Solution Manual For Design Of Fluid Thermal Systems, 4th Edition

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Solutions Manual to AccompanyDESIGN OF FLUID THERMALSYSTEMS,4THEDITIONWILLIAM S. JANNADesign ofFluidThermal SystemsWilliam S. Janna

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Chapter 1Conversions and Unit Systems1.Consult an appropriate source to determine the conversion factors associated with thefollowing conversions:a. number ofdashesper teaspoonb. number ofteaspoonsper tablespoonc. number oftablespoonsper cupd. number ofcupsper quarte. number ofquartsper gallona) 4 dashes = 1 tsp (some cookbooks say 8 dashes = 1 tsp)b) 3 tsp = 1 tablespoon (one would think that 2 tsp = 1 tablespoon)c) 16 tablespoons = 1 cupd) 4 cups = 1 quarte) 4 quarts = 1 gallon2.Consult an appropriate source to determine the meaning of the following units(remember to look up the proper pronunciation as well):a. coombb. scruplec. cord of woodd. ream of papera) coomb is an English unit of capacity; 1 coomb = 4 imperial bushesl = 4.13 U.S.bushelsb) scruple = 20 grains, an apothecary measurementc) cord = cut fuel wood, 4 f t x 4 f t x 8 f t = 128 ft3d) ream = formerly 480 sheets, now 500; printer's ream = 5163.Consult an appropriate source to determine the meaning of the following units:a.gillb. degree-dayc. ton versus metric tond. long ton versus short tona) gill is a liquid measure; gill = 4 fluid ounces (1/4 pint) or 7.216 in3in the U.S.customary system; gill = 5 fluid ounces (1/4 pint) or 8.670 in3in the British imperialsystem.b) degree day is used to estimate the quantity of fuel and power consumption.c) ton in the U.S. customary system = 2240 pounds = a long ton; 2000 pounds is a shorttonmetric ton = 1000 kg which is a unit of massd) long vs short; there is 240 pounds difference (a unit of weight)4.How many "hins" are in a "bath"? How many "baths" are in a gallon?1 bin = 1.012 gallons; 1 bath = 6 hins = 6.073 gallons5.What is the relationship between an ounce (16 ounces per pound) and a fluid ounce (16ounces equals one pint)?Ounce is a unit of weight 16 ounces per pound; Ounce is a unit of volume 16 ounces perpint; A pint of liquid should equal a pound in weight; good subject for an experiment.1-1

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6.What is the origin of the “horsepower"? Why would anyone wish to express power inthe unit of horsepower? How many watts are in one horsepower?Horsepower was originated to show farmers the number of horses that could bereplaced by farm machinery. 746 W per HP.7.The unit for volume flow rate is gallons per minute, but cubic feet per second is preferred.Use the conversion factor tables in Appendix A to obtaina conversion between these twounits.gpm x 2.228 x10~3= cfs8.Which is heavier—a grain or a dram? Express both in theappropriateEnglishfundamentalunit.A grain is a unit of weight in the U.S. customary system; a grain is anavoirdupoisunitwhich equals 0.002285 ounces or 0.036 dram. So 1000 grains = 36 drams; a dram istherefore heavier.1grain = 0.002285 ounces1dram = 0.06347ounces1ounce = 437.6 grains1ounce = 15.76 drams9.How many years does a furlong designate? Furthermore, if a furlong is a linearmeasurement, what does this have to do with "years"? Why?1furlong = 220 years; 220 became associated with the furlong because Britishplowmen dug furrows equal in length to 220 yards.10.What is the difference between troy weight and avoirdupois weight? Express a poundin each of these systems in terms of grains.Avoirdupois weight is a system of weights & measures based on1pound = 16 ounces = 7,000 grains = 453.59 gramsTroy weight is a system of weight in which the grain is the same as in theavoirdupois system, but the pound contains 12 ounces, 240 pennyweights or 5760grains.1grain avoirdupois =1grain troy11. Is something called a "log" a emit of measure for liquid or dry goods? What is theconversion between a log and the appropriate SI unit?4.731 764 73 x 10’4m3A log is a liquid measure. 1 log = 0.674 pintx ~-------------------- = 3.189 x 104m31-2

