流体力学与传热习题参考解答(英文)

1 Water is pumped at a constant velocity 1m s from large reservoir resting on the floor to the open top of an absorption tower The point of discharge is 4 meter above the floor and the friction losses from the reservoir to the tower amount to 30 J kg At what height in the reservoir must the water level be kept if the pump can develop only60 J kg 22 2211 2f1 UPUP w Z g h Z g 22 U1 0 W 60j kg 12 1 0 f h30 kg 2 U 1m s 2 60300 5 g3m 21 ZZZ431m 2 The fluid density 1200 kg m3 is pumped at a constant rate 20 m3 h from the large reservoir to the evaporator The pressure above the reservoir maintains atmosphere pressure and the pressure of the evaporator keeps 200 mmHg vacuum The distance between the level of liquid in the reservoir and the exit of evaporator is 15 meter and frictional loss in the pipe is 120 J kg not including the exit of evaporator what is the pump effective work and power if the diameter of pipe is 60 mm 22 1122 12f UU Z g WZ g h 22 1 0 542 2 200 Px1 013x102 67x10 N m 760 3 1200Kg m 1 U0 f h120J kg 2 2 V20 U1 97m s A3600 4 0 06 1 Z0 2 Z15 42 2 67x101 97 W15x9 81120246 88J kg 12002 NW Q246 88x1200 x20 3600 1646W 3 Water comes out of the pipe 108x4 mm as shown in Fig The friction loss of the pipeline which does not cover the loss at the exit of pipe can be calculated by the following equation hf 6 5U2 where U is the velocity in the pipe find a water velocity at section A A b water flow rate in m3 h 22 1122 12f UU Z g Z g h 22 1 U0 12 1 Z6m 2 Z0 2 f h6 5U 2 2 U 6x9 816 5U 2 U2 9m s 23 V UA 2 94x01 x360082m h 4 Water passes through the variable pipe The velocity in the small pipe is 2 5 m s The vertical glass tubes are inserted respectively at the section A and B to measure the pressure see fig If the friction loss between two section is 15 J kg what is the water column difference between two glass tubes By the way draw the relative liquid column height of two tubes in the Fig aabb U AU A 2 b U2 5 33 47 1 23m s 22 aabb abf UU Z g Z g h 22 ab Z Z 22 abba f UU h 22 22 1 23 22 5 2 1512 63 ab PPR g 3 3 12 63 R 1 29x10 m 9 8x10 5 A centrifugal pump takes brine density 1180 kg m3 viscosity 1 2 cp from the bottom of a supply tank and delivers it into another tank The line between the tanks is 300 m of 25 mm diameter pipe inner diameter The flow rate is 2 m3 h In this line there are two gate valves four elbows 90o and one return bend what is the friction loss if the roughness of pipe is 0 025 mm 22 ffstflocal UU hhh4fk d 22 l 3 1180kg m 300m d 0 025m l 3 3 v2m h 1 2cp 1 2x10 Pa s k 0 025mm k d 0 025 25 0 001 clr k 0 4 k 1 k 2x0 07 0 14 elre k4x0 753 k1 5 2 2 2 uv A2 3600 x 4x0 025 1 13m s 4 u d Re2 78x10 f0 063 2 f 2 h4x0 0063x300 0 025x1 13 2 0 4 1 2x0 07 4x0 7 1 5 x1 13 2 197 86J kg 6 The orifice meter diameter of orifice 0 0001 m is installed for measuring the flow rate The indicating liquid of orifice is mercury if U shape pressure gauge reading is 0 6 meter and orifice coefficient can be taken as 0 61 what is the flow rate of water 0 oo 2gR uc 2 0o 0 2gx0 6x 13600 1000 Vu s0 61x 4x0 0001 x 1000 83 5 8x10 m s 7 Water flows through a pipe with a diameter di 100 mm as shown in figure a when the valve is closed R is 600 mm and h equals 1500 mm While the valve opens partially R 400 mm and h 1400 mm f 0 00625 Finning factor and kc 0 5 contraction coefficient what is the flow rate of water in m3 h b If the valve opens fully what is the pressure of section 2 2 in N m2 The equivalent length of the valve is 1 5 m and the Fanning factor f keeps the same H2O 1000kg m3 Hg 13600kg m3 1 the valve opens partially for selection 1 1 and 2 2 we have 22 1122 12f1 2 uu gZgZh 22 2 2 12HgH o 0 g Rh 39630N m 22 12f1 2c uu u0 Z 0 h4f k2 13u d 22 l We can get Z1 from the