Transpo Compilation Hey

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

Problems: 1. The distance between the two parallel plates is 0.00914m and the lower plate is being pulled at a relative velocity of 0.3 m!s m !s greater than the top plate. The fluid used is soy bean oil with #$ a viscosity of 4 " 10  Pa.s at 303%. &a' (alculate the shear stress and the shear rate in fps and )* units. &b' *f glycerol at $93 % having a viscosity of 1.09 +g!m#s is used instead of soybean soybean oil. oil. ,hat relative relative viscosity viscosity in m!s is needed needed using using the the same distance between the plates so that the same shear shear stress stress is obtained as in part &a'. -lso what is the new shear rate/ -nswers: &a' shear stress  3.34 " 10 #$ lbf!ft$ shear rate  40.0 s #1 &b' relative velocity  0.0139 m!s shear rate  1. s #1

2*5:

dy0.00914 m du0.3 m!s  4610#$ Pa.s

78: a. du!dy  in Pa.s  b. du c. du!dy

);

du dy

 

   

=

1.0$ Pa

du

1.09 Pa.s

dy

   1.499!s

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

$. - 1#cm 1#cm long cylindrical metal rod slides inside a tube filled with oil. The inner diameter of  the tube is  cm and the clearance is 0.0 mm. The mass of the bar is 0. +g when immersed in the oil. ,hat is the viscosity of the oil/ *f * f the steady#state velocity of the rod is 0.1 m.s/

2*5:

clearance  0.0 mm

dy0.0 mm

mg  p dhgc

=

&0.'&9.A' p &0.1'&0.0'&1'

$0=.9$ &0.1 ! 0. 0.0' !1 !1000



 $0=.9$ Pa

0.1039A Pa.s  103.9A cp

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

$. - 1#cm 1#cm long cylindrical metal rod slides inside a tube filled with oil. The inner diameter of  the tube is  cm and the clearance is 0.0 mm. The mass of the bar is 0. +g when immersed in the oil. ,hat is the viscosity of the oil/ *f * f the steady#state velocity of the rod is 0.1 m.s/

2*5:

clearance  0.0 mm

dy0.0 mm

mg  p dhgc

=

&0.'&9.A' p &0.1'&0.0'&1'

$0=.9$ &0.1 ! 0. 0.0' !1 !1000



 $0=.9$ Pa

0.1039A Pa.s  103.9A cp

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

3. ,ater ,ater at $0B( flows at a velocity of 1 m!s over a plane surface 0 cm wide and * cm long. &Ta+e critical 5 7e"  3.$ " 10 . (alculate: &a' the at a distance of cm from the leading edge &b' the at which transaction from streamline to turbulent flow occurs on the boundary layer  &c' the at a distance of 0 cm from the leading edge  

2*5:

C$; D $0(  1 m!s  57e"  3.$"10 

cm

1m

" 78?*7: a'thic+ness of the boundary layer  b'distance from the leading leading edge c'thic+ness of the boundary layer as well as of the laminar sublayer  ); pipe> &b' air at $atm pressure pressure and 1A0B@ flowing flowing at 0 ft!s in a 1$#in.duct> 1$#in.duct> &c' oil with a specific gravity of 0.=A and a viscosity of $0 cP flowing at ft!s in a $# in. pipe> &d' polymer melt with a density of 900 +g!m 3 and a viscosity of 1 Pa.s flowing at 0.$ m!s in a 1#mm tube.

 

); L  M � �dy � �dy a' +  $0.0$ n  0.=

b' +  1.9 n0.1A

if du!dy  10!s

L  $0.0$ [ 10]

if du!dy  10!s 0.=

  = 1.9 [ 10]

0.1A

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

  =.$4$ Pa

M

  $.4344 Pa

L =.$4$ Pa  du 10 dy

M

L $.4344 Pa  du 10 dy

 =.$4 Pa#s

 0.$4344 Pa#s

if du!dy  1000!s

  = $0.0$ [ 1000]

if du!dy  1000!s 0.=

  = 1.9[ 1000]

  10$.A3 Pa

M

0.1A

  .=0= Pa

L 10$.A3 Pa  du 1000 dy

  =

  .=0= Pa = du 1000 dy   Pa#s  .=0A"10 #3

 1.0$A3 Pa#s

FLUID FLOW Problems: 1. - $0 wt. J sucrose solution having a density of 10=4 +g!m 3 is flowing through the piping system shown:

3 E in. 1 E in. 1 H # in

The steel pipes are schedule 40 pipes. The flowrate entering pipe 1 is 1.A9$ m 3!hr. the flow divides eGually in each of pipes 3. (alculate the following using )* units: &a' the total mass flowrate in pipe 1 and pipes 3. &b' The average velocity in pipes $ and 3. &c' The mass velocity in pipes $ and 3.

