FE Review-Fluid Mechanics
3. At a:particular temperature, the surface tension of
water is 0.073 N/m. Under ideal conditions, the contact
angle between glass and water is zero. A student in a
laboratory observes water in a glass capillary tube with
a diameter of 0.1 mm. What is the theoretical height
of the capillary rise?
(A)
(B)
(C)
(D)
0.00020 m
0.013 m
0.045 m
0.30 m
k=A 'rtr
o
/f't'I!
t
r, -=
L,
::=
0-CD�
rd
LI ( CJ
J3
67 _) J ( Co S D)
(c, y10) ( 0. C:>c,DI)
.:-
CJ
l-'? g/
0
6) What is the atmospheric pressure on a planet if the
�solute pressure is 100 kPa and the gage pressure is
10 kPa?
(A)
(B)
(C)
(D)
10 kPa
80 kPa
90 kPa
100 kPa
BlP144 6/89
-
-- J>
/;'J 100 g of water are mixed with 150 g of alcohol (p =
�O kg/m3 ). What is the specific gravity of the resulting
mixture, assuming that the two fluids mix completely?
(A)
(B)
(C)
(D)
0.63
0.82
0.86
0.95
/w
Jw
ATH £/95
J.,_1c
::::""'
"-o/
I Ooo
1 'i 0
A::..
�
,Iv\ l,.
W�l(,f+Tt='D
,4\/t'e-A--4 �
0. -, ~ ( I s-l?)
+ {I ) ( / t.Y2>) ::--
I c.;---0 t- I u
O.
3 1
c.)
1
A
FE Review-Fluid Mechanics
@Kinematic viscosity can be expressed in which of the
following units?
(A)
(B)
(C)
(D)
ft 2 /sec .
sec2 /ft
lbm sec2 /ft
lbm/sec
5. Which of the following does not affect the rise or fall
of liquid in a small~diameter capillary tube?
(A) adhesive forces
(B) cohesive forces
(0) surface tension
(D) viscosity of the fluid
cBJP126 6/89
6. The film width in a surface tension experiment is
10 cm . If mercury is the fluid (surface tension =
0.52 N/ m), what is the maximum force that can b e applied without breaking the membrane? Neglect gravita tional force .
£
L
---,=--- _
rJ__ a-L
= ('L) ( 0. )
2.
~
)
L
6 • / ""-)
(A) 0.1 N
(B) 1.0 N
(C) 2.0 N
(D) 3.4 N
\
2
FE Review-Fluid Mechanics
1. What height of mercury column is equivalent to
· a pressure of 100 ·psig? The density of mercury is
848 lbm/ft 3 .
(A)
\"j_
/0'/
'.? ft
( 8) 4 ft
(C) 11 ft
./-.-
r~cit t )(~)~
(D) 17 ft
/ lJ L) D o
-=-
CH
IS (,)
IA_
2. A fluid with a vapor pressure of 0.2 Pa and a specific gravity of 12 is used in a barometer. If the fluid's
column height is 1 m, what is the atmospheric pressure?
(A) 9.80 kPa
(B) 11.76 kPa
(C)
(0)
101.3 kPa
117.7 kPa
Y,
= L:>._L
~ C,
=IL
0
~
cc-
f
(12.)( qi10
V\."" \
h)
f"'-
M.,
0
One leg. of a mercury U-tube manometer is con-
¼ted to a pipe containing water under a gage pressure
of 14.2 lbf/in 2 • The mercury in this leg stands 30 in below the water. \Vhat is the height of mercury in the
other leg, which is o~t__o~? The specific gravity
of nwrcury is l 3.6.
p tLD\3 L~ JI\ ,J Ft, L.-='"'-TS
P5.
I 03
R,"' = l '-\. 1
R,....._
fS I ~ I D 1 ·3
k. P"'--
14.2 lbf/in2
= ()~
)\..1.2..psi + (J~t?
Z. 5" ~
mercury
30 in
(, (II L
1 ~---) (
if)L- +-( 6l.
( z,c1
(A)
( B)
(C)
(D)
0.7
1.5
2.6
3.2
ft
ft
ft
ft
l)
t l
t )( z.
+./LI) P~I
5"t) ~
>
JL)(t._""' \) ++-{
/LI.N 11 Mrf'f.
2 ,:fi~;;-~) l J;)
. fr~
:> 0
L
Q!.,J
t,.. = (I;,,'=-) ( h ?. .L/ ~ )
)""-:: &'-/'6,.&Lf~
3
b
FE Review-Fluid Mechanics
di) Wha t is the resul tant force on one side of a 10 in
~an iete r vertic al circu lar plate stand ing at
the botto m
of a 10 ft pool of wate r?
(A) 326 !bf
( I3) 386 lbf
(C) 451 ]bf
(D) 643 !bf
A.:
V
l,\
7f (0,
== C.
-= D.
fsJ)L
L,L(
>~
h
1.-
J:-;,
)~
IA: c,.s -~
I~
5. A speci al closed tank with the dime nsion
s show n
conta ins wate r. If the press ure of the air is
100 psig,
what is the press ure at poin t P, whic h is locat
ed halfw ay
up the inclined wall?
100 psig
I
\ 1....,, ·~=ioo ft
(A)
(B)
(C)
(D)
/L/</
DO -
/0
ftL
115 psig
128 psig
134 psig
4060 psig
CA4F Pf3S #7 1/93
?f
::-
~~' "'
-+
L~
-f;, : I
l
Lf
=
-r;-G
/1/l) b
L)
11
:h:; L
!£-(#,:-')L
+
~
6 2.
LI
} 2-
;J ( ;;-A)
6
i
~
If'-(
s/.,,
ll
k'-
--I i
} V\ -
4
FE Review-Fluid Mechanics
6. A trian gular gate with a horiz ontal base
4 ft long
and an altitu de of 6 ft is inclin ed 45° from
the verti cal
with the verte x point ing upwa rd. The hinge
d horiz ontal
base of the gate is 9 ft below the wate r surfa
ce. What
norm al force must be appli ed at the verte x
of the gate
tu keep it closed?
fixed
wall
Ow
~'-A~ O:,l.'-1
t,)(7.)qJ.+')(iL iL)
9 ft
F~
s-c ~-s. '--1 U.
l
A~"-----.\
F
(!)
f - - ·= - - - - - - -.,f'
L
- , :::-1'
{ 1"1\\':
f-;--;_/(!,.1+hLl
2-
.::--..1.. (1,z :·j) l,'f + li, 7 c..')=-~L,;
)_
h_ ::- t S,A4 :S ::::- I. '-I il\
j-t-
(A) 1430 lbf
(B) 1570 !bf .