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12.In the plastics industry, what is a gaylord?A gaylord is 1000 Ibm of plastic (pellets used in an extrusion process are usuallymeasured in terms of gaylords).13.A shotgun gauge refers to what dimension of the firearm?The gauge of a firearm is a unit of measurement. It expresses the diameter of barrel,found by the weight of a solid lead sphere that fits in the bore of the firearm.However, it is expressed as the inverse of the sphere's weight as a fraction of apound. Thus, a l/12th pound lead sphere fits into a 12-gauge bore.14.Nine gage wire and eleven gage wire are both used extensively in making chain linkfence material. What are the diameters of these wires? What other wire diametersexist, and what is the standard used in sizing wires?The standard used in sizing wires is found in the Table of American Wire Gagesizes. There are wire sizes for electrical conducing wire, for sheet metal and muchmore.15.Sheet metal screws are sized according to what standard? What is the differencebetween a machine screw and a sheet metal screw?Sheet metal screws come in sizes that range from #4 to #14 (diameters that rangefrom 0.11 to 0.25 inches). These screws are made to fasten sheet metal and aredesigned to be self tapping.Machine screws are threaded, and they range from size 000 to size 12 (diametersranging from 0.034 in to 0.216 inches).Published charts are available on the internet.Measurement Scales16.What is the Forel Ule scale used to measure?The Forel-Ule Scale is a specially developed color standard, used to provide ameasure of color in water. Each color standard or designation is identified by aroman numeral: at one end of the spectrum is eep sea blue; at the other is a muddyyellowish-brown.www.lamotte.com/pages/ common/pdf / instruct/5907.pdf17.What is the Snellen Fraction?A Snellen Fraction is expressed as a ratio (such as 20/20 or 20/100), and is used formeasuring the acuity or sharpness of a person's eyesight for objects at a distance,and named for the Dutch ophthalmologist Herman Snellen (1834-1908).1-3

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from http:/ / www.unc.edu/~rowlett/units/dictS.html18.The Scoville Unit is a measure of what?A Scofill Unit is a measure of the concentration of capsaicin in a substance.Capsaicin is the "hot" ingredient in chile peppers. A measurement of 40 000Scoville units indicates that an extract from the pepper can be diluted 40 000 to 1with sugared water; the "heat" of the capsaicin will still be barely detectable bythe human tongue.Such measurements are now made with a liquid chromatograph.The Scovill Unit was developed in 1912 by the American pharmacologist Wilbur L.Scoville. Actual chile peppers have capsaicin concentrations from 5000 to 500 000Scoville units.http: / / www.unc.edu/ ~rowlett/emits/ dictS.html19.What is the Shore Hardness scale used to measure?The Shore Hardness scale is measured with a Shore durometer. The hardness is ameasure of the hardness of plastic, rubber, or similar material. The durometer usesa steel pin to indent the material. The depth of the indentation is read by acalibrated spring meter.http:/ /www.imc.edu/ ~rowlett/units/dictD.html#duro20.The Shade number is used as a measure of what?The Shade Number is a unit of light transmission for the protective glasses used inwelding. If T is the fraction of visible light transmitted, the shade number isSN = 1 + 7(-logl0 T)/3.So, for example, if 1% of the light is transmitted, the shade number is 4."http: / / www.unc.edu/-rowlett/ units/ dictH.html21.The Beaufort scale measures what?The Beaufort Scale is an empirical measurement used to estimate wind speed byobserving the effects of the wind. Thus sailors can judge wind speed by observing thewind's effect on the waves. The scale was first devised by the British admiral SirFrancis Beaufort (1774-1857).http: / / www.unc.edu / ~rowlett/units / dictB.html1-4

