Review Problems

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Go to Appendix G for a setof review problems with answers. De_tailed solutions can be found i" sn,i"nii"it,iiiilIii^ "ro

rra 9:i!:!:f Fund.amentats of Ftuid Mechanics, Uu,\(@ 2009 John Wiley and Sons, h".1.--- -*"'-"' -r 'runsou, et al.

Problems

tItIrItrIIIIrIIIIrII

lo{ote.:. Unless specific values of required Iluid properties aregiven in the statenrent of the pro6ler", "r.'if,. ,ifues found in4ire tables on the inside o{ the iront .""* ir."lf .*s clesignatedrvith an ('iJ are intended to be solved *i* tf-r" Jj"i a program-matrle calculator or a comput€r. eroliems a*sfiiated with a (r)are o,open-ended" protrlems and require-.;,il thinking inthat to il'ork them one must tnaL" ur"i"r, ursimptions andprovirie the necessary dl

these pro6lems. l'ra' There is not a unique ansver to

where R.is the pipe radius,.Ap the pressure drop alcp. a fluid properry calledprpe whar are rhe dimen::i:':y,i:tj]i5 i'l::r:f-iii:r

il

Ansr.r,em to fhe even-nurnbered problems are iisted at theend of the tiook. Access to rhe videos r;;;;;;;;p""y probtemscas be obtained through. rhe book's ;;;;;r.,';*"rwire"v--.conr,/college/munson, The lat_typ" p.oUt"*,

"ur'"f." n. accessed onthis weh site.

Section 1.2 Dimensions, Dimensional Homogeneity,and Units

).{n"force, F, of tlre wind.blowing against a building is given by' F : CopV2 A/2, where Vis_the winJsp-eed, p the Jensiry of the air,A the cross-sectionat area of rh".b"ift;;:;; 6;;;."srant termedthe drag coefEcienl Determine Ae Am#sions "?rl"

A*g.r"fficient.1.2 Verifu the dimensions, in-both the FLTand Mli.systems, ofthe following quantities

),.lich ap;;;"-i;; i.,, trt volume,(b) acceleration, (c) mass, <al ."."ilt "ii""".i**1, and (e) work.1.3 Detennine the dimensions, in-both the FLT system and theMLT system. for (a) the product-of forc;i;;r;;;."tion, (b) theproducr of force times vetocity di"id;Jl;;;;, i"i[l momentumdivided by volume.

1.4 Verify the dirnensions, in.both the FLTsystem and rhe MLTsystem, of the following quantities. *t i"f, upp"u, io"fuUl" l.l : (a)rrequency, (b) stress, (c) srain. ta) torque,lialJ*ort.1.5 If a is a velocifv. x a length,-and r a time, what are thedimensions (in tteJitf sysrem) of @) 6u/dr, (b) 02u/0xAt,andlc) [(au/at) dx?

1.6 If p is a pressure, Vavelociry, wtd p afluid density, what arethe dimensions (in the(c) p/pv2? MLT svstem) of (4 p/p, fti pvp,

^i1.7 It V is a velocirv. { a.lengr}, and y a fluid property (the kine_*,tt visco.sirr).having oirn"i.ion, ori,i:i,"*"*.6 of the fol_

i|Y'Xf;;^o^ations are dimensionless , 1"1 w),'ai wn, k) v2a,

1.8 If y is a velocitv. determine the dimension s of Z, a, and G,which appear in the dimensiordly;;;;;"# "n""ura"v : 4" _ 1I,&&,

.