(C) 1670 !bf
-> (D) 1720 lbf
~
s ' "' LI ',-= ~
I~
I
1"°1
I,.
~!,
WILL
r6'
D, I }'lo
"v;..p
~f'
aZ)
lb
,.~
~
~
·,
./iD Water
-·· ···· ······ ········· ··:··········· .. ··········· ················
,e,_
flows through a. multisection~ p~pe placed
~oriz onta lly on the ground. The velocity lB
3.0 m/s
at the entrance and 2.1 m/s at the exit. Wha
t is the \l t --:I
press ure differ ence betw een these two point s?
Neglect :;, _ __
1
friction.
->
W
~'
V~
41/Jyf;"
..._,,o\
1\l..1A. Jc)\JI.- .L. II--
2-. \\:
c,,.,A.'-1 .-
0
~~~ ~:~ ~~: ~ +
(C) 28 kPa:
(D) 110 kPa
C..1 , 7. L/ )
CC
_h
1- \_,: LJ . I
I.{,..
• ~=Y·A =L1u / 1f)"' "nr-o .8"
DFAI P#9 6/87
"
V\ =
I:,
/'
i',
i.,,
>
~
~
u
2
;
2.j
+
~
/
+
_ _ __
IJZ
'LJ
d"t.J
CA6o. FLP& S#41 1/94
PL - p,
Kw
~
\J;- - \Ji.
\"~ - f, = Q,. (
z.':r
'0.~~c) = ~ 8
IC
::-{6 n
S-" } '2-7.- D
'.)
P..
5
L>\L. ~
"r-"t.=,,(" \_
A. Q.;;,;- ~
FE Review-Fluid Mechanics
@What is the mass flow rate of a liquid (p = 0.690 ?1- ID'-\
g/cm 3 ) flowing through a 5 cm (inside diameter) pipe
at 8.3 m/s?
M :::
J-"1 /:\
(A) 11 kg/s
(B) 69 kg/s
(C) 140 kg/s
(D) 340 kg/s
CA6aFLPfiS#-4 +
7/9-.
3. The mean velocity of 100°F water in a 1.76 in (inside
diameter) tube is 5 ft/sec. The kinematic viscosity is
11 = 7.39x 10- 6 ft 2 /sec. What is the Reynold's number?
(A) 7.9 x 103
(B) 8.3 x 103
(C) 8.8 X 104
-> (D) 9.9 x 104
\)
oc=S
J.._
-b
7, )>""! (ID>
Jo--<---
-=
CAJBaFMP&S #++ 3/9+-
Ccr.7 (ID)
l/
D ==- I, 1 1,,, ,V\,(it"::\ = 6 , 1 1 J.__
'j
-J
~ 7, "? c, { It>
-6
)
£
',..L<---
What is the head loss for water flowing through
a horizontal pipe if the gage pressure at point 1 is
1.03 kPa, the gage pressure at point 2 downstream is
1.00 kPa, and the velocity is constant?
p9
4.
(A)
(B)
(C)
(D)
3.1 x 10-3 m
3.1 x 10- 2 m
2.3 x 10- 2 m
2.3m
~ -?l-
-=
l
10 ~
~
CA6aFLP&S# 42 1/94
->
-
{:)
00
_3
=:-
'3 {/I!))
5. The hydraulic radius is
(A) the mean radius of the pipe.
(B) the radius of the pipe bend on the line.
(C) the wetted perimeter of a · conduit divided by
the a.rea of flow.
·
(D) the cross-sectional fluid area divided by the
wetted perimeter.
-
c;,
'
B1P19J 6/89
6
f-1\..
FE Review-Fluid Mechanics
For the following problems use the NCEES FE
Reference .Handbook as your only reference.
c:c 107
I -->
Cwhat horizontal f~rce is required to hold the plate
stationary against the water jet? (All of the water leaves
parallel to the plate,)
.::TMP\J'-- 5~
r ::- C? J (_ V
1.-
MoMo-..rrvAA
-v,)
0 • 0.05 m3/s
(A)
(B)
(C)
(D)
H.7 N
35.4 N
42.2 N
67.5 N
B1P139 6/89
A-n:--c
- l/ 0,3)._ ::-
o.
07I M.
1..
0-}water flows with a velocity of 17 ft/sec through 18 ft 'G} 10 l,
ca.st-iron pipe (specific roughness:;:: 0.00085 ft). The
pipe has an inside diameter of 1.7 in. The kinematic
viscosity of the water is 5.94 x 10- 6 ft 2 /sec. The loss
\-or
coefficient for the standard elbow is 0.9. What percentage of the total head loss is caused by the elbow?
lc-c,, =- ~ ::
,)
½: } -_
----=-\,
17 (
5, C,'/ (11))
\(._=ti (10)
~
\7 ;c_h2,,. 0 ,l'i2-}-e
I 2-
V:::
.
17ft/sec~---------
A:: 1:; ( \L )'
~
\7
10 ft
:::- c::>'
:c
o.
0 1""
.t-t---....
8 ft
C, CJ C,
:JS-~ CJ . <:>
c:, (:,
0,lc/L
-1,;,
-V ::- S-:Ci~ {10)
(A) 5.5%
(B) 7.1%
(C) 10%
(D) 18%
CA1 6FMPe!S#6 11/ 93
7
FE Review-Fluid Mechanics
1. A 70% efficient pump pumps 60°C water from ~\O'\
ground level to a height of 5 m. How much power is
used if the flow rate is 10 m 3 /s?