valve closed 2 1HgH O h 1 5m R 0 6m ZgR h6 66m 22 9 81x6 66u 22 13u39630 1000 23 h u 3 13m s V3600 x 4x0 1 x3 1388 5m h 2 when the valve opens fully for section 1 1 and 3 3 we have 22 3311 13f1 3 uu gZgZh 22 311 Z0 Z6 66m u 0 2 2 e f1 3c u3 1 5 h 4fk 4x0 00625x 0 5 4 81u d20 01 ll 22 9 81x6 66u 24 81u u3 51m s For section 1 1 and 2 2 22 1122 12f1 2 uu gZgZh 22 11212 0 Z6 66 Z0 u0 u3 51 2 2 f1 2c lu h 4fk 4x0 00625x15 0 1 0 5 3 51 226 2J kg d2 2 2 2 2 9 81x6 663 15 226 2 N 32970 m 8 The rotameter is installed to measure the water flow rate as shown in figure If the total length including equivalent length of pipeline A is 10 m and the reading of rotameter is 2 72 m3 h what is the flow rate for pipeline B fA 0 0075 fB 0 0045 For parallel pipe line fAfBtotalAB 2 2 A fAA 2 A hh VV V u l le 2 72 h4f4x0 0075x10 0 053 2 d23600 x 4x0 053 0 333J kg 2 2 B fBBB B 23 BBBB u l le h4f4x0 0045x2 0 3 2xu0 333 d2 u2 36m s V u A2 36x 4x0 23600m h 10 A flat furnace wall is constructed of 120 mm layer of sil o cel brick with a thermal conductivity 0 08 w mo C backed by a 150 mm of common brick of conductivity 0 8 w mo C the temperature of inner face of the wall is 1400 o and that of the outer face is 200o C a What is the heat loss through the wall in w per square meter b To reduce the heat loss to 600 w m2 by adding a layer of cork with k 0 2 w mo C on the outside of common brick how many meters of cork are requied a 2 Qt1400200 711N m 11 LR 0 080 8 0 120 15 b 600 1400 200 0 12 0 08 0 15 0 8 x 0 2 x 0 0625m 13 Air at the normal pressure passes through the pipe di 20 mm and is heated from 20o C to 100o C What is the film heat transfer coefficient between the air and pipe wall if the average velocity of air is 10 m s The properties of air at 60 o C are as follows density 1 06 kg m3 viscosity 0 02 cp conductivity 0 0289 w mo C and heat capacity 1 kJ kg K 44 3 u d10 x0 02x1 06 Re 1 06x1010 0 02x10 12 T T20 100 T 60 22 0 14 1 1000 0 02 0 001 0 692 0 0289 p c xx k Pr 0 8 1 3 0 81 34 Nu 0 027RePr0 027x 1 06x10 x 0 69239 66 2 ii i h d 39 66 h39 66x0 0289 0 02 57 22w m k k 14 A hot fluid with a mass flow rate 2250 kg h passes through a 25x2 5 mm tube The physical properties of fluid are as follows k 0 5 w mo C Cp 4 kJ kg K viscosity 10 3 N s m2 density 1000 kg m3 Find a Heat transfer film coefficient hi in w m2 K b If the flow rate decreases to 1125 kg h and other conditions are the same what is the hi c If the diameter of tube inside diameter decreases to 10 mm and the velocity u keeps the same as that of case a calculate hi d When the average temperature of fluid and quantity of heat flow per meter of tube are 40 o C and 400 w m respectively what is the average temperature of pipe wall for case a e From this problem in order to increase the heat transfer film coefficient and enhance heat transfer what kinds of methods can you use and which is better explain Hint for laminar flow Nu 1 86 Re Pr 1 3 for turbulent flow Nu 0 023Re0 8 Pr1 3 1 44 4N2250 x4 u dGd d3600 x x0 02 Re3 98x1010 0 001 1 3 0 8 0 81 34 2 4 Nu 0 023RePr0 023x 3 98x10220 1 0 5 Nuk220 1x0 5 hi5500w m k d0 02 2 12 w2w 44 21 ReRe 2 2x1010 0 8 0 8 22 11 NuRe 0 5 NuRe 0 8 i2 i1 h 0 5 h 0 82 i2 h5500 x0 53159w m k 3 44 33 3 ud2000 x0 01 Re2x1010 0 001 0 81 3 Nu0 023RePr 2 hi 6347w m k 4 iiww Q h A t t 400 500 x2 x0 02 t t w t 40t39 41 5 there methods increase u or hi or decrease d The first is better 15 In a double pipe exchange 23x2 mm the cold fluid Cp 1 kJ kg flow rate 500 kg h passes through the pipe and the hot fluid goes through the outside The inlet and outlet temperatures of cold fluid are 20 and 80 o and the inlet and outlet temperatures of hot fluid are 150 and 90o respectively The hi film coefficient inside pipe is 700 w m2 