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MEEN 3320 Fluid Mechanics Homework Set #0 1-02 Problem 1-26 Name: Date: Determine the mass and the weight of the air contained in a room whose dimensions are 6 m x 6 m x 8 m. Assume the density ofthe air is 1.16 kg/m3. Answers: 334.1 kg, 3277 N
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These are solutions to various fluid mechanics problems for chapters 1-3 of the cengel and cimbala 7th edition fluids mechanics textbook.

### Transcript of Fluids Mechanics Homework

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-26

Name: Date:

Determine the mass and the weight of the air contained in a room whose dimensions are 6 m x 6 m x 8 m. Assume the density ofthe air is 1.16 kg/m3. Answers: 334.1 kg, 3277 N

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-32

Name: Date:

-rA . The value of the gravitational acceleration g decreases with elevation from 9.807 m/s2 at sea level to 9.767 m/s2 at an altitude of 13,000 m, where large passenger planes cruise. Determine the percent reduction in the weight of an airplane cruising at 13,000 m relative to its weight at sea level.

\Jl~,qh~ \~ ~V'O~'ON'tD~ -k> -Jlte Cjft:\J1~o~ . tACt~le~"ton- , t. CJ.~ #us fl.tR-~ ve&,K.Pl

• MEEN 3320 Fluid Mechanics Homework Set #0 I -02

Name: Date:

Problem 1-33 At 45 latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a - bz, where a = 9.807 m/s2 and b = 3.32 x 10-6 s-2. Determine the height above sea level where the weight of an object will decrease by 1 percent. Answer: 29,500 m

_[ 1

1o/o ~ o.qqm/JJ. we~~~. o.qqtAJs

w : ~~ ~ ~ c o.- ~ t > ";; o . r1 h1ffJ . ~ ( q tJ 1 /2 z -let 2. :!7) =- 0. CfCJ Ws -::: 6 Cf Cfml!l J ). ~ t1'\ oO IH J - 3- ~ 'I 10 ~- c 0 _

tE- 9 8o?f"'h'2 _, o.q ~ { q.f>o!JM~L) 3. ~z Jl'a-" /s"Z.-

-

-

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-34 {Connect}

Name: Date:

A 4-kW resistance heater in a water heater runs for 2 hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kWh and kJ.

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-37

Name: Date:

Based on unit considerations alone, show that the power needed to accelerate a car of mass m (in kg) from rest to velocity V (in m/s) in time interval t (in s) is proportional to mass and the square of the velocity of the car and inversely proportional to the time interval.

car nt~r.I : m. ~'(~V

-/::7~ : f-.

w - ~. ~~t/s:~ :: ~~ . . ( m~t ) ~I .s .

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-38

Name: Date:

An airplane flies horizontally at 70 m/s. Its propeller delivers 1500 N ofthrust (forward force) to overcome aerodynamic drag (backward force). Using dimensional reasoning and unity conversion ratios, calculate the useful power delivered by the propeller in units ofkW and horsepower.

___...

' . or

(ft..l,v : /DOO ~-~ I k'1l-=- (. ~ltr hf

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-40E {Connect}

Name: Date:

The boom of a fire truck raises a fireman (and his equipment-total weight 280 lbf) 40ft into the air to fight a building fire. (a) Showing all your work and using unity conversion ratios, calculate the work done by the boom on the fireman in units of Btu. (b) Ifthe useful power supplied by the boom to lift the fireman is 3.50 hp, estimate how long it takes-to" lift the fireman.

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-42 {Connect}

Name: Date:

Water at 20C from a garden hose fills a 2.0 L container in 2.85 s. Using unity conversion ratios and showing all your work, calculate the volume flow rate in liters per minute (Lpm) and the mass flow rate in kg/s.

b u tJ =

L(-J I Lpm .

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-43 {Connect}

Name: Date:

A forklift raises a 90.5 kg crate 1.80 m. (a) Showing all your work and using unity conversion ratios, calculate the work done by the forklift on the crane, in units ofkJ. (b) If it takes 12.3 seconds to lift the crate, calculate the useful power supplied to the crate in kilowatts.

~

~ooo w) ::: t 'C,J( ~

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-50 Solve this system of three equations with three unknowns using EES:

2x- y + z = 9 3x2 + 2y = z + 2

xy + 2z = 14 Problem 1-52 Determine a positive real root of this equation using EES:

3.5x3 - 10x05 - 3x = -4

Name: Date:

• MEEN 3320 Fluid Mechanics Homework Set #0 I -02

Problem 2-12E {Connect}

Name: Date:

The air in an automobile tire with a volume of 2.60 ft3 is at 90F and 20 psig. Determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. Assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant. Answer: 0.128 Ibm

0 Gr-eV -~-bl'Jtt 3

T!: qo cF /7-:: %r~'~

~ '1. ~ ~ ~ -z- + ~ uxt~ ~ ?o -t 1l\- . ~ ::: LnL ~ ~sl~ .

~v 0 Vhr2.1 ,;) M ~ ~ (3lfb~(2.6'0~ = ~ ((L)I}ocf J?'~b'",A (t#

\ ~ n Iii l"{? ( 44, b ~J(CA ) ( Q b o -t ~ )

:::.._ (o, ~not.t ri1fl\ . .r{>J , ) r WJ~ ) ~ - /(b~IA rt ,. -......

• MEEN 3320 Fluid Mechanics Homework Set #0 I -02

Problem 2-66 {Connect}

Name: Date:

Determine the speed of sound in air at (a) 300 K and (b) 800 K. Also determine the Mach number of an aircraft moving in air at a velocity of 330 m/s for both cases.

e " k/lT GtveJ

• b)

MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-79 {Connect}

Name: Date:

A 50-cm x 30-cm x 20-cm block weighing 150 N is to be moved at a constant velocity of0.80 m/s on an inclined surface with a friction coefficient of0.27. (a) Determine the force Fthat needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of 0.012 Pas is applied between the block and inclined surface, determine the percent reduction in the required force.

l! r o) 1;g . ~ _. . .''=~ w ~ l-t;u rJ . 'J ~ 0 l \ 0 I f,p ~ J Ffj I I /f - ~ 30 Clll. ~

v, .'----F, - ~to52() ~) F!(), Co5w - J? ~r .... :ro -!Al = v . J..) \?)

f!2 - JrN, c) (c) ~ (k) FN I (fl Srx) - t FN (S it1?1J rAJ- v

(-Nt ( Co> UJ -J' S~ fVI 1-0) ~\) :: 0 w tro /J ;ro

- - ::_ (!)r; N ~J-10- (~ ,J.1Sit.A!k;) / ~ . rsLIJ c\~'t1?-f sr vv'VU Fl ::::.. Ft- ~~V() + ~N I sflJ)'Z-Q "'- (o .)f( fbi( )ws'l/0 f !11'1 t;l/12, vo

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-81 {Connect}

Name: Date:

A thin 30-cm x 30-cm flat plate is pulled at 3 m/s horizontally through a 3.6-mm-thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3 m/s, as shown in the figure below. The dynamic viscosity of the oil is 0.027 Pas. Assuming the velocity in each oil layer to vary linearly, (a) plot the velocity profile and find the location where the oil velocity is zero

., l and (b) determine the force that needs to be applied on the plate to maintain this motion. G(t~) II ( \ ) ( ) _ () oC/ h\ ,.._ Fixed wall ~u3 ,~ ~'('-"' \ ~ \ j 1M - I ~..:..1 mm= :..' -~=:s;::::::::::;:~-......::F-

., , f ~ ) , b lM tM.. ~. 0 . Oo "3 ~ IN\ . 2.6mm -~--x ~ = 0.3 mls

J?) 'J:Mor . 1 ;;.. A/Js

fs~"'rl ";)_ .Av\ A\$" --

V - 0 ---It_, v- Vt.J

/tc2.-

Moving waU

(oe lf) ( o .!IJm~) tru(> -f:o ~ .... (,). =}, ~Sifr.. ({) ~ O(])h~ ') :::: 7. L?t\J + 3, oB N ~ fD .J'lAJ

• ()

MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-94 {Connect}

Name: Date:

A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 em apart, and the medium between them is filled with oil whose viscosity is 0.9 N s/m2 The part ofthe plate immersed in oil at any given time i\$ 2-m long and 0.5-m wide. If the plate moves through the mid-plane between the surfaces, determine t"t:i-e-fu-de required to maintain this motion. What would your response be if the plate\\'&@ from the bottom surface (h2) and 3 em from the top surface (h 1)?

o ."13M Staoonary surface

M ::- 0 . I A}5/w..~ r As::~~xo.s~ I -:: /vn;; F

F,>u., tl - N\ As ~ (J' '1 ~ Sj.., I ( I,.;' Y;~~ ) Stationary surface

::- us-,A) -f&b,r~-

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-101 {Connect}

Name: Date:

Consider a 0.15-mm diameter air bubble in a liquid. Determine the pressure difference between the inside and outside of the air bubble if the surface tension at the air-liquid interface is (a) 0.080 N/m and (b) 0.12 N/m.