{A) 80 kW
(B) 220 kW
-, (C) 700 kW
(D) 950 kW
Y) ::::-
Q
7/9-t
CA6aFLP&S#39
0,
r
-:::- / 0
AA½
lJ ":>-S- ?~D\?=- rz ....-Y ot" l,v-A,e"IL-T Al)Lc
~
~
(~6 Ll2-
bO 'e-
0 :=- f>cJ,
~... )(.CN.)(10~)
o,J rrA ~
0 .7
@_
-
(A)
(B)
(C)
? (D)
c;,, specific hea.t at constant pressure
p5
s_
k, ratio pf specific heats
Cv, specific heat at constant temperature
T, absolute temperature
F1..v,P~A.A-V1A
Dv<=' TO
>
2. The acoustic velocity in a specific gas depends only
on which of the following variables?
10
'?CJ 1i'I
bD .. (_ ,
l,J L\c v
/NU::S'l 12-cCT
o F _/
J.
001...'/)
Ui-1 IT.:>
L-E-( u.->. u,J,,~
\)
Ow
y
\Z"' L..A- , E r,
CA6aFLP&S#,13 7/ 9,4
8
0
J
FE Review-Fluid Mechanics
4. The velocity of the water in the stream is 1.2 m/s.
What is the height of water in the pitot tube?
V~ \\\
V
-/
-
h
atmospheric
=:
/1
L
.\'
Ys
- - - -
l -1 .~- v ~
s (
=-
"DA\°"v M-.
z., c:- 0
D. ()1
>
f'\
-= -z.,_
@c.v7J11::>c::
(A) 3.7 cm
\l=-o, I A.I --i--v 14i;=-
--iu-g,;;
(B) 4.6 cm
- > (C) 7.3 cm
(D) 9.2 cm
5.) A venturi meter with a diameter of 6 in at the \<S \\I
-rtiroat is installed in an 18 in water main. A differential
manometer gauge is partly filled with mercury ( the remainder of the tube is filled with water) and connected
to the meter at the throat and inlet. The mercury column stands 15 in higher in one leg than in the other.
Neglecting friction, what is the flow through the meter?
The specific gravity of mercury is 13.6.
'6~:t.
l.'-1C
\1.. ~ /) \ C-1 I,, }ti.-
A-- <l.%'
1 \'L ;.
,--------J
I , l '- 7
sc;,,.__ ::-
\1, , I., ~
\;A
6ow
:e- 13, l ( e, 2:-1 !1 ) -::
f,.._ = \',,
~--1 )
lo (;;, 2.
l(,
r:
I
A=:~
~) - '
l._
I
",nL-"-'\-~-- +-"",:_. . .------
o = ~- -_c="=A===t.
J(- (~~)
r_
(A) 3.70 ft 3 /sec
{B ) 6.29 ft 3 /sec
(C) 8.62 ft 3 /sec
(D) 10.5 ft3 /sec
9
~ 'I z,, 1. '-I \b.t
w
FE Review-Fluid Mechanics
6. What is the velocity of water under a 50 ft head discharging through a 1 in diameter round-edged orifice?
\>;
..._) CJ
I CJ
'
--r'C
\)~....JP..
( 0 -..JTQ.kC.TA.
PS \17-
1A-D,'- ~
50 ft
(A)
(B)
(C)
(D)
-">
3.6 ft/sec
9.8 ft/sec
25 ft/sec
56 ft/sec.
7. A 1: 1 model of a torpedo is tested in a wind
tunnel according to the Reynolds number criterion.
At the testing temperature, Vair = 1.41 x 10- 5 and
Vwater = 1.31 x 10-6 • If the velocity of the torpedo
in water is 7 m/s, what should be the air velocity in the
wind tunnel?
(A) 0.6 m/s
(B) 7.0 m/s
(C) 18 m/s
-::>
(D) 75
m/s
-J =-
cvy -t
/A
1\>
~%1.~ ~
µ
.f
\ :\ / ¾ L-W
:=-
=
\ , 1.1 I (
-
to)~ ( 7 ~)
-
-l
) ,s l(luJ
10
FE Review-Fluid Mechanics
Problems 8 and 9 refer to the following situation.
?-1 \\1--
A sharp-edged orifice with a 2 in diameter opening is located in the vertical side' of a large tank. The coefficient
of contraction for the orifice is 0.62, and the coefficient
of velocity is 0.98. The orifice discharges under a hydraulic head of 16 ft.
8. What is the minimum diameter of the jet?
(A)
(B)
(C)
(D)
~
1.24 in
1.57 in
2.00 in
2.54 in
~s
V
(__L ::::. 0 ' b
L
Cv-::: o. q
~
11'L-.
What is the velocity at the vena. contracta?
(A)
(B)
(C)
(D)
5.54 ft/sec
10.8 ft/sec
17.4 ft/sec
31.5 ft/sec
A \J
L
~1'-re= lvt
-==-
c..1
?~
I
tJ'
Q
==
C Ao
fi-'J Lt
\J - (_ v jz 7J V\.
11
FE Review-Fluid Mechanics
Problems 10-13 refer to the following situation.
The bottom of a tall tank sits on level ground. The tank
is kept filled to a depth of 15 ft, while water discharges
at a constant rate through a 0.5 ft diameter hole in the
tank side. The center of the hole is 10 ft from the water
surface above. The coefficient of velocity for the hole is
essentially 1.0.
\)::c6 . .:;-./-
C....,
=- \
'
10. What horizontal distance will the water jet travel
before hitting the ground?
(A) 6.5 ft
(B) 7.1 ft
(C) 7.5 ft
(D) 14 ft
- ) X..::: \) • t
~
=- a
-+-
>-
o
+
:=
'"C'.
> LU= (o
-.S-~7
$-e1....-
-1 (~z. :z..1-t""t..J-
lb -I t2-
Q \<..
11. What is the velocity of the water jet?
(A)
-:;;, (B)
(C)
(D)
21.9
25.4
26.9
30.6
ft/sec
ft/sec
ft/sec
ft/sec
p-au
,..__J
1>
A.. 86 \] ~
12
u-,_)
FE Review-Fluid Mechanics
12. If the hole is represented by a sharp-edged orifice
with a coefficient of discharge of o:61, what will be the
rate of discharge?