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22.What scale is used to measure the"strength"of anearthquake?What is actually beingmeasured?The Richter scale is used. It ranges from 4 (strong enough to crack plaster), to 9(widespreaddestruction).The Mercalli scale is also used. It ranges from I (people cannot feel a tremor,butmachines are able to record it) to XII (extensive damage).23.What is the Numeric Rating Scale (NRS-11) used to measure?Pain24.To what does "CaratPurity"refer?1carat = 200 mg; used as a unit of weight for precious stones.Carat purity is measured or expressed by an equation:Carat Purity = 24(mgold/mtotal)in which mgoldis the mass of pure gold orplatinumin the material, and mtotalis thetotal mass of the material. So 18 carat gold is 18 parts gold, and 6 parts of anothermetal that forms an alloy with gold.25.Canned foods are quite common. How are can sizes measured or expressed by canmanufacturers? What are the difference in can size specifications used in the U.S.?What is used in the metric system?Can dimensions are shown by numbers such as "502 x 512 can." Three digits in eachnumber. The numbers in the preceding designation: the first number (502) refers tothe can diameter, the second number (512) refers to the can height. The three digitsindicate a measurement. Referring to "502", the first digit represents an inchmeasure, and the second two digits represent 16ths of an inch. So "502" means 52/16in. A good source of information is can companies or manufacturers, or experiencedcooks who studied home economics in the 1950's.Miscellaneous Measurements26.Why is a mile 5,280 ft?The word "Mile" comes from the Latin "mille" meaning one thousand.The Roman army measured a mile as 1000 paces and this was equal to 2000 steps.The average marching stride- 5 ft. Romans measured the mile (1000 paces) asroughly 5000 ft.© 2015 CeugageLearning. All Rights Reserved. May not be scanned, copied or duplicated, orposted to a publicly accessible website, in whole or inpart.1-5

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Britain adopted mile as a unitofmeasurement, but farmers insisted it be related tothe furlong (used extensively in Britain).The Roman mile is a little longer than71/2furlongs. Rather than change thefurlong, Britain changed mile and made it equal to 8 furlongs, which is 1760 yardsor 5280 ft.27.By what must a quart be multiplied to obtain a bushel?Note that a bushel is a dry measure while a quart is normally thought of as aliquid measure. However, in ancient times,1bushel-7.68dry quarts.28.What is a "hat trick"?A hat trick is an informal unitofquantity which equals 3.It is used in sports in counting goals, especiallyifthe goals are scored by the sameplayer. It is familiar in North American ice hockey.http://www.imc.edu/~rowlett/units/dictH.html29.How long is the circumferenceofa racetrack;i.e., how many laps must be made in a onemile race?1mile = circumferenceofracetrack30.What is the significanceofan acre, and how many square feet are contained in one?Which is larger, an acre or an arpent?An acre = amountofland that could be plowed in one day with a teamofoxen.An arpent ~ French equivalent, roughly.1acre = 160 square rods =4840square yards =43,560ft2.31.What is the definition of the body mass index? What is yours?The Body Mass Index or BMI is a measure of weight to height ratio in humans usedin studies of weight managment. The BMI is equal to a person's mass ("weight") M(in kilograms) divided by the square of his or her height H (in meters): BMI =M/H2.Ifmeasurements are made in traditional English units, the equivalentformula is BMI = 703.07-M/H2, where M is measured in pounds and H in inches."http:/ / www.xmc.edu/ ~rowlett/ units/ dictB.html32.How many barleycorns are in an inch?3 barleycorns - 1 in.© 2015Cengage Learning. AU Rights Reserved. May not be scanned, copied or duplicated, orposted to a publicly accessible website, in whole or in part.1-6

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33. How many inches are in a fistmele?A fistmele is a traditional unit of distance, which equals the widthofa clenchedfist with the thumb extended. This length is about 6.5 inches or 16.5 centimeters.The unit is used in archery, and also in kayaking.http://www.imc.edu/-rowlett/ units/ dictB.html34. Use the conversion factor tables in Appendix A to develop a conversion factor betweengallons and cubic feet.„„3.785411 784 xIO31ft318alIonX------ *2.831684-6592 x 10-2 =°-1 3 3 735. What is the equation for calculating the heat index?The heat index is a measureofthe combined effectofheat transfer by convectionand by vaporization on the human body.The heat index is calculated from temperatureT(in °F) and relative humidity H(expressed as a fraction; that is, H = 0.65 if the relative humidity is 65%). Theformula used isHI =-42.379+2.04901523T+1014.333127H-22.475541TH -.00683783T2- 548.1717H2+0.122874P H+8.5282TH2-0.0199P H2.http://www.unc.edu/~rowlett/units /dictH.html36. How long is a "handbreadth"? How long is a "finger"? How many fingers are in ahandbreadth?A handbreadth is a linear measurement approximating the width of the hand,from2P2to 4 inches, but most often taken to be 4 in.Ancient measurement, 1 handbreadth = 2.915 in. = 4 fingers1 finger = 0.728 in.37. Consult an appropriate source to determine the conversion factors that apply toa. parsecs per mile b. stadia per milea) 1 parsec-1.918 x1013miles1 mileb) 1 stadium = 607ft xr n o n,, = 0.115 miles5280 ft1-7