1.9 The volume rate of flow, ^r,

*g"J-*pe containing a slowlymoving liquid is given by Lne equatlon

- rfrAn() - '8p(

pipe. what are rhe dimension, oitr,l "o;J#;;rffi:T:,i;l;ffn,?

this equation as a general homog"n"o-us equatilni

l.l0 According to information found in an old h

:x:;;",:'rJff }fi :H;";it*i$r#x'l*H::T':',:::[1' : (0.0a to O.(D)(D/ eaV2 /2g

where ft is the enersv l":: q., unir weight, D the hose diarn^,^_t]te 2ozzt9

rip diamlier, V the fluid ";f;;,, i"";. " ^ --*rrctgr, dl

acceierarion -or

g'auirv.' oo fo;ilJil.'Jq;lxi."'il'i;,il1"-:t.sYstem of units? Explain. .- {ry1.11 The pressure difference, Ap, across a partial I*"ty i;;l[;; ;],ri,. uoo.o"imared by,r,.

"q,?ll#8. io *

u:K.#*r.(*-,)'or,w!er9 V is the blood velociry, p the blood viscop me brooa aens irt liL:;1rpfi"l"r.yat#"#;"ily"9;il1unobstructed artery, and A, the area of th" stenosis. #lffi ji:ff :ffi

ilil iq *d ;. w;;ilil;':';# "TH'"h'.i;

1.I2. Assume that rhe speed of sound, c, in a fluid d

ilii,;*?i*::i;j?;if ir":{r,i':.l-;:r*{L*.""*uil1':::H:#T:[ijii are the varues *; ilJ,",X"fl'J.1i.(s.. d. i.l9,g.i"'' "'" sandard formula for the speed

"f *".i1.13 A. formula to estimate the volume rate of flo\rover a dam .i i""g,h, i, i. given by the equarion

r' 0, flowin*i

$

Ig

slailil

Q : 1.7O aH3n

where.I{ is the depth or *_:.:lr"j above,rhe top of the dam (calleathe head) This formula grves e in mj/s when B and H "-^ . -meter. Is rhe consranr. r.70, ai,iensio"rl,rri w.r"r,r t; :oiliJlbe valid if units other than meter and second.q were used?iI.tJ cire an examole

"f^r.:::q:"d homogeneous equation s6n_tained in a technical article,found in un "ngi-n-""ri,igiou_ul in you.field of inreresr. Define all ,..r , ii,"'!q"^,ionlr.*pruin *tv i,rs a restricred equarion, and provide a-.;;;i;;.];"rnal citafion(htle, date, etc.). - -v"'Y:erv rt

l.l5 Warer flows from a larg^e drailage pipe at a rate of 4500 L/min.What is rhis volume rate of-flow i",iy!i--'-''*"1,15 An important dimensionless pammeter in certain types sgfluid flow problems is rhe rroua" ,uiniuJ"i"#", vZVg{, where7is a velociry, g lhe acceleration of graviq)-,'."Ji

^L"g,t. Derer-

frT#, f.'; :toffi.Froude ^:"'u"i';; Y: :t2,, l"I

.l:,ilri:j

Sl Ofiepterl llntroduction

Section 1.4 Measures of Fluid Mass and Weight

1.17 Obtain a photograpMmage of a situation in which the den-siry or specific weight of a fluid is important. Print this photo andwrite a briefparagraph that describes the situation involved.

1.18 A tank contains 500 kg of a liquid whose specific gravity is2. Deterrnine the volume of the liquid in the tank.

1.19 Clouds can weigh thousands of newtons due to their liquidwater content. Often this content is measured in grams per cubicmeter G/m3). Assume that a cumulus cloud occupies a volume ofone cubic kilometer, and its liquid water content is 0.2 g/m3. (a)What is the volume of this cloud in cubic kilometers? (tl) Howmuch does the water in the cioud weigh in newtons?

,.5'A' Atank of oil has a mass of 365 kg. (a) Determine its weightlh newtons at the eanh's surface. (b) What would be its mass(in kg) and its weight (in newtons) if located on the moon's surfacewhere the gravitational attraction is approximately one-sixth thatat the earth's surface?

1,.21 A certain object weighs 300 N at the earth's surface. Deter-mine the mass of the object (in kilograms) and its weight (in new-tons) when located, on a planet with an acceleration of gravity equalto 1.2 m,/s2.

