreamfrom the enlargement" ,se the data from 34ample5roblem "1 "

&irst. we write the energy e6uation7


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E#$%&' 2.13 (So' t"on)8f the enlargement is hori9ontal. 9 : 9 1 ' 0" 3$en if itwere $ertical. the distance between points 1 and istypically so small that it is considered negligible" 2ow.calculating the $elocity in the larger pipe. we get


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E#$%&' 2.13 (So' t"on),sing ; '


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2.3./ 0r$d $' En'$r- % nt• 0f the transition from a smaller to a larger pipe

can be made less abrupt than the s+uare1edged sudden enlargement, the energy loss isreduced.

• This is normally done by placing a conicalsection between the two pipes as shown in 'ig.(.)2.


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2.3./ 0r$d $' En'$r- % nt• 'ig (.)3 shows the resistance coe$cient

gradual enlargement.


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2.3./ 0r$d $' En'$r- % nt• The energy loss for a gradual enlargement is

calculated from

• 4ata for various values are given below


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2.3./ 0r$d $' En'$r- % nt• The energy loss calculated from #+. (1)/ does

not include the loss due to friction at the wallsof the transition.

• 'or relatively steep cone angles, the length of

the transition is short and therefore the wallfriction loss is negligible.


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E#$%&' 2.1/Determine the energy loss that will occur as 100 L/min ofwater flows from a 1-in copper tube (Type K into a !-incopper tube (Type K through a gradual enlargementha$ing an included cone angle of !0 degrees"

&rom the pre$ious e4ample problems. we =now that


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E#$%&' 2.1/ (So' t"on)&rom &ig" "1+. we find that K ' 0" +" Then we ha$e

>ompared with the sudden enlargement described in34ample 5roblem "1 . the energy loss decreases by !!percent when !0 degrees the gradual enlargement isused"


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2.3.5 D" * r• Another term for an enlargement is a difuser .• The function of a di5user is to convert !inetic

energy 6represented by velocity head7 topressure energy 6represented by the pressure

head7 by decelerating the uid as it ows fromthe smaller to the larger pipe.

• The theoretical maximum pressure after theexpansion could be computed from ernoulli8se+uation,


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2.3. S dd n Contr$!t"on• The energy loss due to a sudden contraction,

such as that s!etched in 'ig. (.)2, is calculatedfrom

where v ( is the velocity in the small pipedownstream from the contraction.

• 'ig (.)3 shows the resistance coe$cientsudden contraction.• 'igure (.): illustrates what happens as the ow

stream converges. The lines in the gurerepresent the paths of various parts of the ow


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2.3. S dd n Contr$!t"on


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2.3. S dd n Contr$!t"on


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E#$%&' 2.15Determine the energy loss that will occur as 100 L/min ofwater flows from a !-in copper tube (Type K into a 1-incopper tube (Type K through a sudden contraction"

&rom 36" ( -1 . we ha$e

&or the copper tube.


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E#$%&' 2.15 (So' t"on)&rom &ig" "1+ we can find K ' 0" "

Then we ha$e


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2.3. 0r$d $' Contr$!t"on• The energy loss in a contraction can be

decreased substantially by ma!ing thecontraction more gradual.

• 'igure (.(; shows such a gradual contraction,

formed by a conical section between the twodiameters with sharp brea!s at the junctions.


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2.3. 0r$d $' Contr$!t"on• As the cone angle of the contraction decreases

below the resistance coe$cient actuallyincreases, as shown in 'ig. (.((.

• The reason is that the data include the e5ects

of both the local turbulence caused by owseparation and pipe friction.• 'or the smaller cone angles, the transition

between the two diameters is very long, whichincreases the friction losses.


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2.3. 0r$d $' Contr$!t"on


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2.3.4 Entr$n! Lo**• A special case of a contraction occurs when a

uid ows from a relatively large reservoir ortan! into a pipe.

• The uid must accelerate from a negligible

velocity to the ow velocity in the pipe.• The ease with which the acceleration is

accomplished determines the amount ofenergy loss, and therefore the value of theentrance resistance coe$cient is dependent onthe geometry of the entrance.

• 'igure (.(@ shows four di5erent con gurations

and the suggested value of K for each.


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2.3.4 Entr$n! Lo**


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2.3.4 Entr$n! Lo**• 0n summary, after selecting a value for the

resistance coe$cient from 'ig. (.(@, we cancalculate the energy loss at an entrance from

where v ( is the velocity of ow in the pipe.


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E#$%&' 2.1Determine the energy loss that will occur as 100 L /min of water flows from a

reser$oir into a 1-in copper tube (Type K (a through an inward-pro ecting tubeand (b through a well rounded inlet"

5art (a 7 &or the tube.