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38. The quantity called a "measure" is used in measuring the capacityofdry goods as wellas liquid goods. What is the conversion between a measure and a bushel (dry goods)?What is the conversion between a measure and a gallon?39. How is blood pressure expressed? Why isn't the result expressed in psig or kPa?40. How are shoes sized;i.e.zwhat is the relationship between shoe sizes and any othercommonly used unit?Shoe sizes express the approximate lengthofthe shoe, or of the length of the last,the form on which the shoe is made.http://www.unc.edu/~rowlett/units/dictS.html#shot1-8

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Chapter 2Density, Specific Gravity, Specific Weight1.What is the specific gravity of 38°API oil?141.5141.5131.5 +°API“ 131.5 + 3838°API oilsp.gr.141-5„sp. gr. =’ 169.5 ~0 , 8 3 52.The specific gravity of manometer gage oil is 0.826. What is its density and its °API rating?sp. gr. = 0.826;p =1000(0.826) = 826 kg/m3p= 62.4(0.826) = 51.54 lbm/ft3141.5SP- S1’ ~ 131.5+0API141.50.826131.5 + °API“API = 171.3 - 131.5;“API = 39.8°API = 40“API3.What is the difference in density between a 50°API oil and a 40°API oil?141.5141.5S p’S r"=131.5 +°API=131.5 + 50=0 7 7 9 6f o ra 5 0°011141.5141.5S p' g1"'=131.5 +°API=131.5 + 40=0 , 8 2 6f o ra4 0°0110.825 - 0.7796 = 0.0455 density difference2-1

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4.A 35°API oil has a viscosity of 0.825 N-s/m2. Express its viscosity in Saybolt Universal Seconds(SUS).n141-5141.5„„„35 API oilsp. gr. -5+.A p i=1 3 1 5 + 3 5= 0.850p = 0.825 N-s/m2v == Q g3 0(1 0 0 0) = 10 X10Highly viscous; tryv = 0.2158 x 10-6(SUS)if SUS > 215S U S0.2158 x 10~6“ 14 6 3 3S U S5.Air is collected in a 1.2 m3container and weighed using a balance as indicated in Figure P2.5. Ontheother endof thebalance armis 1.2 nFofCO2.The air andthe CO2 are at 27°C andatmospheric pressure. What is the difference in weight between these two volumes?FIGURE P2.5.Air at 27°C = 300 K has p = 1.177 kg/m3CO2at 27°C = 300 K hasp= 1.797 kg/m3For a volume of 1.2 m3, the weight of air is(1.177 kg/m3)(1.2 m3)(9.81 m/s2) = 13.86 NFor CO2(1.797 kg/m3)(1.2 m3)(9.81 m/s2) = 21.15 NWeight difference is 21.15 - 13.86 =7.29 N6.A container of castor oil is used to measure the density of a solid. The solid is cubical in shape, 3cm x 3 cm x 3 cm, and weighs 9 N in air. While submerged, the object weighs 7 N. What is thedensity of the liquid?Castor Oilp= 0.96(1000) kg/ m3buoyant forcerngm air- mgsubmerged=pgvolumeV-gcgc9 - 71-----------------P =(0.03)39.81=I7551kg/m37.A brass cylinder (Sp. Gr. = 8.5) has a diameter of 1 in. and a length of 4 in. It is submerged in aliquid of unknown density, as indicated in Figure P2.7. While submerged, the weight of thecylinder is measured as 0.8 Ibf. Determine the density of the liquid.© 2015 Cengage Learning. AU Rights Reserved. May not be scanned, copied or duplicated, orposted to a publicly accessible website, in whole or inpart.2-2