1.22 The density of a certain type of jet fuel is 775 kg,/m3. De-termine its specific gravity and specific weight.

1.23 A hydrometeris used to measure the specific gravity of liq-uids. (See Video V2.8.) For a certain liquid, a hydromerer read-ing indicates a specific gravity of 1.15. What is the liquid's den-sity and specific weight?

1.24 An open, rigid-walled, cylindrical tank conrains 0.1 m3 ofwater at 4 oC. Over a 24-hour period of time the water tempera-fiire varies from 4 to 32'C. Make use of the data in Appendix Bto determine how much the volume-of water will change. For atank diameter of 0.6 m, would the corresponding change in waterdepth be very noticeable? Explain.

f1.25 Estimate the number of newtons of mercury it would taketo fill your bathtub. List all assumptions and show all calculations.

7,26 A mountain climber's oxygen tank contains 4.45 N of oxy-gen when he begins his trip at sea level where the accelerationof gravity is 9.81 m/sz. What is the weight of the oxygen in thetank when he reaches the top of Mt. Everest where the acceler-ation of gravity is 9.78 m,/s2? Assume that no oxygen has beenremoved from the tlnk; it will be used on the descent portion ofthe climb.

1.21 The information on a can of pop indicates that the can con-tains 355 mL. The mass of a tull can of pop is 0.369 kg while anempty can weighs 0.153 N. Determine the specific weight, den-sity, and specific gravity of the pop and compare your results withthe corresponding values for water at20"C.*1,28 The variation in the density of water, p, with temperature,7, in the tange 2O "C < T < 50 'C, is given in the following table.

Density (kg,zmr) 1998.2 | 99'1.1 | 99s.7 | 994.r I 992.2 | 990.2 | s8}.t

Temperaturel.c) I 20 | zs I :o I rs I 40 I +s I so

Use these data to determine an empirical equation of the formp : c r * c2T * caT2 which can be used to predict the density overthe range indicated. Compare the predicted values with the datagiven. What is the density of warer at 42.1 "C?

7,29 If 1 cup of cream having a density of 1005 kg/m3 is turnedinto 3 cups of whipped cream, determine the specific gravity andspecific weight of the whipped cream.

t1.30 The presence of raindrops in the air during a heavy rain-storm increases tbe average deniity of the air-water mixtur€. Esti-mate by what percent ihe average air-water density-is greater thanthat of just still air. State all assumptions and show ealculations.

Section 1.5 Ideal Gas Law

1.31 Determine the mass of air in a 2 m3 tank if the air is at roomtemperah-rre, 20 'C, and the absolute pressure within the tank is200 kPa (abs).

L.32 Nitrogen is compressed to a density of 4 kg/ml under an ab-solute pressure of 400 kPa. Determine the temperature in degreesCelsius.

1.33 The temperafure and pressure at the surface of Mars duringa Martian spring day were determined to be -50 "C and 900 Pa.respectively. (a) Determine the density of the Martian atmospherefor tlese conditions if the gas constant for the Martian atmosphereis assumed to be equivalent to that of carbon dioxide. (b) Comparethe answer from part (a) with the density of the earth's atmosphereduring a spring day when the temperature is 18'C and the pres-sure 101.6 kPa (abs).

1.34 A closed tank having a volume of 0.06 m3 is hlled with1.3 N of a gas. A pressure gage atkched to the tank reads 83 kPawhen the gas temperature is 27 "C. There is some question as rowhether the gas in the tank is oxygen or helium. Which do youthink it is? Explain how you arrived at your answer.

1.35 A compressed air tank contains 5 kg of air at a temperatureof 80 "C. A gage on the tank reads 300 kPa. Determine the vol-ume of the tank.

ry6 e rigid tank contains air at a pressure of 620 kPa (abs) anda temperatue of 15 "C. By how much will the pressure increaseas the temperature is increased to 43 "C?