C\) \)5 ~ OtO'f;ON/VA t::.f 2(D,O~o'N/:j7l

biA..bbt.e :: ~ lf, S y 'o -~~~

~c o , 10. N 10-. ) II t; Y 1'0 '1, 1M,.

• er~

MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-109 {Connect}

Name: Date:

Contrary to what you might expect, a solid steel ball can float on water due to the surface tension effect. Determine the maximum diameter of a steel ball that would float on water at 20C. What would your answer be for an aluminum ball? Take the densities of steel and aluminum balls to be 7800 kg/m3 and 2700 kg/m3, respectively.

. T. ') .f'\ 0 - 1/V c.

WQ.fe.r J e - 0~co \C~ ( Vv\

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-34 {Connect}

Name: Date:

A 4-kW resistance heater in a water heater runs for 2 hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kWh and kJ.

~ !Bt~A-L = (lf kW )(z kl[) ~ B kWIA

'0 ~),!J lA II !yWIA II

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-40E {Connect}

Name: Date:

[5 QU-..) \IV'- (}...A.A ~0 \ \).__,--\ t 0-yt ~

The boom of a fire truck raises a fireman (and his equipment- total weight 280 lbf) 40 ft into the air to fight a building fire. (a) Showing all your work and using unity conversion ratios, calculate the work done by the boom on the fireman in units of Btu. (b) If the useful power supplied by the boom to lift the fireman is 3.50 hp, estimate how long it takes to lift the fireman.

~ t~ ~o ze,o~ 5.SlC6s g 60 ~50 ~-~ /s

Oore~ ~ -t ~~ e&fc~-e "--~~LJJvv~6? s too'1o Q f~,'d.fUJ\~ ut ~ kjd 1["-vJ ~~ l ~~~ ~cJ.Ao.M(

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-42 {Connect}

Name: Date:

Water at 20C from a garden hose fills a 2.0 L container in 2.85 s. Using unity conversion ratios and showing all your work, calculate the volume flow rate in liters per minute (Lpm) and the mass flow rate in kg/s.

M ::: ~-t/ : :=? -> Go fo T oJole__ A--~ 1

ft"1e. ?t.f-z L) Use.. Sad- :S.\bu__~ ?

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 1-43 {Connect}

Name: Date:

A forklift raises a 90.5 kg crate 1.80 m. (a) Showing all your work and using unity conversion ratios, calculate the work done by the forklift on the crane, in units ofkJ. (b) If it takes 12.3 seconds to lift the crate, calculate the useful power supplied to the crate in kilowatts.

UJ ::=. SFls = (Vv\j )[s.'- -s,l = VVtjAS =- (crol)kj)(9.2:>(~~~)(t.e,Ow. ) - l~qB.o Ltq ~:.X 2-

( q lJJ. DLf_q ~- Jh(;z: { JJ lT !. S9

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-12E {Connect}

Name: Date:

The air in an automobile tire with a volume of 2.60 fe is at 90F and 20 psig. Determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. Assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant. Answer: 0.128 Ibm

1/) \) ? e ~ 'I J e.~ C-c V- c.:. L 0-Jv.) 1v p t.f eJ \c_t ~ o .. '1M o LVv'\, + o+ V\A&-.(.C crt CA., \[" tv ~ e o.c\c:\ed ~ p v- ::: W\ f?_ 0.:1\/ \ P, : '2. D pstj + P~ ~ 3 '-/. ~ psi

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-66 {Connect}

Name: Date:

\3cu.')w..ON\ S::.o l \.d \ D)'\ s

Determine the speed of sound in air at (a) 3 00 K and (b) 800 K. Also determine the Mach number of an aircraft moving in air at a velocity of 330 m/s for both cases.

/DOD VU-z..-

f v--tJ"V'A SE\$~ ~ Adu..oQ t_c4--r, 3ook.. -= I .I-/ 0 -z_ v~, 30o~ = 3 ~t-.4~ 'M,(s 3ti1-~ 58~ Mf> -"-> --=/

~~'~I ?Pf/- ~ /. 3_S'-{ -;:;") Vs, ~co (t_ =- 551-. 6 Lf 2- -=-> 55 t-. 0

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-81 {Connect}

Name: Date:

A thin 30-cm x 30-cm flat plate is pulled at 3 m/s horizontally through a 3.6-mm-thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3 m/s, as shown in the figure below. The dynamic viscosity ofthe oil is 0.027 Pas. Assuming the velocity in each oil layer to vary linearly, (a) plot the velocity profile and find the location where the oil velocity is zero and (b) determine the force that needs to be applied on the plate to maintain this motion.

Ct.lu -

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-79 {Connect}

Name: Date:

A 50-cm x 30-cm x 20-cm block weighing 150 N is to be moved at a constant velocity of0.80 m/s on an inclined surface with a friction coefficient of0.27. (a) Determine the force Fthat needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of0.012 Pas is applied between the block and inclined surface, determine the percent reduction in the required force.

0-.-) 'ft>' =D l=c.o;e - ~~vlc:\-c~- Mj S~vtB -

t0 -= f-t~rc / I rr.,.c..-[ 5 ee- EES 5Dlu:h'uvt~

• File:P2-79.ees 9/9/2013 3:06:35 PM Page 1 EES Ver. 9.475: #292: Mechanical Engineering- Marquette University

150~

Problem 2-79

A 50-cm x 30-cm x 20-cm block weighing 150 N is to be moved at a constant velocity of 0. 80 mls on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of 0.012 Pa-s is applied between the block and inclined surface, determine the percent reduction in the required force.

Given:

J..lfriction = 0.27 J..l = 0.012 [kg/m-s]

e = 20 [deg] V = 0.8 [m/s]

A = 50 . 20 . I 0.0001 . ~ I cm2

Part a) Dry Sliding of Block with friction

Sum ofF in x-Direction

Fa cos [ 9 ] - F friction - m g sin [ 9 ] = 0

Sum ofF in y-Direction

Na - Fa sin [e J m g cos [ e J = o Law of Friction

F friction = J..l friction W = m g

Part b) Sliding of Block with oil and viscous drag

Sum ofF in x-Direction

W = 150 [N]

= 0.4 . 10.001 . mmm I

F b cos [ 9 ] - F viscous. drag - m g sin [ 9 ] = 0

Sum ofF in y-Direction

m g cos [ e J = o

Law of Viscous Drag

g = 9.807 [m/s2]

• File:P2-79.ees 9/9/2013 3:06:35 PM Page 2 EES Ver. 9.475: #292: Mechanical Engineering- Marquette University

F viscous, drag

6V =V-0

tN t

Reduction in Force Calculation

SOLUTION

Fviscous,drag = 2.4 [N] ll = 0.012 [kg/m-s] Nb = 160.5 [N] V = 0.8 [m/s]

No unit problems were detected.

jlfriction = 0.27 t = 0.0004 [m] W = 150 [N]

/';. V = 0.8 [m/s] Ftriction = 4 7.8 [N] m = 15.3 [kg] Na = 177 [N] e = 20 [deg]

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-94 {Connect}

Name: SoLU\AAtu/\. Date: Sol vci-fOY\.~

A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 em apart, and the medium between them is filled with oil whose viscosity is 0.9 Ns/m2. The part ofthe plate immersed in oil at any given time is 2-m long and 0.5-m wide. If the plate moves through the mid-plane between the surfaces, determine the force required to maintain this motion. What would your response be if the plate was 1 em from the bottom surface (h2) and 3 em from the top surface (h1)?