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weightsubmerged—objectFIGURE P2.7.Buoyant force = mgfaair- m gsubmerged= mg -0.8gc= 1 in this systembuoyant forcemg -0.8nD2rr------------ =7— =pg= —h = - (1/12)2(4/12) = 1.818 x 10-3ft3volume-V---------°------------------44mg = pbV-g = 8.5(1.94)(1.818 x 10’3)(32.2) = 0.965 Ibfmg -0.80 . 9 6 5 - 0 . 8P~gV-~ 32.2(1.818 x 10-3)p= 2,82 slug/ft3Viscosity8.Actual tests on vaseline yielded the following data:T in N / m202006001 000d V / d y i n l / s050010001200Determine the fluid type and the proper descriptive equation.0050010001500strainrateCan be done instantly with spreadsheet; hand calculations follow for comparisonpurposes:2-3

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dV/dyln(dV/dy)TIn Tln(T)-ln(dV/dy)0—0—5006.2152005.29832.9310006.9086006.39744.1912007.09010006.90848.98Sum20.2118.60126.1m = 3Summation (ln(dV/dy))2= 136.6,3(126.1) -20.21(18.60)b l =3(136.6) - 2 0 . 2 F=1 7 6 6b0=1*01.766~= -5.697ODK = exp(b0) = 0.00336;n = bj = 1.766dV\l-766dyIldyJ0.00336T =ro+9.A popular mayonnaise is tested with a viscometer and the following data were obtained:T i n g / c m240100140180dV/dyin rev/ s03715Determine the fluid type and the proper descriptive equation.The topmost line is the given data, but to curve fit, we subtract 40 from all shearstress readings.2000shearstress5101520strainrate/dV\n/dV'\nT = r0+ Kl-lwhich becomes T/= T- To=Can be done instantly with spreadsheet; hand calculations:2-4

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dV/dyln(dV / dy)TT'In hln(r')-ln(dV/dy)0—400——31.099100604.0944.49971.9461401004.6058.961152.7081801404.94213.38Sum5.75313.6426.84m = 3Summation (ln(dV/dy))2= 12.333(26.84) -5.753(13.64)b l"3(12.33) - 5.753213.64„5.753-— - 0 . 5 2 6r~”bo= 3.537K = exp(b0) = 34.37;n = bj = 0.526/dV\n7dV>0.526T = ro+ KH -= 40 + 34.37-r~I dyJI dy\where dV /dy is in rev/ s and r in g/cm2; these are not standard units.10.A cod-liver oil emulsion is tested with a viscometer and the following data were obtained:T in lbf/ft20406080120dV/dyin rev/s00.51.736Graph the data and determine the fluid type. Derive the descriptive equation.Cod liver oil; graph excludes the first data point.002468strainrateT = KH -2-5

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Can be done instantly withspreadsheet;hand calculations:dV/dyln(dV/dy)TIn Tln(T)-ln(dV/dy)0.5-0.6931403.689-2.5571.70.5306604.0942.17231.099804.3824.81661.7921204.7878.578Sum2.72916.9513.01m= 4Summation(ln(dV/dy))2= 5.181U4(13.01) -2.729(16.95)b l4(5.181)-2.7292~0 4 3 5 616 952 729b0=—j --0.4356-,-= 3.53744K = exp(b0) = 51.43;n= bj = 0.4356MVA*zdV\0.4356to+K H -= 51.43-j—I dyII dyIwhere dV/dy is in rev/s and TinIbf/ft2;these are notstandardemits.11.A rotating cup viscometer has an inner cylinder diameter of 2.00 in. and the gap betweencups is 0.2 in. The inner cylinder length is 2.50 in. The viscometer is used to obtainviscosity data on a Newtonian liquid. When the inner cylinder rotates at 10 rev/min,the torque on the inner cylinder is measured to be 0.00011 in-lbf. Calculate the viscosityof the fluid. If the fluid density is 850 kg/ m ,calculate the kinematic viscosity.Rotating cup viscometerR = 2/2 =1inch = 0.0833 ft8 = 0.2 in = 0.01667 ftL = 2.5 in = 0.2083 ftdV(10 rev/min)-(27t rad/rev)(l min/60 s) = 1.047 rad/s=iW= 0.09167 x10-4ft-lbf10412 inp = 850kg/m3sp.gr. =0.850p= 62.4(0.850) = 53.04 Ibm/ft3T8P“2nR2(R + 8)Lco0.09167 x10~4(0.01667)211(0.0833)2(0.0833 + 0.01667)(0.2083)(1.047)2-6

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