1.37 The helium-filled blimp shown in Fig. P1.37 is used at var-ious athletic events. Determine the number of newtons of heliurnwithin it if its volume is 1926 m3 and the tempemture and pres,sure are TI "C wrd 98 kPa (ab$, respectively.

dFIGUFIE P1.37

*1.38 Develop a computer program for calculating the densin'of an ideal gas when the gas pressure in pascals (abs), the tem-perature in degrees Celsius, and the gas constant in J/kg .K arespecified. Plot the densiry of helium as a function of temperaturefrom 0 oC to 200 "C and pressures of 50, 100, 150, and 200 kP:(abs).

Section 1.6 Viscosity (Also see Lab Problems 1.98and 1.9.)1.39 Obtain a photographr/image of a situation in which the vis-cosity of a fluid is important. Print this photo and write a brie:paragraph that describes the situation involved.

Ll40 For flowing water, what is the magnitude of the velocity gri-dient needed to produce a shear stress of 1.0 N/mz?

Chapter 1 I Infroducfion

available the constants canbe obtaiqed,.direc(1 fton\. l.t0 with-out rewriting the equation)

yy'for^uparallel plate arrangement of the type shown in Fig.f.4 it is found ttrat when the diitance berween'plates is 2 mm, ashearing shess of 150 pa develops at lhe uooei olate when it ispulled at a velocity of I m/s. Deiermine the'v'iscosity of the fluidbetween the plates.

1,54 Two flat plates are oriented parallel above a fixed lower plateas slown in Fig. P1.54. Th. top plate, located a distance 6 ibovethe fixed_plate, is pulled along with speed V. The other thin plateis located a distance cb, where 0 <;< 1, above the fixed plate.This plate moves wirh speed V', which is determined by the vis_cous

:t]ealfgr,ces imposed on it by the fluids on its top and bortom. The fluid on the top is twice as viscous as that on the bortom. Plot the ratio Vr/V as a function of c for 0 < c < 1.

ib

-----> v

lvt

IFIGURE P1.57

1.58 A 10-kg block slides down a smooth inclined surfacr

shown in Fig. P1.58. Determine the terminal velocity of the b.

if the 0.1-mm gap between the block and the surface contains i30 oil at 15 oC. Assume the velocity distribution in the gap is

ear, and the area of the block in contact with the oil is 0.1

IFIGURE P1.58

1.59 A layer of water flows down an inclined fixed surface

the velociry profile shown in Fig. P1.59. Determine the magniand direction of the shearing stress that the water exerts on the Isurface for U : Zm/s and /r : 0.1 m.

_C,L T-'h-h2

IFIGURE P1.59

x1.60 Standard air flows past a flat surface and velocity meaments near the surface indicate the following disfribution:

y(m) | 15x t0-o l3 x l0-1 16x t0-4 lt2x l0-ol18x l0-ol 24 x

,(*/,)Io.z: Io.ou Io.n, It.no lr.tt Io,n

The coordinate y is measured normal to the surface and r ivelocity parallel to the surface. (a) Assume the velocity disttion is of the form

u:CJ*Czy3and use a standard curve-fitting technique to determine thestants Cr and C2. (b) Make use of the results of part (a) rtermine the magnitude of the shearing stress at the wall {-r

and at Y : 0.015 m.

1.61 A new computer drive is proposed to have a disc, as sl

in Fig. P1.61. The disc is to rotate at 10,000 rpm, and the nhead is to be positioned 0.012 mm. above the surface of the

Estimate the shearing force on the reader head as a result of ttbetween the disc and the head.