Stanonary surface

~) h 1 = ~ -z_. ::; '( z__ ('--I (!.~) = 0 . 0 z. I.N\. E ~ "'- A\/ F. , = 1: A- = .J..AA d> =-AA ~ V l5L- ~

V= 5 mls F

Sta ionai)' surface

OJ..AS.

Fvtsr, +of ;: (o.q "-'fw.. -'- ) (1.D """) (D. f, ""\ [6 - O ""!!.] .,. YSD tJ 0 , 0\ ""'

Fv\~,b~~(b.q~)l-z.oM-)(o.s~) [_~-o ~] /5o0 D 03 W\

CMAS .

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-101 {Connect}

Name: Date:

Consider a 0.15-mm diameter air bubble in a liquid. Determine the pressure difference between the inside and outside of the air bubble if the surface tension at the air-liquid interface is (a) 0.080 N/m and (b) 0.12 N/m.

Fcr.t - b. p A = D

z\J -

LP = R-

CA) \f = o . DeD NfW\ ~ Q;. Y't.~ = o.o+~ V\AW\ == l.t;x;o-sM

L j:J = ( o, o ~o yJ r wt ) z. ~ z r 3 3 . -n Po-- == L P ().)A~. ( f- ,Sto-sw..)

• MEEN 3320 Fluid Mechanics Homework Set #0 1-02

Problem 2-109 {Connect}

Name: Date:

Contrary to what you might expect, a solid steel ball can float on water due to the surface tension effect. Determine the maximum diameter of a steel ball that would float on water at 20C. What would your answer be for an aluminum ball? Take the densities of steel and aluminum balls to be 7800 kg/m3 and 2700 kg/m3, respectively. .

f~-r 16 tJ e.--\--e:{ \A.A_~ \1\Q_ ~ I 6-v-7-e sf d \ Ov\M e_ ~v ---"-rL ___ 1.Gji D ' '? ''6tl__\.l 11 tY--~ w\l~ .\ll,)a..+ ChA 'v.J~-e-v \-tz.D i d \.JJ2.. to Su-.'f{lk..Q. +-~~c OV\.J p~-ctov M 't\J-.j (.),__ ~\I ~ "() o.J~ Fs-r = t lAA

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 1 | 8

Homework Set #1 Date:

Problem P1.10

The Stokes-Oseen formula for drag force F on a sphere of diameter D in a fluid stream of low velocity

V, density , and viscosity is given by:

22

16

93 DVDVF

Is this formula dimensionally homogeneous? That is, what are the dimensional units of the first and

second terms on the right-hand side of the equation and are they both units of force?

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 2 | 8

Homework Set #1 Date:

Problem P1.13

The efficiency of a pump can be defined as the (dimensionless) ratio of the power developed by the flow to the power required by the pump:

powerinput

pQ

where Q is the volume rate of flow and p is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure rise of 35 lbf /in when its flow rate is 40 L/s. If the input power is 16

hp, what is the efficiency?

Note: 1 L = 110 -3 m; 1 hp = 745.7 W; 1 W = 1 J/s and 1 J = 1 N-m.

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 3 | 8

Homework Set #1 Date:

Problem P1.39

Knowing for air at 20C from Table 1.4 (page 26), estimate its viscosity at 500C by (a) the power law

and (b) the Sutherland law. Also, make an estimate from (c) Figure 1.7 on page 27. Compare with the

accepted value of 3.58 10-5 kg/m-s.

{Hint: For air, Tc = 132.4 K, pc = 37 atm, c = 1.9310-5

kg/m-s}

IMAS.

Tt- s S~: llct -d!l ) (!!~Vr \r .. ( r ~

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 4 | 8

Homework Set #1 Date:

Problem P1.48 A thin plate is separated from two fixed plates by very viscous liquids 1 and 2, respectively, as shown

in the figure below. The spacing of the plates, h1 and h2 are unequal, as shown. The contact area is A

between the center plate and each fluid. (a) Assuming a linear velocity distribution in each fluid, derive

the force F required to pull the plate a velocity V. (b) Is there a necessary relation between the two

viscosities, 1 and 2?

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 5 | 8

Homework Set #1 Date:

Special Problem SP1.1

The information on a can of soda pop indicates that the can contains 355 mL. The mass of a full can of

soda pop is 0.369 0.410 kg while an empty can weighs 0.153 N. Determine the specific weight, density,

and specific gravity of the soda pop and compare your results with the corresponding values for water at

20C. Express your results in SI units.

'~ McLMA,~u.\\ =- 0. '-t 10 \:-_j ((I\.) -0.,A = 3 s s lv--Q_

.M Ctw-1 ~ll = 0. '-1 I e l~ w t~Lv~., = 0 . l ~ 3 tJ F~\\~ --. OJ ilM. s l1 ( fc;: o ~ = c\1-SD ~ (tM?> Sb~ D.C1..t.tL\

?...-ole~~~ ~v..3o-.'("e~ ~Ddo- \ s ~f'e d.Su.A.s ~ ~ wed."

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 6 | 8

Homework Set #1 Date:

Special Problem SP1.2

A 1-inch-wide space between 2 horizontal plane surfaces is filled with SAE 30 western lubricating oil at

80F. What (net) force is required to drag a very thin plate of 4-ft area through the oil at a velocity of

20 ft/min if the (thin) plate is 0.33 inches from one surface?

{Hint: Use = 0.0063 lbf-sec/ft for SAE 30 oil at 80F}

C::~=============:::J - F. \1

2 f.:~ f. -rt:~ = AV(~ .~. ~) = AV ( ~ ~ ~~ ) = A-Vbio).

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 7 | 8

Homework Set #1 Date:

Special Problem SP1.3

Water at 20C stands in a clean glass tube of 2-mm diameter. What is the capillary rise of the water in

the tube?

~e_.(o.,-!M (}. ..\v"..v\.~ -.a.J.. w; t\t.- ~ .. ~.Hv: ~,...... d- H~ v.J ~ r I' o ( \..1-AVI lA

I,

Y (z.1rR-) tos e - lM:! =- o = ') viA '" ~ v "' ~ (Jr R. ... h )

Q-0-lfVo/V\j e. +v coso = I

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS 8 | 8

Homework Set #1 Date:

Special Problem SP1.4 A car tire having a volume of 3 ft contains air at a gage pressure of 35 psig and a temperature of 70F.

Determine the density of the air and the weight of the air contained in the tire. In racing applications

average tire temperatures often exceed 200F. Assuming that the air in the tire reaches this average

temperature, calculate the tires gage pressure under this condition.

C., I v tU.A. o~ +f f.) t c. -::. '"3 ~ ~ ~~~If'Srj T~t r-e :. i-O., f

-:."'/ ~tl~,c....::. '1c;+ 11./b~b f~)CA. '=-'-19 .b~ bfs.i6._ ? lt'-re.lo.. = T0+-'1Bcr.(ot I.R. =- S"Z.~.Io-:t R.

Ma....v- =- ~ = L-{q . t,Cf" psco.. 3 \~~ l~w. '/L 5 29 . (g '=l VL D .J'fo~ ps~ct ~ r

• MEEN 3320 Fluid Mechanics Page 1/18 Chapter 2 Example Problems

Example Problem 2.1 Lake Michigan, a freshwater lake has a maximum depth of 250 meters (see figure below) and an elevation of 177 meters (581 feet) above sea level with a mean atmospheric pressure of99.2 kPa. Estimate the absolute pressure in kPa at this maximum depth.

l"tiV

• MEEN 3320 Fluid Mechanics Page 2/18 Chapter 2 Example Problems

Problem P2.11 In the figure below, pressure gage A reads 1.5 kPa (gage). The fluids are at 20C. Determine the elevations z, in meters, of the liquid levels in the open piezometer tubes B and C.

Cih.J .... re. "' Pa:l-w.; o

f'- = p~ " 0

lm 0 l._

Jl Air

Gasoline

Glycerin

8 c

' 'i.

