ce 6451 fluid mechanics

7/23/2019 CE 6451 Fluid Mechanics

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RAJALAKSHMI ENGINEERING COLLEGE

DEPARTMENT OF AUTOMOBILE ENGINEERING

QUESTIONBANK

WITH ANSWERSSUB CODE/NAME: CE 6451/FLUID MECHANICS & MACHINERIES

YEAR/SEM: II/ IIIUNIT I

1! D"#$" %'()*!Fluid may be defned as a substance which is capable o lowing. It has nodefnite shape o its own, but conirms to the shape o the containing vessel.+! W,-. -" .," 00".("* % ()"- %'()2Ideal luids have ollowing propertiesi) It is incompressibleii) It has zero viscosity iii) Shear orce is zero3! W,-. -" .," 00".("* % "- '()2Real uids have ollowing propertiesi) It is compressibleii) !hey are viscous in natureiii) Shear orce e"ists always in such uids.4! D"#$" )"$*(. -$) *0"(%( 7"(8,.!#ensity is defned as mass per unit volume $%g&m

')

Specifc weight is deined as weight possessed per unit volume$(&m

')

5! D"#$" S0"(%( 9'" -$) S0"(# G-9(.!

Specifc volume is defned as volume o uid occupied by unit mass $m'

&%g)Specifc gravity is defned as the ratio o specifc weight o uid to thespecifc weight o standard luid.6! D"#$" S'%-" ."$*($ -$) C-0(-(.!

Surace tension is due to the orce o cohesion between the liuid particles at

the ree surace.*apillary is a phenomenon o rise or all o liuid surace relative to thead+acent general level o liuid.;! D"#$" <(**(.!

It is defned as the property o a liuid due to which it oers resistance to themovement o one layer o liuid over another ad+acent layer.=! D"#$" >($"-.( 9(**(.!It is deined as the ratio o dynamic viscosity to mass density. $m&sec?! D"#$" R"-.(9" S0"(# 9(**(.!

It is the ratio o dynamic viscosity o uid to dynamic viscosity o water at-/*.1@! D"#$" C0"**(((.!

It is the property by virtue o which uids undergoes a change in volume underthe action o e"ternal pressure.11! D"#$" N"7.$(-$ -7 % <(**(.!

0ccording to (ewton1s law o viscosity the shear orce F acting between twolayers o uid is proportional to the dierence in their velocities du and area 0o the plate and inversely proportional to the distance between them.1+! W,-. (* ,"*($ -$) -),"*($ ($ '()*2

*ohesion is due to the orce o attraction between the molecules o the sameliuid.

0dhesion is due to the orce o attraction between the molecules o twodierent liuids or between the molecules o the liuid and molecules o the

solid boundary surace.13! S.-." "$.' % "$.' "'-.($2



It states that the resulting torue acting on a rotating luid is eual to the rateo change o moment o momentum14! W,-. (* "$.' "'-.($2

It is based on the law o conservation o momentum or on the momentumprinciple It states that,the net orce acting on a uid mass is eual to thechange in momentum o ow per unit time in that direction

UNITII

1! M"$.($ .," 8"$"- ,--."(*.(* % -($- %7!

a) !here is a shear stress between uid layers

b) 2(o slip1 at the boundaryc) !he low is rotationald) !here is a continuous dissipation o energy due to viscous shear

+! W,-. (* H-8"$ 0(*"'("* %'- 2

3453- & pg 6 h 6 '- 789 & g#-

!he e"pression is %nown as :agen poiseuille1s ormula .

;here 3453- & <g 6 9oss o pressure head 8 6 0verage velocity7 6 *oeicient o viscosity # 6 #iameter o pipe9 6 9ength o pipe3! W,-. -" .," %-.* ($%'"$($8 .," %(.($- ** ($ 0(0" 7 Frictional resistance or the turbulent low isi. 3roportional to vn where v varies rom 4.= to -. .ii. 3roportional to the density o uid .iii. 3roportional to the area o surace in contact .iv. Independent o pressure .v. #epend on the nature o the surace in contact .4! W,-. (* .," "0"**($ % ,"-) ** )'" . %(.($ ($ D- %'-2

h 6 >9?& -g#;here 6 *oeicient o riction in 9 6 9ength o the

# 6 #iameter o pipe ? 6 velocity o the

5! W,-. ) ' '$)"*.-$) .," ."* - - "$"8 **"* ($ "$"8 **"*@a+or energy losses A 5

!his loss due to riction and it is calculated by #arcy weisbach ormula andchezy1s ormula .@inor energy losses A5 !his isdue toi. Sudden e"pansion in pipe . ii. Sudden contraction in pipe . iii.Bend in pipe . iv. #ue to obstruction in pipe .6 ! G(9" -$ "0"**($ % ** % ,"-) )'" . *'))"$ "$-8""$. %.," 0(0" :

he 6 $?45?-)&-;here he 6 9oss o head due to sudden enlargement o pipe.?4 6 ?elocity o low at section 454?- 6 ?elocity o low at section -5-

;! G(9" -$ "0"**($ % ** % ,"-) )'" . *'))"$$.-.($ :

hc 6.= ?-

&-g;here , hc 6 9oss o head due to sudden contraction .? 6 ?elocity at outlet o pipe=! G(9" -$ "0"**($ % ** % ,"-) -. .," "$.-$" % .," 0(0"5 hi 6.=?-&-g

where hi 6 9oss o head at entrance o pipe .