!FIGURE P1.54

1.55 There are many fluids that exhibit non_Newtonian behavior(see, for-exarnple, Video V1.6). For a given fluid the distinctionbetween Newtonian and non-Newtonian behavior is usually basedon measurements of shear stress and rate of shearing strain. As_sume that the viscosity of blood is to be determined by measure_m9nt1 9f shear stress, z, and rate of shearing strun,'du/dy, ob_tained from a small blood sample tested in a iuitable viscometer.Based on the dara given below determine if the blood is a New_

l::#.:t non-Newtonian fluid. Explaia how you anived at your

r(N/m2) | 0.04 | 0.06 i0.12 10.18 I 0.30 I 0.s2 I l.l2 I 2.10du/dy (s-') I z.zs l+.so I rr.zs lzz.s I +s.o I qo.o I zzs I +so

L56 The sled-shovrn h Fig. p1.56 slides along on a thin horizontallayer of water between the ice and the runnerslThe horizontal forcethat t]r9 water puts on the mnnen is equal to i.S N when ttre sled,sspeed is 15 m,/s. The total area of both runners in contact with the wa_teris 0.007 m2, and the viscosity of the wateii, 16g ; i0-5 N:V;r.Determine the thiclqpess of the water tuy", unJ"i tt

" runners. Assume

a linear velociry distribution in the w#r Uyer.

IFIGUFIE P,I-56

1.57 A 25-mm-diamerer shaft is pulled through a cylindrical bear_lnq as shown in Fig. p1.57. Tr," fi;;;-'that filts the0.3-mm gap between the shaft and bearin! i, * oif having a kine_matic viscosity of 8.0 X i0-a m% unO u"*p""in" gravity of O.lt.Determine the force p required to pu1 thJ;h;ft ;; a velocity of3 m/s. Assume the velocity distribuion in tf," gup1, fin"*.

F-0.5 m-__________l

FFIGT-''FIE F1.61

tr.62 The space between two 15 cm-1ong concentric cylinders isfiiled with glycerin (viscosity : 407 x 10-3 N . s,/m2). The innercylinder has a radius of 7.6 cm and the gap width between cylin-ders is 0.25 cm. Determine the torque and the power required torotate the inner cylinder at 180 revlmin. The outer cylinder is fixed.Assume the veloc'ity distribution in the gap to be linear.

1.63 A pivot bearing used on the shaft of an electrical instrumentis shon'n in Fig. P1.63. An oil with a viscosity of 1t : 9.479 N.s,/m2fills the 0.025 mm gap between the rotating shaft and the station-ary base. Determine the frictional torque on the shaft when it ro-tates at 5,000 rpm.

Problerns 35 ,7

For this viscometer & : 6.3S cm, R, : 6.22 cm, and ( -- 12-7 cmMake use of these data and a standard curve-fitting program to de-termhe the viscosity of the liquid contained in the viscometer.

Fixedouter

cyl inder

TFIGUFIE P.I.64

1.65 A 30 cm-diameter circular plate is placed over a fixed bor-tom plate with a 0.25 cm gap between the two plates filled withglycerin as shown in Fig. P1.65. Determine the torque required rorotate the circular plate slowly at 2 rprn- Assume that tbe velocitydistribution in the gap is linear and that the shear stress on the edgeofthe rotating plate is negligible.

I4

_l

c-ntn-elofgs

lgi-cfte

v.1-

:d

rs

)-

alJt[1

5,000 rpm

p=0.479N'Vm2

1.64 The viscosity of liquids can be measured through the use of arotaring cylinder viscometer of the [pe illustrated in Fig. P1.64. Inthis device the outer cylinder is fixed and the inner cylinder is rotatedwith an angulm velocity, rr.r. The torque I required to develop ar ismeasured and the viscosity is calculated from these two measrrements.(a) Develop an equation reiating.p,u,g,(,R0, and R,. Neglectend effects and assume the velocity distribution in the gap is lin-ear. (b) The following torque-angular velocity data were obtainedwith a rotating cylinder viscometer of the type discussed in part (a).