(A)
(B)
(C)
(D)
2.68
3.04
3.27
3.72
ft 3 /sec
ft 3 /sec
ft 3 /sec
ft 3 /sec
Q, ""
C · \} · A_
= ( 0 , 6 IJ (
2.. ~ , l\
__b_
J ( ~ (o. :s-~ ') '- =
l-'<....---I
"7
o '-1
..>,
13. Assume the orifice can be moved to any point on
the side of the tank. What distance below the water
surface should the orifice be located such that the horizontal distance traveled by the jet (before hitting the
ground) is the greatest?
(A)
(B)
(C)
(D)
h-"J
<::,.,,,&.__
7.5 ft
8.8 ft
10 ft
11 ft
13
FE Review-Fluid Mechanics
14. A 2 m tall, 0.5 m inside diameter tank is filled with
water. A 10 cm hole is opened 0.75 m from the bottom
of the tank. What is the velocity of the exiting water?
Ignore all orifice losses.
(A)
(B)
(C)
(D)
4.75 m/s
4.80 m/s
4.85 m/s
4.95 m/s
14
FE Review-Fluid Mechanics
1. Reynolds number may be calculated from:
/
yj
\l0-::,
(A) diameter, velocity, and absolute viscosity
(B) diameter, velocity, and surface tension
(C) diameter, density , and kinematic viscos ity ,!:(D) diameter, density, and absolute viscosity
(E) characteristic length, mass flow rate per un it area,
v : :.~
-
\J
l/
and absolute viscosity
2. Roughening the leading edge of a smooth sphere
will reduce its drag coefficient because
(A) the wake width increases
(8) the separation points move to the front of the
f-
sphere
(C) the wake eddies increase
{DJ the boundary layer becomes turbulent
(E) Stoke's law becomes applicable
'3') What is the hydraulic radius of a rectangular flume
~ feet high and 4 feet wide wh ich is running half full?
/ilvater flows at 10 ft/sec in a 1" inside diameter pipe.
½ifh~t is the velocity if the pipe suddenly increases in
diameter to 2"?
h. J ,..... , ..
011
/ //~ o, o c- "?, ;--ctr- ....., · o --->
V, A\ _:- \I, f
1
CJ
(A) 5 ft/sec
i
{B) 2 _5
{CJ 40
{DJ 20
11
Z.. ~
0, I
/
.i . r.
6"7 _fr"-
u,
bl/ ~
/(){O ,bo,S'\1.:::-
~l...(
C>- bl_lC,.)
(E) answer depends on the flow direction
5. What pressure differential exists across a perfect
venturi with an area reduction ratio of (3 : 1) if water
is flowing through the throat at 40 fps?
(A) .6 feet of water
(B) 17
(Cl 22
(D) 27
{E) 1378
i:t.~
-0
1) .:- 7,)
(V~\ ~Nl)2-
~
3: '
~ () Jp_j,LI) ::: \)L (
\J
7-,
~ \~
?:,)
:~
ty__J
.,__
~-==- 2--'l.,)
zt,1..1-")
15
FE Review-Fluid Mechanics
6. If 'L' is defined as the characteristic length, what does
the quantity (v2/Lg) represent?
·
(A) velocity pressure ~
(B) Reynolds nurnbe-r
(C) Froude number
( D) total pressure
(E) static pressure
7. Minor losses through valves, fittings, diameter changes,
and bends are proportional to
)')
(Al total head
(B) dynamic head
(C) static head
(D) wet head
(E) velocity
e-(:! /
8. The horsepower of an ideal pump used to move 2 cfs
of wpter into a tank 50 feet above the pump is most
nearly
\'QC,._"- Vv.,,__("
(A) 2
(B) 11
0
q
1\:-1
)/. 3
(C) 290
(D) 1213
(E) 6240
9. A horizontal pipe section 1000 feet long has a total
energy loss of 26.2 feet. If the inside pipe diameter is
12 inches and the flow velocity is 10 ft/sec, what is
the Darcy-Weisbach friction coefficient?
->
(A) 0.0170
(B) 0 .0080
L
(C) 0.0017
(D) 0 .0002
(E) 0.0008
0,}- = 2. 0 , z._ j.-e-
r~, 6 ro
L .
J'Z
hJ- ~}· o ~
j+
=100u
}) =-
l 2-.iv\
\J:::
10
2c2- ~ } ~ )
=-It
b~
10. The Reynolds number for a 1-fQot diameter sphere
moving through a fluid (speci~ic gravity of 1.22, absolute
viscosity of 0.00122 lb-sec/ft ) at 10 ft/sec is approximately
(A)
(8)
- t {C)
(D)
20
200
2,000
20,000
{E) 200,000
~C., -= I, -z "L.- =
J ::-
'< 0,
l) : [
1:
l.2.-'LC..02-'-1)~ 7~.\~
~
16
HP
FE Review-Fluid Mechanics
11. Water is flowing in a circular pipe between points 1
and 2. The pressure at point 1 is 16.8 psia. The pressure
and velocity at point 2 are 17 .2 psi a and 6.2 ft/sec,
respectively. Points 1 and 2 are at the same elevation.
Neg lecting friction , what is the velocity at point 1?
(A) 97.8 ft/sec
-7 (B) 9.9
(C) 21.0
(D) 1.52
(E) 4.58
.. -· ·--·
,@The critical depth in a rectangular channel 8 feet wide
flowing at a critical velocity of 2 ft/sec is approxi mately
?5 1 '-
~
:gll 6-.~~
(E) 0 .08
~
~
A -=-
1---
Yr--
-
Q.::-
=
j~ :- ~ -3 A :i
(,1\) 0.12 feet
(8)2.00
' \
...,
JJ----c
'iJ y(..
1=- s ~
0.::-\J._·A =-\t_ '0}(..
j (_ ~-Yv)-,,
z_
(~,~
Cs i:~ll ~. '/__>
~ ,_ -- 0. I "2- 1.1
13. At a certain section of pipe, water is flowing at a pressure
of 80 psi and with a linear velocity of 9 ft/sec. What is the
total flow work for 1.5 cubic feet of water which pass that
section?