I II f lc_. I ~=0

* " D&-e.-,.,.-~V\Il.. : =ts ~ ~c.. Vv~~~ ~ ~Jlv-oif~k ~-.rw.vl(.o.. j

J~ l

~!"Df~-rtt ::> '0'. ~~ fl,t,ft?~ tJ/u/~ jiJ" 1, l~O "#~ => ~f" ;ri>1JO-f "'{w. (lsoo t~)t { tt-~'iw.'~>)('Z.w.)f (G:t"bf 10/MA~)(Lr.-...\ - (~,b~~w.~) ll8 -I ~) ~ D fJ~e]

L> S o[ue.. k le -~ 'la ~ z .~ 3 1M.

fA-t ~AV- (z...,_) t O'st-s (t.5~) f ~If- (lw-.} - ~If' ( e~) =: tl ::. 0 [~~~ 1 Qsoo p.._) -+ (I{, fb v{w~ )(-z C&A.) -t { br b(Q~ OfKl~ )(t , 5 M) + ( IZ, '351 ~~~) {I -i.e... M) -= D

0-MS.

• MEEN 3320 Fluid Mechanics Page 3/18 Chapter 2 Example Problems

Example Problem 2.5 {page 80} The gate shown in the figure below is 5 feet wide and hinged at point B, and rests against a smooth wall at point A. Compute the (a) force on the gate due to the seawater pressure, (b) horizontal force P exerted by the wall at point A, and (c) reactions at the hinge B.

L1iv.w..~ Se..a.wcrl-t.~ wiH.r-- (;... h~ "'"~~c. 8~e. ~IJ) ; (pt.{ lb+l+t~ 0 t\-:. I~ ~ lJJ = b (-t H~'" cz, Y- ~ tC; ~ ~ ~\ I ) ft'~ 'o 0...) f o..d 1'1\~ ()"111. -\-WL j ~e_

b)~ to~~'~e "? ~ \ V'\. \ k lb4+- P~"+ -\ l

• MEEN 3320 Fluid Mechanics Page 4/18 Chapter 2 Example Problems

Example Problem 2.5 continued ...

~tore toe C()..AA s I.JJvv'-. ~ 1 fu !t~~c'wt tk (~ ~s+ 'oe d-e.-+-e~~"v-M~!.

lAJ L3 1 XX: -= 'T-2._ f f~ L l~ f~ e:){ = ( S -C-1 } ( \ o ~) :. :: t...(l fo . lo 1 {+ ~

(?...

~CP ::: - l (ot.f lb%; "\ J ( ~~ { fo . ~ i (+ \{) ( 0 (o ) ( 3 8/t'CO lk.f. J

l'~\ ' p ' ' ' ' ' '

:r (p(;

'S'tv..e -= /Of.+. '::: D b

lj c.~ -=- - o. 4 1 t- -t-t- ~ J = 4: (to -'+) - ~L~ =- '-{. 5 ~3 {4

1 'M fS = 0 v - FQ tf>(s~li\e)L -=0 - -(38,LLOOihf-)(t.t.s'b3\-t) + -p ( ~4) ==D

-=> p ~ z q 333.3 tto+-

.._ P + 12B+\ + F S~V\ (;) = 0 = (-29,3?,3, 3 \~4)+ 'Rett -+ (32/100 &~) ( ~J ~ 12~ = t..P, 2'\""?:>.3 lbt-

J2~,v - f CCbe = 0 :::- \2~V - [3~'frolht)( :11-) . ?> ~'8\J = 3 o, 1-zo l~-f-

• MEEN 3320 Fluid Mechanics Page 5/18 Chapter 2 Example Problems

Problem P2.52 Example 2.5 (page 80) calculated the force on plate AB and its line of action, using the moment-of-inertia approach. Some teachers say that it is more instructive to calculate these by direct integration of the pressure forces. Using the figures below, (a) find an expression for the pressure variationp(;) along the plate; (b) integrate this expression to find the total force F; (c) integrate the moments about point A to fmd the position of the center of pressure.

Ra... pr-ti

• MEEN 3320 Fluid Mechanics Page 6/18 Chapter 2 Example Problems

Problem P2.65 tree Gate AB in the figure below is semicircular, hinged at point B, and held by a horizontal f6t Pat point A. What force Pis required for equilibrium?

F=ok~6A A == t (trR.1..)-= ~-rr(3 """y-:: 4.6rr ~t. r, ~ cc e~ f.)l~ \\ .... o t ~C(."'::: t; ~ + (3- ~) tf}2. 13~

-:::: 6 W\. + 3 W\. - Lf ( 3 ~) ::: ~. +Z+ wt..

f ~ {Ci 1 CO(i~~~~3)(L..t-t:+~)(tq.r31-AM"'-) %q3z 1 &lo rJ

~ =: _ ( ~ .tt>'rb5to w.:) ( l) c~ lto. =iZt-w..}(IL-1. /3-:t""'~) ~ e~ -::: - 0, D 't '3 Lf '1 W\

2.,_ Me:, == o -to J e--\-ef'~\"'"e.. f ". ~;

{ VevHcJ..\ ~ltd~~

• MEEN 3320 Fluid Mechanics Page 7/18 Chapter 2 Example Problems

Example Problem 2.7 {page 83} A tank of oil has a right-triangular panel near the bottom, as shown below. Omitting Pa1m, find the (a) hydrostatic force and (b) center oforessure (CP) on the panel.

{., t'v l i'sL.)

0' 0: I : i-, ~ '1 IM..~-\-v-J 1 ~ ~

• MEEN 3320 Fluid Mechanics Page 8/18 Chapter 2 Example Problems

Example Problem 2.7 continued ...

f =- C1,C2J10 ~,1M!>)( ct ~ )( 3 &> ~"L) ~ Z1 5'i'Z, ':1-5 2.. t0 ~ 2 -5'-/Z. tt..\J

b) lo~oJ.e C. P re.\.,_-\hJe.. h:> Cb u.s~nj ~~f -.t :J~p U = - r~e Lx-JC - 'f ?.~f7 I~')(

~~f - r Pc~ A r

_ 0' ~ ~e r .,j - F

• MEEN 3320 Fluid Mechanics Page 9/18 Chapter 2 Example Problems

Problem P2.84 Determine (a) the total hydrostatic force on the curved surface AB in the figure below and (b) its line of action. Neglect atmospheric pressure, and let the surface have unit width .

.tc\-C.N" ~ :, r f>V.- ft1--'r -\, 0 t \ :: (~, ~~IM.~ )(l ""-) ( I - q(l)'~}

F"l. = F"'&. ~ F""t-t Tf"e~,VV\. o+ F ~

-t Nv\_ e =-- 0 I Frt

- 1, 35. 25 f.)

~ '1-/3'55.L~ _ ).S !.-/,'10'3 , 5

l> e = s1o-3 o

B

Water at 20 C

OMS ..

• MEEN 3320 Fluid Mechanics Page 10/18 Chapter 2 Example Problems

Problem P2.74 Find the height H in the figure below for which the hydrostatic force on the rectangular panel is the same as the force on the semicircular panel below.

Sol"'-*lwt : !..-;> W ,..\f~ ~ eb ~'\:1t-{ ~ ~ ~

-Ccq-c~ 0"\A. ~~ ~()Me.-\. ~ ~

• MEEN 3320 Fluid Mechanics Page 11/18 Chapter 2 Example Problems

Problem P2.82 The dam in the figure below is a quarter circle 50 meters wide into the paper. Determine the horizontal and vertical components of the hydrostatic force against the dam and the point CP where the resultant force strikes the dam.

.t\o~ I~ Av..~~?( c;.. r\'\ =- r~-~!.C ~ce:, A ~~0~

wl t, ~ cr ~=t ~,w.'!. lito

~ tL1 ::: I D IV\. I'L . = (6D ~\(zo\M. \ !"" rvo ~ ..... I ooo ""'-'L.. I

v ~-r~l eJ Jb.4s't ~ 1'L o torc.e o\-~ wo~\(" fu... cok\IAJ do1..0v-.

F ~ \N\ ~ ::: ~ ~ = 1+1-

w) V ~ ~ ( rr~'LL) ~ ~ (zo~t(so-...) = 5DDC>1Y M~ = IS, =1-D-=t. q low?

F, =- ( 1 I 'best ~,w."":. )( SOQJf" w:) fv -::. 154, oll+, qcp; .co ~ ::= J c; Lf MN :::- tv

itJM.e =- :: ~ G =- 51.S o ~ C P @.. 10,1-YM V'l\$k\- j 3 .{'3 \M.. o...\oove.. A

p = 0 {/

• MEEN 3320 Fluid Mechanics Page 12/18 Chapter 2 Example Problems

Problem P2.83 Gate AB in the figure below is a quarter circle 10 feet wide into the paper and hinged at B. Find the force F just sufficient to keep the gate from opening. The gate is uniform and weighs 3000 lbf.