 

2iven: *nside diameter: 1 in  1.049 in

in  1.10 in 3 in  3.0A in   7eGd:

r 10=4 +g!m3

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

a' m in 1 in. I 3in. pipes  b' v in $in and 3in pipes c' 2 in $in and 3in pipes )oln: m3m1!$ a' mGr m1  1.A9$ m3!hr&10=4 +g!m3'  $03$.00A +g!hr  m3 m1!$ $03$.00A!$ +g!hr 100.004 +g!hr  b' v G!s

v$ 

1.A9$m3!hr  N 4

v3 =

( 3.0A ( .0$4 ) ) 1.A9$ m3 ! hr 

p  4

( 1.1 x0.0$4)

$

$

 0.11 m!s

= 0.40 m!s

c' 2  m!s

� 1hr  � $.03$.00A +g!hr � � �300 s �= 11A.3 +g G$ = $ p  m$ #s ( 3.0A ( 0.0$4 ) ) 4 $. ,ater is being pumped from an open water reservoir at a rate of $.0 +g!s at 10B( to an open storage tan+ 100#m away. The pipe is 3 H # in. )chedule 40 pipe and the frictional losses in the system are $ O!+g. The surface of the water reservoir is $0#m above the level of the storage tan+. The pump has an efficiency of =J. ,hat is the +, power reGuired for the  pump/ 2iven: a 

3 H sched 40 $0m

C$; D 10(

0.= m $ +g!s> hf  $ O!+g

7eGd: Power reGuirement

b datum 

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

)oln:

P b #Pa g a b $ #a $ Q ( Rb #Ra ) Q Qh f   , p  gc $gc  r  PaPb1 atm a  b0 &negligible due to large cross#sectional area' Ra$0 m Rb0

W p = h f -

 g   g c

Z a = $

O +g

-

9.A 1

( $0m )

 4$9 O!+g

wp

=

4$9 0.=

P=$

= =$

O kg 

O � +g � �1 KW  $ � � � kg � s � 1000W  �

P 1.44 %,

3. - pipeline laid cross country carries oil at a rate of =9 m 3!d. The pressure of the oil is 1=93 +Pa gage leaving pumping station 1. The pressure is A$ +Pa gages at the inlet to the ne"t  pumping station $. The second station is 1=.4 m higher than the first station. (alculate the lost wor+ &friction losses' in O!+g mass oil. The oil density is =9 +g!m 3.  

2iven:

1=.4 m

 

7eGd:

hf 

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

 

)oln:

P b #Pa g a b $ #a $ Q ( Rb #Ra ) Q Qhf   , p  gc $gc  r  Pa  1=93 Q10.3$  1A94.33$ %Pa Pb A$ Q 101.3$  93.3$ %Pa Ra  0> Rb 1=.4 m ,p 0 &no pump bet pts. - I S'

m  rvs vavbG!s

� P #P � g h f   � b a �# R b � T � gc � � 1A94.3$"10 3 Pa # 93.3$"10 3Pa h f   � +g =9 3 � m �

� �� 9.A � ( 1=.4 ) �# �1 � � � � �

hf   1040.143 O!+g 4. - pump delivers water from a holding tan+ at atmospheric pressure &100 +Pa' to a process eGuipment at 40 +pa at a flowrate of .$

but m  Gr

9m 3 �1 hr � kg �   � m 99A.$04 3 �= $. +g!m 3 � � � hr � 300 s � m � � 1000W  � � 0.1 KW  � � 1 KW  � � W  p = = $. +g!s $. +g!s

 , p 

40 =

P b #Pa  r 

9.A 1

Q

g gc

( Rb #Ra ) Q

(  - Z a ) +

Ra 1.$m

a b $ #a $

1&1.$=' $ $&1'

$gc

+ $.

Qhf 

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

. - pump ta+es water at 0B@ from a large reservoir and delivers it to the bottom of an open elevated tan+ $ ft above the reservoir surface through a 3#in. * pipe. The inlet to the pump is located 10 ft below the water surface and the water level in the tan+ is constant at 10 ft above the reservoir surface. The pump delivers 10 gal!min. if the total loss of energy due to friction in the piping system is 3 ft#lb f !lb calculate the horsepower reGuired to do the  pumping. The pump motor set has an overall efficiency of J.  