? 6 ?elocity o liuid at inlet and outlet o the pipe .



?! D"#$" .," ."* - H)-'( 8-)("$. ($" HGL T.- E$"8($" TELa) :ydraulic gradient line A5:ydraulic gradient line is deined as the line which gives the sum o pressurehead and datum head o a lowing luid in apipe with respect the reerence line.b) !otal energy line A5

!otal energy line is defned as the line which gives the sum o pressure head, datum head and %inetic head o a owing luid in a pipe with respect tosome reerence line .1@! W,-. (* *0$ 2 7,"" (. (* '*") :

Sypon is along bend pipe which is used to transer liuid rom a reservoirat a higher elevation to another reservoir at a lower level .8ses o sypon A 54. !o carry water rom one reservoir to another reservoir separated by ahill ridge.-. !o empty a channel not provided with any outlet sluice .11! W,-. -" .," -*( ")'-.($* . *9" .," 0"* ($ 7.,'8, -$,") 0(0"*2i. *ontinuity euation . ii. Bernoulli1s ormula .iii. #arcy weisbach euation .1+! W,-. (* D'0'(.* "'-.($ 2

94&d4=

C9-&d-=

C9'&d'=

6 9 & d=

;here94, d4 6 9ength and diameter o the pipe 49-, d- 6 9ength and diameter o the pipe -9', d' 6 9ength and diameter o the pipe

UNIT III

1! W,-. -" .," .0"* % '() 72

Steady D unsteady luid low8niorm D (on5uniorm lowEne dimensional, two5dimensional D three5dimensional owsRotational D Irrotational ow

+! N-" .," )(%%""$. %"* 0"*"$. ($ '() 7Inertia orce?iscous orceSurace tension orceravity orce3! W,"$ ($ - %'() $*()"") *."-)2

In steady low, various characteristics o ollowing luids such as velocity,pressure, density, temperature etc at a point do not change with time. So itis called steady ow.

4! G(9" .," E'"* "'-.($ % .($2$dp&p)CgdzCvdv65! W,-. -" .," -**'0.($* -)" ($ )"(9($8 B"$'(* "'-.($24.!he luid is ideal-.!he low is steady.'.!he low is incompressible.>.!he low is irrotational.6! W,-. (* B"$'(* "'-.($ % "- '()2$p4&pg)C$v4-&-g)Cz46$p-&pg)C$v--&-g)Cz-Chlwhere hl is the loss o energy $p&pg)53ressure energy. $v-&-g)6Ginetic energy. z5#atum energy.;! S.-." .," -00(-.($ % B"$'(* "'-.($ 2



It has the application on the ollowing measuring devices.4.Erifce meter.-.?enturimeter.'.3itot tube.=! S.-." .," ".,)* % )("$*($- -$-*(*!4. Rayleigh1s method-. Buc%ingham1s H theorem?! S.-." B'>($8,-* .,""

It states that i there are 2n1 variables in a dimensionally homogeneouseuationand i these variables contain 2m1 undamental dimensions $@,9,!), then theyare grouped into $n5m), dimensionless independent H5terms.1@! S.-." .," ((.-.($* % )("$*($- -$-*(*!

4. #imensional analysis does not give any due regarding theselection o variables. -.!he complete inormation is not provided bydimensional analysis.

'.!he values o coeicient and the nature o unction can be obtained onlyby e"periments or rom mathematical analysis.11! D"#$" S(((.')"

Similitude is defned as the complete similarity between the model

and prototype.1+! S.-." F')"* )" -7

Enly ravitational orce is more predominant orce. !he law states 2!heFroude1s number is same or both model and prototype1

UNITI<1! W,-. (* "-$. P'02

0 pump is device which converts mechanical energy into hydraulicenergy.

+! M"$.($ -($ 0$"$.* % C"$.(%'8- 0'0!

i) Impeller ii) *asingiii) Suction pipe,strainer D Foot valve iv) #elivery pipe D #elivery valve3! W,-. (* "-$. P(($82

!he delivery valve is closed and the suction pipe, casing and portion o thedelivery pipe upto delivery valve are completely illed with the liuid so thatno air poc%et is let. !his is called as priming.4! D"#$" M-$".( ,"-)!It is the head against which a centriugal pump wor%.5! D"#$" M",-$(- "%#("$!It is deined as the ratio o the power actually delivered by the impeller to thepower supplied to the shat.;! D"#$" 9"- "%#("$!It is the ratio o power output o the pump to the power input to the pump.?! D"#$" *0"") -.( 7 -.(!