\-\olf'tZOl,th~.Q \\jdvo sf-~t'c.. ~~tree_ F\\-= Pee:, A f110j = ( ~+ rl\z.(i~G) Aro1

~ FH ~ (~l.lf ~~)(4~+)(?>~XID4) f'"" ':: I q I q fcB l~~

L oc.-td-e. -tk ftov IwuluQ f u..s+ ck C-\) ~ u .... - r -st-"' e I~'l' jc.p

~

F

Water

B

~

C.0 ~ Yep T f.r-

Jb+t

V ~;.t+k J .fk~j v-o

• MEEN 3320 Fluid Mechanics Page 13/18 Chapter 2 Example Problems

Problem P2.83 continued ... Fv

1 ==- ('+!, ;_ ((pZ.l.f 1"Y.w-~){B -t+)(e-

• MEEN 3320 Fluid Mechanics Page 14/18 Chapter 2 Example Problems

Example Problem An aquarium has the phys ical dimensions shown in the figure below. The aquarium is filled with water (y = 62.4 1btlft3). Find: (a) the pressure distribution on the curved window; (b) the resultant force acting on the curved window; (c) the line of action and (d) the point of application relative to point A.

(o.) ? "e:>su-...r e. d',.:;fr ;k ~::heW\ 01"-.~ C.\}.N v-c..l W\~ z:>\..0 '

A '1 E) 7m r~ ~~k e_u. ... v~~

. ~ -re.s'-'--'\,~ \o.r-c.e. o...c*s ~~ wkv"e ~ \ 1'Nl.. ck ~-h\':M

4-t"v-rtCM.hJ A-vtJjs::s +\\ = fcG A-pro~

~ (tf+ r~-e~)Ari F\i ~ ( ~~ ~-=~- "'fw.3 )(c:;M -\-liM )(IZIAl)

-:::. +o&,JoY N

• MEEN 3320 Fluid Mechanics Page 15/18 Chapter 2 Example Problems

Example Problem continued ..

\le~'c~\ ~Sc> SMO..ffl\ed bj tl,q_ l--.J.l.,o~+d-t'c.. p-r-e~{;u..lf'-e., 1.0e cet.\~~&~..*e. ~ V..e\1-Ht.U ~-.rce.. ,1-S (pt.L:!-elf' 0-~ove ~ fj r~-te .

(.

'\J=O-D

fv ~ Y Qz~)l6~)(?M iJ t ot [s. \15 w-~ ==-

• MEEN 3320 Fluid Mechanics Page 16/18 Chapter 2 Example Problems

Example Problem continued . ..

M,~ X, ~ IAA7..~ Z1..- .f M3j ~3

f.v, j z, ~ i ~ j z'- + :f Vi ~rxJ r v, -r-, = ~~ +~2- -x'l- + b'f ~ X-3 A 1t- ~ A ,_ --t~ -t-- ;4-, 'X-3 I f

-=/ if= 0 ,4. i LAAM1 J-y+k~ ~ ~(kl. )(~R) = (R.~-1~'-)x-z.. t (~R.~)( ~- ~) ~ L s~f1W ~ Solve k -t .. : I'll. - "70 '~ft.,

... . JV"l,. - ' - fP U' e. 21..(- h11-

\=',

'tA-rA- = tt, r. +- ~'1-r"l-~+ (~5Z,'ZG,f31J ) = (~z""')(5B~4z,oAJ)-t- {R -~-z.)(5o,~o

• MEEN 3320 Fluid Mechanics Page 17/18 Chapter 2 Example Problems

Example Problem 2.10 A tank 20 feet deep and 7 feet wide is layered with 8 feet of oil, 6 feet of water, and 4 feet of mercury. Compute (a) the total hydrostatic force and (b) the resultant center of pressure of the fluid on the right-side of the tank.

"~l'vllc ~ +~~ ~~ ~ fo-.vts WVvJ. CMNJ..-1:Z.c.. -tv ~t-v.d ~ kJA-ro-

• MEEN 3320 Fluid Mechanics Page 18/18 Chapter 2 Example Problems

Example Problem 2.10 continued ...

~ = ~ '-''vl ~ -to~ ~ .. ce.. e.->Ce\f4-e-d. oA 4k ./tffk:t .:;;J.e. o(_ ~ -\-~I

Fw ~ /OC6/6th lbt- tw.~. 10 !otd-e. ~ re.-stt.l-\-IM.d- c ~-\-~v- ~ p.r~~u..'f"'.- 1 ~(...IMA ~

VvutrM.~ U.e_. ~v-~~ ~e.s +k,t.-J dl-s~-e +o ~ c.~ ) o\-e..c-ck a{ ~ ~v--ee_ r--v+s o1ot..U-~ 7!- ~:~ .

r~ 1;1!~ ~ .2 ~ ce-r,~ : rl ( k~t?,t + ~~~,, \) + ~ (1Accv + 13 4) lloB,S II.?\~) te.~ - 1, 51+1 (olb . ~ ~-l~

~ ~ap ~ 13. C('{fob f.t iloJow =l-)

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 1 | 12

Problem P2.7 {6 ed}

The deepest known point in the ocean is 11,304 meters in the Mariana Trench in the Pacific Ocean. At

this depth the specific weight of seawater is approximately 10,520 N/m (at the surface, 10,050 N/m). Estimate the absolute pressure at this depth, in atm.

.t{ .. ~ { 0 S IJf...,. ~

='> j:>t. - f, "' - ~1Z.( IC>1 'ZSS 0/w.1) J ~ P1. - (lot. s5o u..l'o. ) = - (lo, -z.s'S ...,/,,.::;> p .. - f', -:::: J01 o~o *' -t ~(o.o'-l ss ) ~ t. {, A ;- l(l,.3(o MP.._

fz. ~ lit,, 3lc31 /09. Pc... P-z "" II 1., . 3 lc M p.._ w.

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 2 | 12

Problem P2.12

In the figure below, the tank contains water and immiscible oil at 20C. What is h in cm if the density

of the oil is 898 kg/m?

A SSvvv--tk~s :. r~ = F.b = rcJ!-'M "'- 0 ~d~e ~ ~ ~'IP =- 1 t>oo ~l/ w-"!>

b --- - .

6cm (/

- - - - L-----y-----'

12 em Oi l

--- -f------1--~ - - --8 Water

Scm

-- - -~-----'

o + u ooo ~rw. .. )(tw ~~- (~~+1M ) - (~1~[/~t~~Jt~.sct u1..)( ~ ~) - ('ms~f~c)(?.wtn~~()~) = D

_,

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 3 | 12

Problem P2.32

For the inverted manometer in the figure below, all fluids are at 20C. If pB pA = 97 kPa, what must the height H be, in cm?

~!.

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 4 | 12

Problem P2.35

Water flows upward in a pipe slanted at 30, as shown in the figure below. The mercury manometer

reads h = 12 cm. Both fluids are at 20C. What is the pressure difference p1 p2 in the pipe?

~+o..\f-+- vA~I.,._ ~ kJjvo

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 5 | 12

Problem P2.45

In the figure below, determine the gage pressure at point A in Pa. Is it higher or lower than atmospheric

pressure?

P:urn

Air~==:::'

Oil,

SG Oz l 40cm

I 15cm

_1_ J Mercury

~,VV-~ ::. 17., I 00.1-~ PCA...

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 6 | 12

Special Problem SP2.1

A 122 gram, 25-mm-diameter, 30-mm-tall brass cylinder slides slowly down a ramp with a constant

speed of 3 cm/s as shown below. The 0.6 mm uniform-thickness oil layer on the ramp has a viscosity of

0.1 N-s/m (SAE 10 oil @ 20C see Figure A.1, page 824). Determine the angle, , of the ramp. {Hint: Assume a linear velocity profile}

'M -::: o . n:z... tt:.~ d. = 0 . 02lj \N\ t ::: b . 0000 lM

t\$. ..Q ':. 0 . 030 ~ )J.:::; Q. \ ~,s?-

M.