0.25 cm gap

IFIGURE P1.65

11.66 Vehicle shock absorbers damp out oscillations caused byroad roughness. Describe how a temperature change may affect theoperation of a shock absorber.

1.67 Some measurements on a blood sarnple at 37 oC indicate ashearing stress of 0.52 N/m2 for a corresponding rate of shear-ing strain of 200s-r. Determine ttre apparent viscosity of theblood and compare it with the viscosity of water at the sametemperature.

Section 1.7 Compressibility of Fluids

1.68 Obtain a photograph/image of a situation in which the com-pressibility of a fluid is important. Print this photo and write a briefparagraph that describes the situation involved.

1.69 A sound wave is observed to travel through a liquid with aspeed of 1500 m/s. The specific gravity of the liquid is 1.5. De-termine the bulk modulus for this fluid.

1.70 Estimate the increase in pressure (in kPa) required to de-crease a unit volume of mercury by O.lVo.

l.ll A 1-m3 volume of water is contained in a rigid container. Es-timate the change in the volume of the water when a piston appliesa pressure of 35 MPa.

lf2 Oeterm:ne the speed of sound at 20 "Cin (a) air, (tr) helium,and (c) natural gas (methane). Express your answer in m,/s.

1.73 Air is enclosed by a rigid cylinder conraining a piston. Apressure gage ailached to the cylinder indicates an initial readingof 172 kPa. Determine the reading on the gage when the pistonhas compressed the air to one-third its original volume. Assume

0.012 mm

EFIGURE P.t.63

velocity (radls)

36 Chapterl llntroduction

the compression process to be isothermal and the local atmosphericpressure to be 101.3 kPa.

1.74 Repeat Problem 1.73 if &e compression process takes placewithout friction and without h€at transfer (isentropic process).

1.75 Carbon dioxide at 30 "C and 300 kPa absolure pressure ex-pands isothermally to an absolute pressure of 165 kPa. Determinethe final density of the gas.

1.76 Natural gas at 27 oC and standard atmospheric pressure of101.3 kPa (ab$ is compressed isentropically to a new absolutepressure of 483 kPa. Determine the final density and t€mperature ofthe gas.

1.77 Compare the isentropic bulk modulus of air at l0l kpa (abs)with that of water at the same pressure.

*1,78 Develop a computer program for calculating the final gagepressure ofgas when the initial gage pressure, initiai and final vol-umes, atmospheric pressure, and the type of process (isothermal orisentropic) are specified. Check your program against the resultsobtained for hoblem 1.73.

1,79 An important dimensionless parameter concerned with veryhigh-speed flow ls the Ma ch numbe4 defined as V/c, where V is thespeed of the object such as an airplane or projectile, and c is thespeed of sound in the fluid surrounding the object. For a projectiletraveling at 1290 kmr/h through air at l0'C and standard atrnos-pheric pressure, what is the value of the Mach number?

1.80 Jet airliners rypically fly at attitudes berween approximately 0to 12,200 m. Make use of the data in Appendix C to show on a graphhow the speed of sound varies over this range.

1.81 (See Fluids in the News article titled "This water jet is ablast," Section 1.7.1) By what percenr is the volume of water de-creased if its pressure is increased to 304 Mpa?

Section 1.8 Vapor Pressure1.82 During a mountain ciimbing trip it is observed that the wa-ter used to cook a meal boils at 90 oC rather than the standard100 "C at sea level. At what altitude are the climbers preparingtheir meai? (See Tables B.1 and C.l for data needed to solve thiiproblem.)

9t'1 Wfr"n a fluid flows through a sharp bend, low pressures maydevelop in localized regions of the bend. Estimate the minimumabsolute pressure,(in kPa) that can develop without causing cavi-tation if the fluidls watei at 70 "C.

1,84 Estimate the minimum absolute pressure (in pascals) that canbe developed at the inlet of a pump to avoid cavitition if the fluidis carbon tetrachloride at20"C.