(A) 18,000 ft-lb
(B) 36,000
(C) 120
(D) 12,000
(E) 0
17
FE Review-Fluid Mechanics
FLUID STATICS
AND DYNAMICS
1001 SOLVED ENGINEERING FUNDAMENTALS PROBLEMS
4-8
FLUIDS-17
Find the pressure in the tank from the manometer readings shown.
Patm
= 100 kPa
pressurized tank
"'I
1.0 m
fluid A, PA "' 500 kg/m3
fluid B, Pe
fluid C, Pc
= 1000 kg/m3
(D) 118 kPa
{C) 112 kPa
(B) 108 kPa
(A) 102 kPa
= 750 kg/m3
--
L( ~0, S
P2 - P1 - pcg(z1 -
T
Pr
z2)
= PB9(Z2 - Z3)
P4 - Pa = PA9(Z3 - z4)
p4 - PI == (p4 - Pa) + (Pa p3 - P2
P2) + (p2 - pi)
p.i, =Pt+ g(pc(z1 - z2)
+ Pa(z2 -za) +PA(Za -
z4))
- 100000 Pa+ (9.81 ~) ( (1000 ~ ) (1 m)
+ (150 ~~) (- 0.3 m) + (500 ~~) (0.1 m))
= 108100 Pa
(108 kPa)
.The answer is (B).
18
I
FE Review-Fluid Mechanics
Ajet aircraft is flying at a speed of 1700 km/h.
The air temperature is 20°C. The molecular
weight of air is 29 g/mol. What is the Mach
number of the aircraft?
.I.
V'J\...-.. :::-- -
0-
~.,._.,,. ~ l . l-\
~~~)
-- /, ;> ~,.,)
-L,t..,.....
- -\..<
\100
:c
(.....,-
Pl
pn
w
,
o
~;i~)
a
2_5ro·c )
oonditiens,()
Whm is dtd,flii1*
.and,
~- with
o:f 450 Dll:tl1 (,J\11unwl 1bat fur oxy·p11i & =
at standard,
-~
l ;t m
1
l~AO
R·~·o'"
---=-
, .t
{,-Sl,,.C..
19
FE Review-Fluid Mechanics
A 2 mm (inside diameter) glass tube is placed in a
container of mercury. An angle of 40° is
measured as illustrated. The density and surface
tension of mercury are 13550 kg/m 3 and 37.5 x
10-2 N/m, respectively. How high will the mercury
rise or be depressed in the tube as a result of
capillary action?
c_,.._ Q1 u..Ae., f?,.\s-;;- ~ ,o3
.
., . . .
./2' rrrm ····
.··1-- : ... ,
\)2.-~l..J-.~ ~
-"".s--·
l) (~-, . .r-Jlto)"t.~ Cos. 140~
t1 L)?.r)(1t>~'t_),J=:j>"'( w~l'-lo
_
_ _ _ ._J5__ __
20
FE Review-Fluid Mechanics
A sliding-plate viscometer is used to measure the
viscosity of a Newtonian fluid. A force of 25 N is
required to keep the top plate moving at a
constant velocity of 5 mis. What is the viscosity of
the fluid?
(J,oc:,//\1\
}'-J.
s
M.~
21
FE Review-Fluid Mechanics
Example: What is the pressure 1 0 feet
below the surface of a swimming pool?
/
'I
y
., \7
22
I
FE Review-Fluid Mechanics
Example: The tank of water has a 3-m
column of gasoline (S.G.
=
0. 73) above
it. Atmospheric pressure is 101 kPa.
Compute the pressure on the bottom of
the tank.
--'
gasoline
( S.G. = 0. 73)
- - --
'.
hg
-
3 m
'l
hw -
2m
,.,
water (y= 9.81 kN/m 3 )
l'H,lo
Pt.._
23
FE Review-Fluid Mechanics
Example : Use the manome ter
measur ements to comput e the pressure
in the pipe.
2.0 ft
1.5 ft
_
--
-
-
'OAo"'\u "'-.
mercury (S.G. == 13.6)
Pi -
tk...
+ ~..... -
0 kw ~
1,, b ( 6Z. ''
! )( z...!..)
j.c';
P, - ,~. b t b'Z_. Lf A') C2-.l ") +
_h,>
I
llt. "'>
~ ·( !:::.!!..)'- _ 02..l/
1
ff\l-
~
-
111 (' ·~
~
~ 76 7.
6
J+-)
SI
-
/b
h_."l-
24
FE Review-Fluid Mechanics
Example: Compute the magnitude and
r;_:: ( ?r,-t;,,. f 3 YL f-1~(9) A
-j--
location of the resultant force.
E
LO
r--....
N
moment of inertia I C -
51VlYC" :::- -~-
'2...( _,
-3
I,>
k_
-
0,70"")
,J
-
2, S-9'4
~
c>'\2-
F;i. ::
Ou '-'. t..-' A
=-
~ <:J
\(
~
25
FE Review-Fluid Mechanics
Example: Compute the force on the
curved corner for a unit wid th.
\
\tA--'-\_
wat e
quarter circle
-r;-
L .lA_ • A : :-
-F.: =
rJ
1
-:/
~j
c:: ( %
('1&- I O
.-~-t
'°
~
,~ _ J F,;
~) (
,o..... l.r"')(3 "-)( J...,,)
"!.O ,.,.-,)
+
f- i=,;-z-
_
)~,
'L
7. C> b 1 "'"]
~
4 "i 6 '7 ~D
:c 3
3"1 11~
-:t "' 2 , ,, 2.
~
t.
...J
Fv
26
FE Review-Fluid Mechanics
Example: Compute the force in the rope.
3 ft
1 ft
~
wood
(y = 40 lb/ft 3 )
1 ft into paper
}tt
rope
Vwo.,~
:c
(Z. f-e J( I 1-) ( {J~)
- z A.%
UIJb YA..Jcy (~~
T
Fr3D
ro-w-F;:- o
p;.. ---w + Fr.,. = -s,o/h
-t- /2V.Si
lb
27
FE Review-Fluid Mechanics
Examp le: Three kN/s of water flows
throug h the pipelin e reduce r. Determ ine
the flow rate and veloci ty in the 300 mm
and 200 mm pipes.