V-=- Q. 0 ~ W..(s l\$ ~t?f~ t cle'[~ e: Z l="x ==- 'M. C....x :::: o

- f;As~ ~ M!S~~e -=> ~l\.e ~

~j dv ~ t:"v\sc._ = '[A ::: AAA- J j

1 ::1\ j2.. f\ 1..( ~ A ~ ~ ~ ~ = "Cj (0 .025 1M) :: (..L{OO ~ A ::: o. ooo~ \\,~ ~ (D I fJ-\$/w.,_Xf!tao.ttorK}(o.o; -o 'IAr. \ (o.ooo ~ow..)

-> Fv ~?c.~ 1~ tJ ~ o. OD2..'-/6L.{ 0

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 7 | 12

Problem P2.55

Gate AB in the figure below is 5 feet wide into the paper, hinged at A, and restrained by a stop at B. The

water is at 20C. Compute (a) the force on the stop B and (b) the reactions at A if the water depth h is

9.5 feet.

N.e~kd- P..A\1\A {~II' fH'~u-re. I!JV.. 1 L b~\... -:,." ~~ al- ~IJ..; e ~it.l> :: {p z . !.[ 11414 2- h

L \f I ~=~MfO~ A ~cc., -: 9 . S Ct - ~ ( L\ ~) =- 1 . S +T F~trJ.~ ~ (~z. Lf ~~~7~ )(?.SC4 Xzo .l-t1.-)

=- q/ 3"'o t~.{- r~

~ MA -: 0 +o ~* ~~ y + F ( z 4 + ~

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 8 | 12

Problem P2.76

Panel BC in the figure below is circular. Compute (a) the hydrostatic force of the water on the panel,

(b) its center of pressure, and (c) the moment of this force about point B.

c.~IJ'C.U..\.~v- bcde w/ 1J = 31M. f.rt, ~= I. r M 1.0~A.t-o+ iJJ fw? )( ~ + -H~ L .... ) -;; lA. -e ( ~ )(3 w. '1.. ,.. (t't,t~o~ t-> j...,.~ \( :,. ~ti.{'+ZO 1M) ( 7. 0 (o2>S S w..'L) -:::. ( '3!>1 f6o~ . + ~~A '1. oro~ss 'M't.. \ ;: z sB, q ~s .y rJ

C.u.J e'f o~ ~ressv--lf"~ --:t

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 9 | 12

Problem P2.86

The quarter circle gate BC in the figure below is hinged at C. Find the horizontal force P required to

hold the gate stationary. Neglect the weight of the gate.

p Ass~~ G. t.d:-e. is LN\\..\+ \0~d+\t-.. \"'-t-o ..fk ~o._r~" c t..e .. b::: t \M)

" tVeJkc:\ ~ we'tq~d J- ~ jtde_ l;JoJ, eY" w~+"'- ~1 ;: 9 SO'":l- ~~~-,!

I

+\olf\io vd cJ rt)'f('e (l~j-6 c\J c

Wat c,Cq '(;\)

I WI. ''Ho~(iaJJ

t~u-\td~o>'l" t, ~ t~Af'i ~ ( ~ + l'kc. \ Ari = ( 1, COOt Nf~~.t~ X~ (ziM)) (1 ~)(z~)

~cr"' - (J~e l xoc

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 10 | 12

Problem P2.105

It is said that Archimedes discovered the buoyancy laws when asked by King Hiero of Syracuse to

determine whether his new crown was pure gold (SG = 19.3). Archimedes measured the weight of the

crown in air to be 11.8 N and its weight in water to be 10.9 N. Was the crown pure gold?

a. w,-= H ,81\) (~"l~) {}.)1-.::. /O.C}tv ( t~A wtrl"t'v-)

f t I I \ - \ . \ :. -t: + I 0 .q l\) - ( /.lb ~

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 11 | 12

Problem P2.113

A spar buoy is a buoyant rod weighted to float and protrude vertically, as shown in the figure below. It

can be used for measurements or markers. Suppose that the buoy is maple wood (SG = 0.6), and

2 inches x 2 inches x 12 feet, floating in seawater (SG = 1.025). How many pounds of steel (SG = 7.85)

must be added to the bottom end so that h = 18 inches?

\7 -r.

-

2f y' : 0 Fb,v->o :;,;,}. ~ == (~1.~lWj~ 7.)(-=l .CJh)(o.or~.t?O~~} - -:f. I O"Z.CP~ lb~

• MEEN 3320 Fluid Mechanics Name: SOLUTIONS

Homework Set #2 Date: 12 | 12

Special Problem SP2.2

If a 100-N force F1 is applied to the piston with the 5-cm-diameter, what is the magnitude of the force F2

that can be resisted by the piston with the 10-cm-diameter? Neglect the weight of the pistons.

"-!;) il\t~\~1 P,A,-r1,-~.=o

Pt ~ f, /At F,

5-l"m diameter ---1 ~ \:>, Oil (S = 0.85)

P'2. ::: h - ~~.,.;_~ ~ = 5 t '=t 7.~ ~ '0 ~0... - Q~ll) Sboll lA o,~-zer. ~16 ? ....... - (q1tG01-tJ(w?)(o.cttS)(zM) Po...

= {3tt;-z.s +- h~ ~o..) (~)(To% ~) -z... - 2.~'1. 05" f.)

• iv!f: l, ' 33211 I !u;d :\k cha ti cs l lol tll' IINk Sct lr03

J~;:ybiem 3-.U!Connf

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-38 {Connect}

Na m~;;: Dntc:

A mercury manometer (p 13:rG kg,i;'U) is connected to an air duct to measure tlli.: pr..:ssurc :n:--1d~.:. 1 :1. difference in the manometer levels is I 0 mm, and the atmospheric pressure is 1 (l0 k Pa. (a) J udg i; lg 1 tl IIi the tigure below, determine ifthe pressure in the duct is above or below the atmospheric pressure. (_h) Determine the absolute press ure in the duct.

Gv-eV\. p = l 7Lb()-Q ~~~ nf. ~ ~~V"7- l'()O'd~ Al it

0 . 0 \ W\ 1' "' '.'

0..) ll1e.. ~~

• MEI:N .H20 rtuid Me-:hanics l loll!cwork Set /i01

Problem 3-45 {Connect}

Name: Date:

rresh vva ter and seawater flowing in parallel horizontal pipelines are connected to each other by a dou ble U-tnbc manometer, as shown in the figure below. Determine the pressure difference between the two pipel ines. Take the density of seawater at that locat ion to be p = 1035 kg/m3. Can the a ir co lumn be ignored in the ana lysis?

GtJ~a, e~- to~t; ~~~~"3 'e~ ... :; l(.')Q:)~ -~,a::rll 1 e~ -=- \ ?, t.o'()o ~I'M~ ~-:= r[ 1 ,.~(~. * ~h.v6-ker -:::'70 CWI. ':: O.t:;m ] 10(;1;-

---. h ~~ -=> lOCW\ ~ 0,\ VV' I ' _ hO:t v :: C')o C-"' " 0 t'"f W\ \-\' O.{m)-(teootta-rm~ o.s-,.,)-Oo35kf(II\Lo.1m)] =- ( q. ro 1 ""(s~) ( f;'f ~ . t; fc~/ m2-) ::

~3?o. h (c3-/111 S,._

( 5J?o . G ~~rll-~) ( ( lqfJ ) ( fOoo ~ ffljs'-

• MEEN 3320 Fluid Mechanics l lomework Set #03

Problem 3-49 {Connect}

Name: ,4/\. Date: I (1

The gage pressure of the ai r in the tank shown in the fig ure below is measured to be 65 kPa. D"tcrnJi ~tc the di fferentia l height lz of the mercury column.

P,,~"oe-=- t;S"\

• MEFN :>320 Fluid Mechani cs lloml!work Set #03

Problem 3-58

Name: Date:

Two water tanks are connected to each other th rough a mercury manometer with inclined tubes, as shown in the figure be low. If the pressure difference between the two tanks is 20 kPa, calculate a and().