1.85 When water at 70'C flows through a converging sectionof ,pipe, the pressure decieases in the direction of flow.-Estimatethe minimum absolute pressure that can develop without causingcavitation.

1.86 At what atmospheric pressure will water boil at 35 .C?

Section 1.9 Surface Tension

1.87 Obtain a photograph/image of a situation in which the sur-face tension of a fluid is important. print this photo and write abrief paragraph that describes the sinration invoived.

1.88 When a 2-mm-diameter tube is inserted into a liquid in anopen tank, the liquid is bbserved to rise 10 mm above the free sur_face of the liquid. The contact angle between the liquid and the rube

is zero,and the specific weight of the liquid is 1.2 x 104 N/rlDetermine the value of the surface tension for this liquid.

@ Small droplets of carbon tetrachloride at zOeC are forrne.:with a spray nozzle. lf the average diameter of the droplets r.

200 pm, what is the difference in pressure between the inside ar,;outside of the droplets?

1.90 A l2-mm-diameter jet of water discharges vertically into tratmosphere. Due to surface tension the pressure inside the jet u-|be slightly higher than the surrounding atmospheric pressure. D:-termine this difference in pressure.

1.91 As shown in Video V1.9, surface tension forces can be strc: senough to aliow a double-edge steei razor blade to "float" on ;.-ter, but a single-edge blade witl sink. Assume that the surface r:',sion forces act at an angle 0 relative to the water surface as sho';:in Fig. P1-91. (a) The mass of the double-edge blade -"0.64 X 10-3 kg, and the total length of its sides is 206 mm. Dr,termine the vaiue of 0 required to maintain equilibrium beru.e;:the blade weight and the resultant surface tension force. (b) T::mass of the single-edge blade is 2.61 x 10-3 kg, and the tcrlength of its sides is 154 mm. Explain why this blade sinks. S.:;-port your answer with the necessary calculations.

Surface tensionforce

1,92 To measure the water depth in a large open tank with opaq-walls, an open vertical glass tube is attached to tfie side of r.*tank. The height of the water column in the tube is then used ;:a measure of the depth of water in the tank. (a) For a true s,a:::depth in the tank of 1 m, make use of Eq. 1.21 (with d - 0.: ::determine the percent error due to capillarity as the diameter -:the glass tube is changed. Assume a water temperature of 30 'ilShow your results on a graph of percent error versus tube dia:-eter, D, in the range 0.25 cm < D < 2.5 cm. (b) If you wanr -_:j

error to be less than lVo, what is the smallest tube diam:::-allowed?

1..93 Under the right conditions, it is possible, due to surface re:-sion, to have metal objects float on water. (See Yideo V1.9.) Cl:-sider placing a short length of a small diameter steel (sp. u.r. =77 kN/m') rod on a surface of water. What is the maxim_rdiameter that the rod can have before it will sink? Assume rir;the surlace tension forces act vertically upward. Note: A stanC,:rpaper clip has a diameter of 0.09 cm. Partially unfold a paper ;,:rand see if you can get it to float on water. Do the results of :r.,experiment support your analysis?

1.94 An open, clean glass tube, having a diameter of 3 mrr.. ,inserted vertically into a dish of mercury at 20 .C. tqo* 1s ;.iJthe colurnn of mercury in the tube be depressed?

1.95 An open, clean glass tube (0 : 0') is inserted verricall-r, :rLra pan of water. What tube diameter is needed if the water 1eve. cthe tube is to rise one tube diameter (due to surface tension).1

1.96 Determine the height that water at 15 .C will rise due :icapillary action in a clean, 0.5 cm-diameter tube. What will be -rcheight if the diameter is reduced to 0.03 cm?

1.97 (See Fluids in the News article titled "Walking on \ri'-::Section 1.9.) (a) The water strider bug shown in Fig. Pl.9- ,r

IFIGURE P1.91