-->
!•
,,
, I
'-J,:::
300mm
,...,_
~-=-
A,
0, 3:,05 g-1
:~ 200mm
t:;~
----
~ Lj,
,A_
>J ---;
28
FE Review-Fluid Mechanics
Example : Water is flowing at 0.884 m 3 /s
through a 1 5 cm diamete r pipe, that has
a 90° bend. What is the reaction on the
water in the z-directio n in the bend?
y
--~_.. ..r---- ----.t----
-
X
I
2-
tz:
=-
f Q ( vl- - v, J
/2_(1
L_~)
I
29
FE Review-Fluid Mechanics
Example: The height of water in the pitot
tube is measured to be 7. 3 cm. What is
the velocity at that point in the flow.
-
-
Z.. , ~ 0
-
D~-rv.}A...
-= Z.1.....
0
/. +
P,
0
?z_
T.
~
C rl/>-t-JC 1 /;
-
\}2~
. ·~
CI-IA,.J4
r:-
1.J
{\; C:.V ;.J Al..,.,S
1>-e.;::<;.Sur?a::
/-f f!!:J..r>
77f~ l)Ct.,._ Oc 111 ;/£.'At>
\....,,...._)
1 .._,
p ~ S.$V'lZ i,,e-"!'}
30
FE Review-Fluid Mechanics
The density of air flowing in a duct is 1.15 kg/m 3 .
A pitot tube is placed in the duct as shown. The
static pressure in the duct is measured with a wall
tap and pressure gage. Use the gage readings to
determine the velocity of the air.
J:-1., ,;;-
z, +
=
LI/•
p,
T
+
~ '?
-
Zo -
7
,:._z
-+
7p
\J'2
+
½
7 AA.
.s
31
FE Review-Fluid Mechanics
Water flows out of a tank at 12.5 mis from an
orifice located 9m below the surface. The crosssectional area of the orifice is 0.002 m 2 , and the
coefficient of discharge is 0.85. What is the
,~ 1,2diameter D, at the vena contracta?
.::r-f-
l)l t-..Jl. T.i'.~ L-E""
\]C-,-JA
·0..0.02 m2·
c
=
'-
C...
t:-
(_\J
L. (o;;
Cv
......
=
f"
r~~'F
=
-
c,. 't'-1I
A~A
C... A
(_.
oF ?ts. e. H""- u ... ~
°F
'\Jt°L-Dc.
,-r-7
( o ,-..),~c,, o ~
\J
\ ] \ l>,;61., AT P~<"Tl-f -
4.8 CQJ~
A
~112.,..
· · · ·. }...
k : . - CoGPF
~ o~
C 0 .JTi2--kTA
0~
J'°l.'.) II\
32
FE Review-Fluid Mechanics
A nuclear submarine is capable of a top
underwater speed of 65 km/h. How fast would a
1/20 scale model of the submarine have to be
moved through a testing pool filled with seawater
for the forces on the submarine and model to be
dimensionally similar?
33
360 m/s
FE Review-Fluid Mechanics
Darcy-Weisbach Example:
For a discharge (Q) of
1 .0 ft 3 /s, compute the head loss in 1,500 feet of
new 6-inch diameter cast iron pipe (c
=
0.00085
ft). Assume a water temperature of 60° F.
p =
b
,~cN
CJ2.::-,J ,A
\} : 9..A -
1,o_f:?
~
_ ~.,
-=---
/
~
->
D. \ C, t,
_
{~ 1~)(_0 .s- J~")
1. z.1 '7
i:-~oM-
(
1o)r
~o~!>>' Ct-1"-i-' l
¥
~ 11 ~
}-- :: 0 · 0 'Z- 3
34
FE Review-Fluid Mechanics
Example: A 6-inch diameter 500 ft long
steel pipe (E = 0.00015 ft) conveys flow
between two reservoirs which have a
difference in water surface elevation of
30 ft. The pipe exit and entrance are
square edge. Compute the flow rate.
'2.1
CY
30
-
t![
CZ)
--
E.. _
D
c,,c,c,o,r h
e; . s;-
J..-
:-: o. ~oc=> .1
FL0...,.)
eA-,G"
Ft o M- Mit:>t!:>~y c.11,~, f!:, 11.t:'
/-.:- 6. 01 b
A A- Yt.,~ Ht"~ '-~~
hl. =-
}~
I:;>
f',/\1,-.)0~
_J:_ =
"l_j
(6,olb)I
l
~ooh)
r
tJ,
_h.
\)? - \
Z_j -
b 'l'l.
zS
\H::-~:s> ~ D.S.>
C--=
(_
::-
'>
I ( s 1-1,.if>
(J. s; C t-\A e..-r ~.Jt~y)
c)( ,."
$
35
FE Review-Fluid Mechanics
Example: - Assume a pump is added to
the previous example and the flow
direction is reversed. What pump head is
required for a discharge of 2.0 cfs.
-
.... -
30
t.![
pump
v=
o.
<h
36
FE Review-Fluid Mechanics
Example: Determine the horsepower
required for the pump of the previous
problem, assuming the pump efficiency is
75%.
Ito 'Ls c
(Pu,).,4_?
2.0 ft 3 /s
Q
Pv'--'
~ \Z--/wA7""T_5
B'e.J..}l..6'
Pe:>vJc;,
L.)
lJJ
58.2 ft
)
::-
bZ.'-(
Ji_,
~.3
0.75
f}
t-70,..rr
77:)
Fo\'2-Ga:-,
/{:(lb)
r::>
Tll--e
5
c:... /
,~-;::'l-r~,1.-
"/EiT
u$o
i
/I.
37
FE Review-Fluid Mechanics
Example: Compute the discharge rate that
causes the pressure to drop to vapor pressure.