Gh"~n. f 0- fA - ~ "-~~ !>

• MEEN 3320 Fluid Mechanics Homework Set #03

Pmblem 3-59 {Connect}

Name: ~~~ -Date: l tJ

Cons ider a hydraulic jack being used in a car repair shop, as shown in the figure beiow. The piston~ have an area of A1 = 0.8 em and A2 = 0.04 m . Hydraulic oi l with a specific gravity of 0.870 is pumped in as the sma ll piston on the left side is pushed up and down , slowly raisin g the larger riston on till: r ighi side. A car that weighs 13,000 N is to be jacked up. (a) At the beginning, when both pistons are nt tho: same elevation (h = 0), calcu late the force F 1 in Newtons required to hold the weight ofthe car (b) Repeat the calculation after the car has been lifted two meters (/z =2 m). Compare and discuss.

Gt-JeM A~ :: o. ~c~~')_ =: o.9tJ'1- \0 - 4 M2. A). ::. o. o 4-rn:t ~tr 0, , -=- () .

• fVlf:E 1\ 3320 Fluid l'vlcchanics J!,,mc:work Set #03

Name: Date:

Problem 3-67 {Connect} Consider a heavy car submerged in water in a lake with a fl at bottom . The driver's side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10m below the water surface. Determine the net force act in g on the door (normal to its surface) and the ]_pcation of the pressure center if(a) the car is we ll-sealed and it contai ns air at atmospheric pressure and (b) the car is filled with water.

b(\J'e'v"\. {0\'Y\ . ~r s-~oe Qo, .

t oao tc~ 1 WI )

rA) . + I.IVVJ ) V'V\ - l.

- ( 0 ~ 4-Cf (;_, k:q-f 1\A. ~ ~l.. ~ {O),t.-IC(l:, lc~ l \-\\.'::.~ ( \k-rV \ .:.. to3 ob tGrV/~:l-

lOOO \

• MEEN 3320 Fluid Mechan ics Ho mework Set #03

Problem 3-68

Name: Dale:

A long, sol id cy linder of radi us 2 ft hinged at point A is used as an automat ic gate, as shown in the fi gur~ be low. When the water leve l reaches 15 ft, the cylindrical gate opens by turni ng about the hinge at po int A. Dete rmine (a) the hydrostat ic fo rce acting on the cy linder and its line of act ion when the gate ope ns and (b) the weight of the cy linder per ft length of the cylinder.

/~ ..... --~ .......

/ 2ft~.~/" /

/ J

-l ~- -~:=.:: ..... :~-' 1' it~

----:, """':o.'.~ ,, ' .. ~. .....-:-~--~----"'"-+--~__,.;;.._ __ .

0\) rH ~ ~ ~ ~ ~CAve A ~ i~h"cf\. I 0 0 - w

e?rVlG ~ =- (~1- .~l~~~n~) (Rifys~)(\f~) (2.\4?)( ( (b~ ) 0 ~~f.t~l-

-=- (nll-n 1 bf--~ = P.w&4 ~ GqhcA = f~o-.,A = (62-t(-l~;f~,)(~-2~ ){ts-~+-) c~~ff} ( :2~~~-L)

-=- I ~fl2- \ b? ~

w "m~ = e'd-v ~ e~ c {

• ~) \..)~V\ -\-k-, \NC\-\ ex ~~ \ --z--::. l '7 .Q-t - h -,9 h 1 -the. ~-t'*" -011-e \nlYl5e a-.c.~,V\~ on --th.e. 0{ \-cnc)ev- 0\'Vtf l b-?-- ( pey-~)

• MEEN 3320 Fluid Mechanics I fomework Set #03

Pmblem 3-75

Name: Date:

A 6-m-high, 5-m-wide rectangular plate blocks the end of a 5-m-deep freshwater channel, as shown iu the figure below. The plate is hinged about a horizontal axis along its upper edge through a point A and is restra ined from opening by a fixed ridge at point B. Determine the force exerted on the plate by the ridge.

=- 2~ ~ fJj tctJ/m~ iht reSv\\bJ..V\-t Yl\.{ciros~..f,e, -to({,e OV\ Qc,c~ Vc"-\ \

FR. -==- 9 o..~ t\ == ( 1lf .tJ) \t-~'it

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-78 {Conne!1 Repeat Problem 3-77 E or a water he ight of 8ft.

Na me: Date:

The flow of water from a reservo ir is controlled by a 5- ft-wide L-shaped gate hinged at point A, as shown in the figure below. If it is des ired that the gate open when the water he ight is 12ft, determ ine the mass ofthe required weight W. Answer: 30,900 Ibm

1 ~ (02Lt \bWif~t7 J ~tf.-?)

(

• MEEN 3320 Fluid Mechanics I lomcwork Set #03

Problem 3-86 {Connect}

Name: Date:

A retaining v,rall agai nst a mud slide is to be constructed by plac ing !.2-m-high and 0.25-m-wide rectangular concrete blocks (p = .:.. 700K.g/m side by side, as shown in figure below. The friction c9efncient between the ground and the concrete blocks is Jtr.s = 0.4, and the density of the mud is about

Wt t k 'i 1 There is concern that the concrete blocks may slide or tip over the lower left edge as the mud leve l ri ses. Determine the mud height at which (a) the blocks will overcome friction and start s liding and (b) the blocks will tip over. ~Wi":)W\ 0~ ~ (JQ~~~ ~"" ~'("

f.= 2f7o\C) k* { ~~ ~) t-=- 0 25 m u:r\\k \e~ (\, == 1\'o\..) c ., . _ . V==.. co. l~~t1) u. 21'11) ( lrv1 l~-1

Ar 5 _ o I 1- _ '2 ') -r-- o.~~

( 1 ::: I 4-o o ~ff I 111:3 .

~l(,~lO~::. }It N\?\oc\" ::.. 0tt) (t[Ci'L\-IoN) - ':,\q9, . L)L{--/\)

I ''t: 1.2 m ,,~.,

FM - s._ ~ Pcw~A:;. f~hcf\ = e.c-c f~)A- - ~ e%cn;2) (\~~) == (/Lf-ook~(VI1~)(Cf.B!'Mjs..L)( ~) ( ~ ) - (p'D~n h2 N

~ \1~1"1k'l-F=Ii ~ l= 4?Y'l:le\oV\ 7 (o~ V;fJ h ~ (\.) -;::.) [7~ N

V1l. = ~~ :9 "'=- (Q . (o

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-162

Name: Date:

A semicircu lar 40-ft-d iameter tunne l is to be bu ilt under a 150-ft-deep, 800-ft-long lake, as shown it th~~ figure below. Determine the total hydrostat ic force acting on the roof of the tunnel.

I

1- T I

Water s-=ofJof-1:..

---=="""~:::--~ I 0 ': lk>~t .-::, r-:. ro ~ 1 e~ -; bL ~ lbn*-t ~

1 ~ :::----~""- 1.~ o n FH:: r~ ~ ~ve A = C?th~ A~ e~( S-i-~) /Jr ---4 ~ ~ (fo tl liM! ( U --- . :wme~~ _l ~~ -

2 ,, ~t 3 ) 32. ~ ~2) ( l~o + ~ ( '20 ~oo ~ ~- __ 40 ft -----~!

( \t~ \ u / ~.2\'rM\S?vf>?-) vv

- \ ;, ~ 9 '1 'f (0 ~ r 0~ ( OV) ea_ch Stde oO -\-hQ_ ~nrul ) II?~ \ few~ A = e0~ c A =- Q~hA =- C G?..!f-lk1Mj~) Crf~t.) (no+-t-) ( tfoxg~~~s'J

:::. 2 _ t)q (o y. Lt}S I k?t- .

W-= V}1 ~ ~ f~V = ~fr C e-- rr ~_._) C Bo~~) +

::- (b2 4- r ~/fif) ( 52. -2~2-) ( 20z- rrC(Q2'2.) ( 6oO.r.L) c I ~~ . ' 4- :rc-2.l\7w-4-fsz] :::. 4 zg; 'f LO(o ll~7? ( ovr erA.ch &(cte)

~Are 1 ~ Mt doc.Jf\~rd v.e.r-t=tcu.Q. .-?ny-ce T.r Fv ~ ~+:aN"' 2.5"1b,cto8+ 2(4-Z.gf7,

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-38 {Connect}

Name: Date:

A mercury manometer (p = 13,600 kg/m3) is connected to an air duct to measure the pressure inside. The difference in the manometer levels is 10 mm, and the atmospheric pressure is 100 kPa. (a) Judging from the figure below, determine if the pressure in the duct is above or below the atmospheric pressure. (b) Determine the absolute pressure in the duct.