Speed ratioA It is the ratio o peripheral speed at outlet to the theoreticalvelocity o +et corresponding to manometric head.Flow ratioA It is the ratio o the velocity o low at e"it to the theoreticalvelocity o +et corresponding to manometric head.1@! M"$.($ -($ 0$"$.* % R"(0-.($8 0'0!4. 3iston or 3lunger-. Suction and delivery pipe '. *ran% and *onnecting rod11! D"#$" S(0 % "(0-.($8 0'0! W,"$ .," $"8-.(9" *(0 )"*'2

!he dierence between the theoretical discharge and actual discharge iscalled slip o the pump.



But in sometimes actual discharge may be higher then theoretical discharge, insuch acase coeicient o discharge is greater then unity and the slip will benegative called as negative slip.1+! W,-. (* ($)(-. )(-8-2

Indicator diagram is nothing but a graph plotted between the pressure headin the cylinder and the distance traveled by the piston rom inner dead centeror one complete revolution o the cran%.13! W,-. (* "-$. C-9(.-.($*2

It is defned phenomenon o ormation o vapor bubbles o a owing liuid in a

region where the pressure o the liuid alls below its vapor pressure and thesudden collapsing o theses vapor bubbles in a region o high pressure.14! W,-. -" .- 0'0*2

Rotary pumps resemble li%e a centriugal pumps in appearance. But thewor%ing method diers. 8niorm discharge and positive displacement can beobtained by using these rotary pumps, It has the combined advantages o bothcentriugal and reciprocating pumps.

UNIT<1! D"#$" ,)-'( -,($"*!

:ydraulic machines which convert the energy o lowing water into mechanicalenergy+! G(9" "-0" % - 7 ,"-) ")(' ,"-) -$) ,(8, ,"-) .'($"!

9ow head turbine Gaplan turbine@edium head turbine @odern Francis turbine:igh head turbine 3elton wheel3! W,-. (* (0'*" .'($"2 G(9" "-0"!In impulse turbine all the energy converted into %inetic energy. From these theturbine will develop high %inetic energy power. !his turbine is called impulseturbine. J"ampleA 3elton turbine4! W,-. (* "-.($ .'($"2 G(9" "-0"!In a reaction turbine, the runner utilizes both potential and %inetic energies.:ere portion o potential energy is converted into %inetic energy beoreentering into the turbine. J"ampleA Francis and Gaplan turbine.5! W,-. (* -(- 7 .'($"2

In a"ial ow turbine water lows parallel to the a"is o the turbine shat.J"ampleA Gaplan turbine6! W,-. (* (") 7 .'($"2In mi"ed ow water enters the blades radially and comes out a"ially, parallelto the turbine shat. J"ampleA @odern Francis turbine.;! W,-. (* .," %'$.($ % *0"- -$) $"2

!he nozzle is used to convert whole hydraulic energy into %inetic energy. !husthe nozzle delivers high speed +et. !o regulate the water low through thenozzle and to obtain a good +et o water spear or nozzle is arranged.=! D"#$" 8** ,"-) -$) $". "%%".(9" ,"-)!ross :eadA !he gross head is the dierence between the water level at thereservoir and the level at the tailstoc%.

Jective :eadA !he head available at the inlet o the turbine.?! D"#$" ,)-'( "%#("$!It is deined as the ratio o power developed by the runner to the powersupplied by the water +et.1@! D"#$" ",-$(- "%#("$!It is deined as the ratio o power available at the turbine shat to thepower developed by the turbine runner.11! D"#$" 9'".( "%%(("$!It is deied as the volume o water actually stri%ing the buc%ets to the totalwater supplied by the +et.1+! D"#$" 9" - "%#("$!It is deined as the ratio o power available at the turbine shat to the

power available rom the water +et



PART B QUESTIONS4.$i) #efne the term 2boundary layer1. $ii) #efne 2minor losses1. :ow they are diKerent rom ma+or lossesL $iii) !he discharge o water through a horizontal pipe is .-=m'&s. !hediameter o above pipe which is - mm suddenly enlarges to > mm at apoint. I the pressure o water in the smaller diameter o pipe is 4- %(&m -,determineA loss o head due to sudden enlargementM pressure o water in thelarger pipe and the power lost due to sudden enlargement.