2iven:

b 

10 ft $ ft atum

  10ft

a  C$;D 0@

G  1 gal!min hf  3 ft#lbf!lbm J 7eGd: P in hp   )oln: Sasis: 1 min operation

V, p 

P b # Pa T

$

gU #  Q ( R b # Ra ) Q gc

b

$gc

$ a

Q hf 

PaPb1 atm a  b0 &negligible due to large cross#sectional area' Ra0 Rb10ft

0.W p =

3$.1=4 3$.1=4

( 10 ft )

,p 34.4 ft#lbf !lbm

lb f lbm

+ 3

ft.lb f   lbm

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

rD0@ 999.013 +g!m3  $.3= lb!ft 3

Power , pm> where m Gr

� 1 ft 3 �  gal � 1min � $.=3 lb!ft 3 ) m  10 ( � � � � min �0 s � �=.4A1gal  � m $0.A lb!s

� � 1 hp � ft#lb f  � lb � � 34. $0.A � \ P � � > � � lbm �  s � � �0 ft#lb f  � � lbm � P  13.4 hp

=. - pump pumps 0.$00 ft 3!s or brine solution having a density of 1.1 g!cm 3 from an open feed tan+ having a large cross#sectional area. The suction line has an inside diameter of 3.4A inches and the discharge line from the pump a diameter of $.0= inches. The discharge flow goes to an open overhead tan+ and the open end of this line is = ft above the liGuid level in the feed tan+. *f the friction losses in the piping system are 1A.0 ft#lb f !lbm what pressure must the pump develop and what is the horsepower of the pump if the efficiency is =0J/ The flow is turbulent.

  2iven: 

=ft

datum

 brine r1.1g!cm3

$.0= 3.4A&'

hf 1A ft#lbf!lbm 0.=0 G0.$ ft3!s

7eGd: a' P in hp b'Pressure that the pump must develop   )oln:

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

P b #Pa g a b $ #a $ Q ( Rb #Ra ) Q Qhf   , p  gc $gc  r  PaPb1 atm Ra0 Rb=ft a0>

 b =

q  s

=

9 ft 3 ! s $

p  �$.0= �

�

= A.A ft!s

�

4 � 1$ � $

� lbf � ft # lb f  ( 1) ( A.A ) 0.=0,p  � 1 = Q Q 1A ( ) � $ ( 3$.1=4 ) lb m �lb m � ,p 134.49 ft#lb f !lbm Power m,p

where m Gr

r brine =1.== lb!ft 3

m 0.$ ft3!s &=1.== lb!ft3'14.34 lb!s

Power  134.49 ft#lb f !lbm &14.34 lb!s'

� � 1hp � ft#lbf   P  3.1 hp �0 � lbm

(onsider the pump:

a



 b



P b #Pa g a b $ #a $ Q ( Rb #Ra ) Q Qhf   , p  gc $gc  r  -ssume Rb#Ra

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

a G!s 

0.$ ft 3 ! s $

p  � 3.4A �

�

= $.91 ft!s

�

4 � 1$ � a G!s

0.$ ft 3 ! s $

p  �$.0= �

�

= A.A ft!s

�

4 � 1$ �

( 0.= ) ( 134.49 ) =

 Pb - P a =1.==

1� ( A.A) - ( $.91) $

+ �

$

$ ( 3$.1=4 )

Pb#Pa  A3.9A lbf !ft $

P7;S viscosity  A4 " 10 #3 Pa.s 2iven: *  0.0$m

oil   v1.$$m!s roil919+g!m3   A4"10#3 Pa.s T$93%  7eGd: Ps 7e f 

f .004 hf   s =

4 ( .004) ( 1 ) ( 4.= ) $ ( 1) ( .040A9 )

c' J reduction 

$

= $A0.34 O!+g

3=. - $A0.301 3=.

 x100 = $3.=3 J

3. ,ater at 0B@ is pumped from a reservoir to the top of a mountain through a #in schedule 1$0 pipe at an average velocity of 1$ ft!s. the pipe discharges into the atmosphere at a level of 3000 ft above the level in the reservoir. The pipeline itself is 400 ft long. *f the overall efficiency of the pump and the motor driving it is =0J and the cost of electric energy to the motor is 4 cents per +,#hr what is the hourly energy cost of pumping this water/ 4. centrifugal pump ta+es brine from the bottom of a supply tan+ and delivers it into the  bottom of another tan+. The line between the tan+s is 00 ft of 4 #in schedule 40 pipe. The flowrate is 400 gal!min. *n the line are two#gate valves four standard tees and four ells. ,hat is the energy cost for running this pump for one $4#hr day/ The specific gravity of  brine is 1.1A the viscosity of brine is 1.$ cP and the energy cost is X400 per hp#year on a  basis of 300 days per year. The overall efficiency of the pump and motor is 0J.

Complilation of Notes in Che 411 Unit Operations 1- uid Mechanics

2iven:

 b

10ft  

datum a

4 sched 40

Srine )21.1A   1.$ cP

G400 gal!min