The pipe between the reservoir and pump has a
length of 1,000 ft, diameter of 3 feet, and friction
factor (f} of 0.02. Neglect minor losses. For a
water temperature of 80°F , the vapor pressure
(Pv) is 0.51 psia.
atmospheric
pressure
f
10 ft
t
'v-==-
;:
!-J---
L-== ll?t..'.)C,
t
J-::
C,,O'L._
;- :::
3o· p
~ ~
o. ;-, ~(~'~) '-
0
38
FE Review-Fluid Mechanics
Example: Compute the discharge in each
pipe. Neglect minor losses.
I(
VALV6: _$
~
I,._) f6:?:tlAP.. J
25 ft
K1 == 0.359
K-f(L)(
1)
D
2gA2
Pipe
1
2
3
4
L(feet)
3,000
3,000
2,000
1,000
D(inch)
16
12
8
16
A (ft2 )
1.396
0.785
0.349
1.396
f
0.020
0.022
0.020
0.020
K=f(LlD) (ll2gA2 )
0.359
1. 663
7.649
0.120
39
FE Review-Fluid Mechanics
The Darcy friction factor for both of the pipes &shown is 0.024. The total flow rate is 300 m 3/h.
What is the flow rate through the 250 mm pipe?
A , =-rr- (
-)'--
(:) , I~
'I
::- o. D \ t(
\6Wb
~
...___;.......;....;....;;.,..__.,~
P,
S-)( c,, c,, ~,,?·) ~t..
+- (o , 6 L\ 4 M._)
\} z_
L2- ~\
= - Pc..'L
"l.
\I 1
"'
OL\"' Mz_
~~o ffiin dlameter
L, \J'"';
0 q
\(
-=- o.
-
~ -= (I,
A-(_::::§ (, 1. S")"l..
;........,.....:.-;..__---
{ 6$0 ~ ;
3.eio
('AL
:::
LLD, '1~
=
L l 'DL
V,
= (,
~ 50'1\}:0, IS°"M) ~ ~
( "32.5"""')(o.lYM.)
O'?~JL-
40
FE Review-Fluid Mechanics
EXAMPLE: Two reservoirs are connected by a
850 feet long 6-inch diameter pipe (f == 0.020). A
pump with the given characteristic curves is used
to lift water from one reservoir to the other.
Determine the discharge rate.
T
100 ft
t
pump
----,0--------:.-- ---
/80
90
/60
80
~0
140
-
+-'
(]}
(]}
'+-
'~
/20
-·
co
80
-0
(]}
I
~
(.)
/00
70
~-
t::
.-~
(.)
~
"I-..
Cl)
<< ()
00
~
~
CJ..~
~
50
-->'cf2(.)
C
(]}
40
·c:;
"+-
~o
30
40
zo
20
/0
"f-
w
0
zoo L/00 soo 800 /000
Discharge Capacity (gpm)
0
41
FE Review-Fluid Mechanics
What is the hydraulic radius of the trapezoidal
irrigation canal shown?
~ ,0 b
1l """
.,,.<-..-••. -•...•• ~
.• ~
•.••..~
... ~
.....~ .~ - ~ ~ ; _ _ _ ~ · · · · · ·
3 :rm: .. ...
. . . . .... ... . . ........
... -- ·-· .. . .
.
. . . . . . ···· · ···· ...
.. .
,
.
,
.5: rn
. ~ · ....... , .,··.-;-;..,--"-=-'-.......=c-.~
.. 3 m .·.·.. ·
1~............._....
·. ---·· ·-· ---· .. __
•···--1. ...
.. ~
····.........
. . '"'!"",. . . . . . .- - , ~ ,
fl/ p
!?...4-vL IC---
le.A P r i./ ~
- - -----
-
1..1
---
-
-
~
42
FE Review-Fluid Mechanics
Geometric Elements of Channel Section
example: trapezoidal section
~,
T
X - ~
;:., -
6~
l
20 ft
top width
T
wette d perimeter : : :
f' ::- ~ \
1Y-t- c,,
't..-
~ I ;;, • l\
-.I
(2-)( /;,. L)
i) + 2--oJ+
= l/ b' CJ~
¥
hydraulic radius
c.. 1w~.J
t,...ts,j.. _
w,r.
-
L/ .
I
--1-+--
hydraulic depth
43
FE Review-Fluid Mechanics
Example: Compute the discharge in a
concrete (n = 0.01 5) channel with the
previous cross-section and slope of
0.10%.
I/\
-
=
C). C) ( ...'.:::,
'.::::> =-
O . Io
\,L
/.
-=-
f?_e:>ul,J-/
;( =-
vr=>.S
PJ lb 7
ce>F~
c::> . 00 I
4 26
0. 015"'
44
FE Review-Fluid Mechanics
Example: Compute the normal depth and
velocity.
Q
400 cfs
·:. ,·
s
0.0016
0.025
n
-'/
- -X -;, 'f. = 2.. 'I
I - }I
,4 =
~z.o
+
(L;
-r =)"-J'- +(ly)'--
j
+ (i){2y)) (y )
J 'IL
/,l)?fb ( ~0 +Cio+L1y
0, /) 'I..S°'
2-
C)
-z./~
A \l-.
Q II\
-=--
A"'
tL.
=-
_
s 1/;_
(to
- (
J,
D
; : ~ ) ( 0,
l/ rs-1o ') (
2-D
'--b
( zo+(~"'+Y,>')\(y)
c
J
)
{ o. 0016)/..
\ --------
(2i{Y z_+ (z y{
-
--
+ C2.)/yL4lz...y)?... =
CJ~S\
;-.-0~ 1b >,,,<_
z._c, +z...o__:\Lz..')(zy').y :-(Lio
2...
p
Z 0
t-
'LO
t a.v'ATIU ,_j
$ 1"""- 'i"> '-_I.S:/-
,L
~ (y
t (tj/ ( 2-} T
_
/ 6 g,', z_
+YY)'/-=-{z..o+cy")y
z_
z_c +
(2.')J"J'-+'-ll- =-2:o4( 2)(·LZ.J()/ :::zo+ '--l'-\ 77.. y
45
FE Review-Fluid Mechanics
Example: Compute the normal depth and
velocity.
\-=- 20 -+(2_){zy)
Q
400 cfs
-- -----------(
s
0.0016
:
X
X
n
j~
--
·:. ~·
I
- - - ::c
J._
z
x~
\. 20 ft~
p~
1
T= Zo + Ljy
A
C '
C 1y
'-!:
AV-:>-:::
+z_<:>
p=
[<2..