&or an inward-pro ecting entrance. K ' 1"0" Then we ha$e

&or well rounded entrance. K ' 0"0 " Then we ha$e


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2.3.9 E#"t Lo**

• As a uid ows from a pipe into a largereservoir or tan!, as shown in 'ig. (.(*, itsvelocity is decreased to very nearly 9ero.

• Therefore, the energy loss for this condition is

• This is called the exit loss .


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E#$%&' 2.1Determine the energy loss that will occur as 100 L/min ofwater flows from a 1-in copper tube (Type K into a largetan="

,sing 36" ( -1 . we ha$e

&rom the calculations in 34ample 5roblem "1 . we

=now that


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2.3.1 R *"*t$n! Co +!" nt* or6$'7 * 8 F"tt"n-*• alves are used to control the amount of ow

and may be globe valves, angle valves, gatevalves, butter y valves, any of several types ofchec! valves, and many more.

• Blobe alve Angle alve


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gate valve. Chec! valve

• utter y alve


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2.3.1 R *"*t$n! Co +!" nt* or 6$'7 * 8 F"tt"n-*

• 'ig (.(2 shows the pipe elbows.


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2.3.1 R *"*t$n! Co +!" nt* or 6$'7 * 8 F"tt"n-*

• ome system designers prefer to compute thee+uivalent length of pipe for a valve andcombine that value with the actual length ofpipe.

• #+uation 6(1)27 can be solved for & e

• Table (.2 shows the resistance in valves andttings expressed as e+uivalent length in pipediameters, Le D D.


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2.3.1 R *"*t$n! Co +!" nt* or 6$'7 * 8 F"tt"n-*


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E#$%&' 2.14

Determine the resistance coefficient K for a fully openglobe $al$e placed in a -in ?chedule 0 steel pipe"

&rom Table "* we find that the e6ui$alent-length ratiofor a fully open globe $al$e is ! 0" &rom Table "+ wefind f T ' 0"01 for a -in pipe"Then.


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E#$%&' 2.19

>alculate the pressure drop across a fully open globe$al$e placed in a -in ?chedule 0 steel pipe carrying0"0 ) m ! /s of oil (?"#" ' 0"+*

@ s=etch of the installation is shown in &ig" " +" Todetermine the pressure drop. the energy e6uationshould be written for the flow between points 1 and 7


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E#$%&' 2.19 (So' t"on)

The energy loss h L is the minor loss due to the $al$eonly" The pressure drop is the difference between p 1 andp " ?ol$ing the energy e6uation for this difference gi$es

Aut 9 1 ' 9 and $ 1 ' $ " Then we ha$e


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E#$%&' 2.19 (So' t"on)

&or the pipe.

&rom Table "+ we find f T ' 0"01* and for global $al$e.Le /D ' ! 0"


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E#$%&' 2.19 (So' t"on)

&or the oil.

Therefore. the pressure in the oil drops by !"< =5a as itflows through the $al$e" @lso. an energy loss of "+0 m

is dissipated as heat from each pound of oil that flowsthrough the $al$e"


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2.3.11 A&&'"!$t"on o St$nd$rd 6$'7 *

• The resistance is heavily dependent on thepath of the uid as it travels into, through, andout from the valve.

• A valve with a more constricted path will cause

more energy losses.• Therefore, select the valve type with care if youdesire the system you are designing to bee$cient with relatively low energy losses.


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2.3.11($) 0'o 6$'7

• 0t is one of the most common valves and isrelatively inexpensive.

• "owever, it is one of the poorest performingvalves in terms of energy loss.

• Eote that the resistance factor K is

• 0f the globe valve were used in a commercialpipeline system where throttling is not needed,it would be very wasteful of energy.


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d


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2.3.12 P"& : nd*

• 'igure (.(.: shows that the minimumresistance for a :;= bend occurs when the ratior>4 is approximately three.


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2.3.12 P"& : nd*

• 'ig (./; shows a :;= bend.


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2.3.12 P"& : nd*

• 0f


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E#$%&' 2.2

@ distribution system for li6uid propane is made from1" )in drawn steel tubing with a wall thic=ness of 0"0+!in" ?e$eral .compute the energy loss to each bend"


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E#$%&' 2.2 (So' t"on)

The radius r must be computed from

where D o ' !1"*)mm. the outside diameter of the tubeas found from @ppendi4 #">ompletion of the calculation gi$es


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E#$%&' 2.2 (So' t"on)

e now must compute the $elocity to complete thee$aluation of the energy loss from DarcyCs e6uation7

The relati$e roughness is

E#$%&' 2 2 (S ' " )


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E#$%&' 2.2 (So' t"on)

Then. we can find f T ' 0"010+ from the oody diagramin the 9one of complete turbulence" Then

2ow the energy loss can be computed7

Eat 259 (Chapter 2) Part 2

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