~) P._ = ? c.d"" -~- s"~ 3 h ~~~ ~2.) p ~tw\

b) P-z_ = ((DO, ODe ~Col-)+ (13,boD~/w')j (D olDW-) ~ "2... ~ l () 0 I 00 0 4 I, 3 3 3. '0 ?CJ....

~, ;-- I D (. 3 3 8 l< ?~ CVv\_ s.

AIR I D = ') l~ .

h = 10111111

_j 1

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-13 {Connect}

Name: Date:

Determine the atmospheric pressure at a location where the barometric reading is 735 mmHg. Take the density of mercury to be 13,600 kg/m3

l-z\v~~ \) o:t(M -:. 1--S 5 M vv...\J j

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-45 {Connect}

Name: Date:

Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer, as shown in the figure below. Determine the pressure difference between the two pipelines. Take the density of seawater at that location to be p = 1035 kg/rrl~. Can the air column be ignored in the analysis?

CD t\ 'J~ \Q) Sf-a;\ \ c c VI .&cdt'o k1

(_ Mo..v-.cCANLt~v- ~~em-< )

P~-P, :::: Lf,9D3.S- I "3; 3'f!-.6- 6~7- + .3,Dt.f5.0 ?o-. c.... N ~~~ 7 ~ble..

L.., ?"1.- ?, ~ - t;1 3cr 1- , -z, Po.- { f'f

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-49 {Connect}

Name: Date:

The gage pressure of the air in the tank shown in the figure below is measured to be 65 kPa. Determine the differential height h of the mercury column.

M ()NvQ IM.-i ~f PI). 6l1( OYt 65 kPa ?~,-r + ft\ 0 (o .-, ....... )- ~,.. ~ - ~o.' (o:~5w.) =-P~r------::--~____, ~.s ' 1 'l:f I Air

~ ~ cy ~1- \.J( IM~ t\-r.-0 I

~ Hj ~ t 33/~{6 \-J( V'A3 ~o~\ ~ ~eX( ~r\-J) : 1, olol t.l(~

I 30 Clll l_

75 em

Oil SG = 0.72

- Mercury SG = 13.6

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-58

Name: Date:

Two water tanks are connected to each other through a mercury manometer with inclined tubes, as shown in the figure below. If the pressure difference between the two tanks is 20 kPa, calculate a and B.

tJ\rMAow..~.:t-

• MEEN 3320 Fluid Mechanics Homework Set #03

Problem 3-59 {Connect}

Name: Date:

Consider a hydraulic jack being used in a car repair shop, as shown in the figure below. The pistons have an area of A 1 = 0.8 cm2 and A2 = 0.04 m2 Hydraulic oil with a specific gravity of 0.870 is pumped in as the small piston on the left side is pushed up and down, slowly raising the larger piston on the right side. A car that weighs 13,000 N is to be jacked up. (a) At the beginning, when both pistons are at the same elevation (h = 0), calculate the force F 1 in Newtons required to hold the weight of the car. (b) Repeat the calculation after the car has been lifted two meters (h = 2 m). Compare and discuss.

t>-~sfoY\. I : 1., r':f ~ D - r, ... t\ A, == o

p\ t;+6'1\ 2 ~ 1) rj = t> f2- A,_,- Is, bOO 1-J -= o

r

.

f A/ v Fl 2 ' " ~_l Hydraulic oil_........ 1--'

.....-lo-"' SG = 0.870

1 \ At L-') F, =- lt3, roo tJ J Tz...

F2

1 "3 ooo'IJ A-z_

A -=- o.6c_\M.,_ = Sxtos M 'l.-' A?..- Q,Ol.fv.;...,_

) '\=z. ::. (l-,1ooo 1-J(~~A"~-J(s~) = Z(p YJ = F-z..

b) ~ -::: Z V\A ~} ~ o~ \ ::o S (; g 1-t-..D = ~"f() ~ /v.K' f-z_ ~ P,- (Bt-o ~/v.?)(ct.w-=+-'')..k-)Cz_IM) :::- P. - li-1 o~!.f 0/w.'-Pz. -=- 1'3/4\0 -::::. 3"Z5

1ooo 'tJ{w.. ..,_ :::> ? 1 -=- 3i1Z1 001{ P(~AA-'-

F1 =- ?1 A,-= (s\fZ1 Dtol-f~{vv.'- )(e.,vtos!Nt't-J ~ 7..-:::t-. 31:,5 'f-0 = F, ~ T{N__s.. ' 1s fNv.._

• Example Problem 2.5 {Fluid Mechanics, 7 ed, White, page 80} The gate shown in the figure below is 5 feet wide and hinged at point B, and rests against a smooth wall at point A. Compute the (a) force on the gate due to the sea water pressure (Psw = 64 lbrnlft3 ; Ysw = 64 lbf/ft3); (b) the horizontal force P exerted on the wall at point A; and (c) the reactions at the hinge B.

C?:v ~ ; ~s~-:: ~'1 tb~/~3. L> o1sw - r.w3/ 7~c,

~~lA.) ~ {r;L( lb ~t . f=?t.f \1- 1~-:,Sl. ~ ,~z.. ~~ ~"r/,f ~~t.(A-(t-

"(15w -::: &/-( lht-f++:! (-w .. +e D~vi s ~ Lz= g 2 .f ~ z tr z.

ltJ ~ s ~ r' ~~ . a..) \= ~ (]YI._ ~ r:1 ()..,-\ ~

b) Fo-r~ e ~ f!_A c.) e'J( t ~~ @.. lS

P-- ~\lelA-r ~- Pc.. A~t(J._-\e r~ (P~ + gj ~L) Apto1c

15 ft

Seawater: 64 lbf/ ft3

Wall

6 ft

-----L---1 )'-----L-9 t> c.:I!M 1

y

\ \

- - Sft - - 1

\ \

\ \

8

tfMA & = tPIB ~'> e:: ~ 0. v=t 0 tS til\, e- = 0 . (o

X

• Example Problem 2.5 continued ...

o To be.-\ -e'f ~ f> we. N2..o}_ 4v I

:J, M.~ = D o ~ ~~-\t'OY\ tD'f e~ Q..)( -e{i vt..cJ wt ~ 0-~oUL..i- ~ b eC'& ~e +kj o ~ -\~\f\)u7 ~,

~ {(.\Q r ~ (r -t YU..e of tk p ~ 0\$; I:J ~0 }11\ f 0Y( -0./\. .L"

/ /

~ M ~ ~ o : - \= ~ .Q +- P st vt e L ':_ o D Ff2- "'-~ s 6 ev c&\c ,l&{C"c\

1 fa~-:\ ds

1M,.

• Example Problem 2.76 {Fluid Mechanics, 7ed, White} Panel AB shown in the figure below is circular. Compute (a) the hydrostatic force (FR) of the water on the panel, (b) the center of pressure (CP), and (c) the moment of FR about point A.

b~v~ : \JJ~e'C -/ f-= l,bCO r-g/..u..'! \J ~ 3 VA-/ A :::-~1)2.~ ~frMl...

~ 1-. D fo~(o tM 7.. G= so~ -/ s>"'e ;;- o :-r-Gtooy

6.) \=" ~ = Pc_ A flae. = (p d+- ~~~ J AfcvJ.e h e__-::: ~C-'Sllt\8 = ('f ,c;w..) c;~vte-

1-tc__-= 3. 'i ~n IN\ 1 } 0 F;_ = ~ (DOD'~.K )( ~. '2>61-"'r')(3. 4 'tfz,._J )yioJ( _ ___, "'( FA. : [ 3 S, t)D0 ol- ~{w-t-1 ( 1. D~:/6~ \Mz._ J

==) ~r'L =- 23~,9 ~s . cr:t-fJ ..:'> tJ... ~ 2..3'6 . ~"Co ktJ ~s.

b ) ~ I' ~ ':lc.. + I.)Q(, c.. { l=b ~ - n lo.) !"}e. "'\I~ Jc A~Oyc = J[ R_'-f := lL (t/;w..)'1 = 3.cri-G,O B 'M~ ;[ToJ.ole 3-31g 17 '-1

~P -= (/..f. sw..) -+ ( :s . q no co ~" ) -=-