C
C>
2 0-+
~I y) F
2 {'
0 )
2-- 0
:=-
y
C
A(Aj3:>=-
6 g . z_
20
<' :=:j Y '-+')'
-=-
fzy)<-t--y'-
0/
-
+ 2- J ) '/ 'L
=- 2. 0
-j--
'i . '11
y
(z.. "' + "L y) '/
1-/;,
"l/4
('Z o+z y)y [(-z.o+-z._y;'!)-= )b~.c.-J.t
p
\2o+Y~J1/
(c. c.o
~ ly)y]
?
y
c
L_(.) +L/ /
=
7. I
y
-
J~
46
'
z.. 1
FE Review-Fluid Mechanics
Q :::-
L(DO
::-
5
{\
l-t~
s:--
(!>. De:> \ ~
--
0 2..~
·-:::- C),
y_ - '/ .
"J__-~--
f.-:2.y
I
1
0-v\_
ic.. :5
p
.:=:
2.0
½_..
- (/ . lJ 1' b) ( o. 6 o
Q'-
5
=
lo) 1/t--
It:,&'. L
+ 2-·r
Y= 3, '"7
F,NT>
I
~{_
f,j,
G
1--t
( Tt-1 I.!,
I_)
I b ')
A~
:::- -
t
A=- (z. 0 +'7 'j)y
/-:::
z.o+
'-I
y
47
FE Review-Fluid Mechanics
Example: Compute th e critical de
pt h and
velocity for Q
40 0 cfs.
~
~
~,
\
___ L__ _
\.
j.
C
\_L-1 \ \ (._A. L
DF o-;---1-4
i3=- 20 ft
f:>---5
I
..,
y
y
I--:::- z. I
t 1
48
FE Review-Fluid Mechanics
Exam ple: A rectan gular concr ete (n = 0.013 )
chann el with a bottom width of 1 2 meter s
abrup tly chang es from a slope of 0.010 to a
slope of 0.005 . A discha rge of 25 m 3 /s is
flowin g in the channel. Deter mine wheth er a
hydra ulic jump occurs•
S-o
.010
Q
=
Co~?A\'c_ ,:
no,I'\
FL oc.v ~'(Pc?
~1...ov;;;..S
25 m 3 /s
49
~
F
FE Review-Fluid Mechanics
Example: A 15-ft wide rectangular channel has a
roughness coefficient {n) of 0.¢015 and bottom
slope of 0.0015. The channel discharges into a
river which may reach a stage of 10-feet above
the channel bottom during floods. For a design
discharge of 500 cfs, calculate y n' y c' and the
distance from the channel outlet to the location
1:2-where normal depth occurs.
~ ::.:~ ;<:-
,1 C
normal depth
It.
.. b,
Q-:--A?-
('
.:a:..
I
1
L--
V\.
A =-
p
~
(, ~ ~ ') '(
I>
y
~
C
-1
,s. :-- ' ., re
1-,:- tl_/
critical depth
S.u \3(-?._, -r-
1 u
!Dk
50
O
"
0
')
FE Review-Fluid Mechanics
Exampl e: A hydrau lic jump occurs in a
triangu lar flume having side slopes of 1: 1 . The
flow rate is 0.45 m 3 /s and the depth before the
jump is 0.30 m. Compu te the depth after the
.
Jump.
T
/
y
C>z_
M
=- -
SA
+A
~L
y -: -
CJ. &- 7
M_
51
FE Review-Fluid Mechanics
Example: Estimate the flow depth in the
downstream channel and the energy loss in the
hydraulic jump at the foot of the 1 00-ft wide
rectangular broad crested spillway for a
discharge of 2, 130 cfs.
- ~
~
\
1-Lf{t
L =- IDDt+-
Compute the depth (Yl) at the toe of the spillway:
-
Z..l'
--·----/L?O
0 ~
V·A
> _- V
y,
(1
7., t
-z '
= -.../
I
i
52
FE Review-Fluid Mechanics
Compute the sequent depth:
C-1
\}\ ==
l
O'l....
'-':>€
-y, -
21,5
c./.3
0
l]
=- \DO
l"'-b""-c..._,._lJ""'-..
_j
l=Cll _':::!_A.'2_''=.
f.ii,l)MC.0\\Jr"- A~E="
<;e~ vt:""--''
f°"~A L
\?~? Tr-\
(1,s::~D(Li; A,-JO Ane 17- ,H-E
1.
v,L,-_ 7-I ,J1 ,
I.
A, :::
-
l
•tt:t.. - c)... '/
(!Do')('{)
A2
.- (11x::,')(
y'-)
-
d- \]
"2..
-
+'/
I--= I
ALI..J.,.'/_:;;.
E
Z..3
f'J I~ 7
=
10 o( ,8, ~ )
~I
__:r-vl'\i>\
1--
Compute the energy loss in the hydraulic jump:
\} 2.-
A,
S
-£2--
53
FE Review-Fluid Mechanics
Example: A 50 acre watershed in Brazos
County has a curve number (CN) of 86.
Compute the direct runoff volume to result
from a design storm with a recurrence interval
of 50 years and duration of 24 hours.
54
FE Review-Fluid Mechanics
Example: A hydrograph representative of
a certain 60 square mile watershed is
given below. The hydrograph resulted
from a rainfall with a duration of 2.0
hours. Compute a unit hydrograph for
the watershed.
Given Storm Hydrograph
Time (Hours)
0
2
4
6
7
10
12
14
16
18
Discharge (cfs)
0
4,000
11,000
16,000
14,000
9,000
5,000
2,000
500
0
55
FE Review-Fluid Mechanics
Example: The watershed described in
the previous example is located in Brazos
County, Texas. A composite curve
number of 80 has been estimated for the
watershed. Design storm rainfall data
are provided below. Compute the runoff
hydrograph for the design storm using a
computationa l interval of 2.0 hours.
Design Rainfall Data
50-year recurrence interval
6-hour rainfall duration
Balanced triangular distribution over time
56