oC and overall heat transfer coefficient Uo based on the outside surface of pipe is 300w m2 oC respectively If the heat loss is ignored and the conductivity of pipe wall steel is taken as 45 w moC find 1 heat transfer film coefficient outside the pipe ho 2 the pipe length required for counter flow in m 3 what is the pipe length required if the heating medium changes to saturated vapor 140 oC and it condenses to saturated liquid and other conditions keep unchanged 4 When the exchanger is used for a year it is found that it cannot meet the need of production the outlet temperature of cold fluid cannot reach 80 oC explain why a 0mo 0iim dl d111230 002x23 hVoh dkd300700 x1945x21 1 h0 1 U0 do hidi bdo kdm 1 300 23 700 19 0 002 23 45 21 2 0 h642 9w m k Q UoAo Tm mcCp Tcb Tca 12 t t LMTD 70 2 300 2 0 023 70L 500 3600 1000 80 20 L 5 4m c 8020 LMTD 86 5 14020 ln 14080 11 22 Lt 70 86 5 Lt 2 L0 81L14 4m d scale is formed on the outside V0 is decreased 16 Water flows turbulently in the pipe of 25x2 5 mm shell tube exchanger When the velocity of water u is 1 m s overall heat transfer coefficient Uo based on the outer surface area of pipe is 2115 w m2 oC If the u becomes 1 5 m s and other conditions keep unchanged Uo is 2660 w m2 oC What is the film coefficient ho outside the pipe Heat resistances of pipe wall and scale are ignored 1 2 oi hhUo 111 oio hhU 1 1 1 1 2 0 80 80 80 8 12 111111 21152660uCuC1 C1 5 C C 2859 ho 8127W m2K io hUoh 111 17 Water and oil pass parallelly through an exchanger which is 1 m long The inlet and outlet temperatures of water are 15 and 40 oC and those of oil are 150 and 100 oC respectively If the outlet temperature of oil decreases to 80 oC and the flow rates and physical properties and inlet temperatures of water and oil maintain the same what is the pipe length of new exchanger Heat loss and pipe wall resistance are neglected hh12cc21m QW CT TW CttVA t hh12cc21 W CT T W Ct t 2 150 10040 15 15080t15 2 t50 212m1 112m2 LTT t15080 92 5 1 85 LTTt150 100 69 8 2m1m2 L1 85m L1 1m t92 5 t69 8 18 Air which passes through the pipe in turbulent flow is heated from 20 to 80 oC The saturated vapor at 116 3 oC condenses to saturated water outside the pipe If air flow rate increases to 120 of the origin and inlet and outlet temperatures of air stay constant what kind of method can you employ in order to do that Heat resistance of pipe wall and scale can be ignored 111cacbpccmii TTCmTAh 1 Q 2212cacbpccmi TTCmTAh 2 Q 1 28 0 1 2 11 2i2 2 12 1 h m m c c mi m T T m m Th T 80 3 116 20 3 116ln 2080 1 m T 80 20ln 2080 2 hh m TT T Th 118 5oC 19 Water flows through the pipe of a 25x2 5 mm shell tube exchanger from 20 to 50 oC The hot fluid Cp 1 9 kJ kgo C flow rate 1 25 kg s goes along the shell and the temperatures change from 80 to 30 o C Film coefficients of water and hot fluid are 0 85kw m2 oC and 1 7 kw m2 o C What is the overall heat transfer coefficient Uo and heat transfer area if the scale resistance can be ignored the conductivity of steel is 45w mo C W 1 25Kg s Cp 1 9Kj kg 2hp12 QW CTT1 25x1 9x 80 30119Kw m 30 10 t 30 ln 10 2 0 0m0 0iim 1 V472w m k dl d1 hh dkd 3 2 i 0m Q119x10 A13 9m Vt472x18 2 20 A spherical particle density 2650 kg m3 settles freely in air at 20 o C density of air 1 205 kg m3 viscosity 1x10 5 Pa s Calculate the maximum diameter of particle if the settle obeys the Stokes Law Re 1 2 p t p D g U 18D 2 3 p 18 D g 3 85x10 5 1 3 10 p 18x10 D 1 205x9 81x 2650 1 205 21 A filter press A 0 1 m2 is used for filtering slurry The vacuum inside the filter is 500 mm Hg One liter filtrate can be got after filtering of 5 min and 0 6 more liter filtrate is obtained after 5 more min How much filtrate will be got after filtering of 5 more min for filter press 22 e V2