-. $i) ;hat is meant by critical Reynolds number $ii) Ebtain a relationship between shear stress and pressure gradient.'. #erive :agen5poiseuille1s euation state the assumptions made.> .#erive an e"pression or head loss through pipes due to riction=. J"plain the losses o energy in ow through pipes.N. #etermine the euivalent pipe corresponding to ' pipes in series with lengthsand diameters 94,9-,9',d4,d-,d' respectively.O. For a ow o viscous uid owing through a circular pipe under laminar owconditions show that the velocity distribution is a parabola. 0nd also show thatthe average velocity is hal o the ma"imum velocity.

P.0 horizontal pipe line > m long is connected to a water tan% at one end anddischarges reely into the atmosphere at the other end. For the frst -= m o itslength rom the tan%, the pipe is 4= mm diameter and its diameter is suddenlyenlarged to ' mm. !he height o water level in the tan% is P m above thecentre o the pipe. *onsidering all losses o head which occur, determine therate o ow. !a%e f 6 .4 or both sections o the pipe.Q.$i) Ebtain e"pression or #arcy5;eisbach riction actor or ow in a pipe. $ii) 0 smooth pipe carries .' m'&s o water discharge with a head loss o '.m per 4m length o pipe. I the water temperature is -*, determine thediameter o the pipe.4. 0 4= mm diameter pipe reduces in diameter abruptly to 4 mm diameter.I the pipe carries water at ' liters per second. *alculate the pressure lossacross the contraction. !a%e coecient o contraction as .N.44$a) !he space between two suare at parallel plate is flled with oil.Jach side o the plate is Nmm.!he thic%ness o the oil flms is4-.=mm.!he upper plate, which moves at -.=m&s reuires a orce o QP.4(to maintain the speed. #etermine

$i) !he dynamic viscosity o the oil in poises$ii) !he %inematic viscosity o the oil in stro%es i the specifc gravity othe oil is .Q=.

4-$a). $i) #erive an e"pression or the capillary rise at the liuid in a capillarytube o radius r having surace tension and contact angle. I the plates are oglass, what will be the capillary rise o water having suracetension6.O'(&m and angle .!a%e r64 mm

$ii) 0 pipe o 'cm diameter carrying .-=m'&s water. !he pipe is bent by 4'= rom the horizontal anti5cloc%wise. !he pressure o water owing through thepipe is >G(.Find the magnitude and direction o the resultant orce on thebend.4'$a)$i) !hree pipes o diameters 'mm, -mm and >mm and lengths>=m,-==m and '4=m respectively are connected in series. !he diKerence inwater surace levels in two tan%s is 4Pm.#etermine the rate o ow o water ico5ecient o riction are .O=, .OP and .O- respectively consideringthe ma+or losses and by neglecting the minor losses.

$ii) #erive #arcy weisbach euation or calculating loss o head due toriction in a pipe.



4>$a) 0 4= mm diameter pipe reduces in diameter abruptly to 4 mmdiameter. I the pipe carries water at 'litres per second, calculate thepressure loss across the contraction. !a%e coecient o contraction as .N.

4=$a) using Buc%ingham1s T theorem, show that the velocity through acircular pipe is given by : head causing ow, # dia o orifce, 7 coeciento viscosity, U mass density, g acceleration due to gravity.4N$a) !he V eciency o a an on U mass density, 7 coeicient o viscosityangular velocity, # dia o rotor, and W #ischarge. J"press V in terms o nondimensional parameters using Buc%ingham1s theorem

4O$a). 0 *entriugal pump running at P rpm is wor%ing against a total heado -.- m. !he e"ternal diameter o the impeller is >Pmm and the outletwidth is Nmm. I the vane angle at outlet is >degreees and manometriceciency is OX

#etermine4. Flow velocity at outlet-. 0bsolute velocity o water leaving the vane'. 0ngle made by the absolute velocity at outlet with the direction o

motion>. Rate o ow through the pump

4P$a). 0 Single acting reciprocating pump running at = rpm, delivers 4 litresper sec o water .!he diameter o the piston is -mm and stro%e length>mm.. #etermine the theoretical discharge o the pump, coecient odischarge , slip and X o slip.

4Q$a) 0 3elton wheel having 4.N m buc%et diameter develops a power o 'NGw at > rpm, under a net head o -O= m. I the over all eciency is PPX andthe coecient o velocity is .QO.#etermine the speed ratio, #ischarge,#iameter o nozzle and specifc speed.-$a). In an inward ow radial turbine , waters enters at an angle o -- degrees

to the wheel tangent to the outer rim and leaves at ' m&s .!he ow velocityis constant through the runner.!he inner and outer diameters are ' mmand N mm respectively.!he speed o the runner is ' mm.!he dischargethrough the runner is radial .

#etermineFind Inlet and outlet blade angles

!a%ing inlet width as 4= mm and neglecting the thic%ness o blades , Find thepower developed by the turbine

ce 6451 fluid mechanics

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