1、6 21.1 A pressure of 2 10 N/m is applied to a mass of water that initially filled a 31,000cm volume. Estimate its volume after the pressure is applied.將2 106N/m2的壓強施加于初始體積為1,000cm3的水上，計算加壓后水的體 積。3(999.1cm)Fig. 1-9 Problem 1.21.2 As shown in Fig.1-9, in a heating system there is a dilatati on water t

2、ank. The whole volume of3the water in the system is 8m . The largest temperature rise is 50C and the coefficient of volume expansion is : v=0.0005 1/K, what is the smallest cubage of the water bank?如圖1-10所示，一采暖系統在頂部設一膨脹水 箱,系統內的水總體積為8m3,最大溫升50C,膨 脹系數:v=0.005 1/K,求該水箱的最小容積？3(0.2m3)1.3 When the in crem

3、e nt of pressureis 50kPa, the den sity of a certa in liquid is 0.02%. Find the bulk modulus of the liquid.當壓強增量為50kPa時，某種液體的密度增加0.02%。求該液體的體積模量(2.5Problem 2.90匚A4 11JftNWaterRercuryProblem 2.62.7 There is an applied load of 5788N on the pist on within a cyli ndrical contain er, i n which is filled w

4、ith oil and water. The oil column height is h 1=30cm when the water colu mn h2=50cm. The diameter of the container is giver as d=40cm. The den sity of33oil is 】1=800kg/m and that of mercury as3=13 600kg/m . Compute the height H(cm) of the mercury column in the U-tube.圓柱形容器的活塞上作用一 5788N的力，容器內充有水和油。當水

5、柱高 h2=50cm 時，油柱高h1=30cm。容器直徑d=40cm，油的密度,=800kg/m3，水銀密度?3=13 600kg/m3。求U形管內的汞柱高 H(cm)。(14.07cm)F/oilyIhFJWater,IProblem 2.72.8 According to the diagram, a closed tank contains water that has a relative pressure on the2 -water surface of po= - 44.5kN/m .(1) What is the dista nee h?(2) What is the pres

6、sure at point M with0.3m below water surface?(3) What is the piezometric head of pointM relative to datum pla ne1-1?如圖所示，一密閉容器內盛有自由表面相對 壓強為po=- 44.5kN/m2的水。求距離h;水面下0.3m處的M點的壓強為多少？(3) M點相對于基準面1-1的測壓管水頭是多少?(h=4.54m, Pm=-41.6kPa, hm=-4.24m)2.9 An upright U-tube is fixed on the hood of a car which trave

7、ling in a straight-line, with a2constant acceleration a=0.5m/s . The length L=500mm. Find the height difference of the two free surfaces in the U-tube.一豎直的U形管安裝在以勻加速度a=0.5m/V作 直線運行的車罩上，長度L=500mm。求U形管 內兩自由液面的高度差。(25.5mm)Problem 2.12Problem 2.9Problem 2.102.10 Accord ing to the diagram, an ope n tank

8、containing water moves with an accelerati on a=3.6m/s, along a slope of 30 What is the inclined angle v with the horizontal plane and the equati on of water pressure p at the free surface?如圖所示，一盛水的開口容器以加速度 a=3.6m/W沿30的斜面運動。求自由液面與 水平面的夾角亠并寫出水的壓強p的分布 方程。(寸=15，p=pa+ -gh)2.11 As shown in the figure, a g

9、ate of 2m wide, exte nds out of the pla ne of the diagram toward the reader. The gate is pivoted at hingeH, and weighs 500kg. Its cen ter of gravity isI. 2m to the right and 0.9m above H. For what values of water depth x above H will the gate remain closed? (Neglect friction at the pivot point and n

10、 eglect the thick ness of the gate)如圖所示，閘門寬2m，重500kg，繞鉸鏈H_轉動。閘門重心在距右端1.2m處且高于H0.9m。問鉸鏈H上方水深x為多少時，閘門將關閉？(忽略鉸鏈摩擦及閘門的厚度)(1.25m)2.12 A flat 1 m high gate is hinged at point O, and can rotate around the point (see attached diagram). The height of point O is a=0.4m. What is the water depth when the gate c

11、an automatically ope n around point O?一 1米高的平板閘門在O點處用鉸鏈連接，且 可繞鉸鏈轉動(見附圖)。O點的高度為a=0.4m。水深多少時，閘門將自動開啟？ (h=1.33m)Problem 2.122.13 As show n in the diagram, a closed tank formi ng a cube is half full of water, find: (a) the absolute pressure on the bottom of the tank, (b) the force exerted by the fluids

12、on a tank wall as a function of height, (c) the location of the center of pressure by water on the tank wall.如圖所示，一密閉立方體水箱裝了一半的 水，求：(a)箱底的絕對壓強；(b)將流體 對一側箱壁的作用力表示為高度的函數；(c)水對箱壁的壓力中心位置。(17.8kPa, F=2h(8000+0.5：gh), 2/3)Side view of tank wallProblem 2.132.14 A circular sluice gate of diameter d=1m is su

13、bmerged in water as shown in the figure. The slant angle ： =60, the submerged depth hc=4.0m, and the weight of the gate FG=1kN. Determine the magn itude of the vertical force T so as to make the gate rotate upward about axis a (neglect friction at axis a).Problem 2.14如圖所示的一直徑d=1m圓形閘門淹沒于 水中。傾角=60，淹深h

14、c=4.0m，閘門 重FG=1kN。求使閘門繞樂由向上轉動的鉛 直力T的大小。(230kN)Water2.15 The gate M shown in the figure rotates about an axis through N. If a=33m, b=13m,d=20m and the widthperpe ndicular to the pla ne of the figure is 3m, what torque applied to the shaft through N is required to hold the gate closed?圖示閘門M繞N軸轉動。如a=33

15、m、 b=13m、d=20m且與圖形垂直的寬度為 3m,要使閘門關閉，需要施加多大的力 矩在轉軸上？(666 1 03kN m)Problem 2.15Problem 2.162.16 Find the horizontal and vertical components of the force exerted by fluids on the fixed circular cylinder shown in the figure, if:(1) the fluid to the left of the cylinder is a gas confined in a closed tank

16、at a pressure of 35kPa, and (2) the fluid to the left of the cylinder is water with a free surface at an elevatio n coin cide nt with the uppermost part of the cylinder. Assuming in both cases that no rmal atmospheric pressure con diti ons exist to the right and top of the cyli nder.求下述流體對圖示圓柱體所施加的水

17、平與鉛 直方向的 分力。(1)圓柱體左 邊是壓強為 35kPa的密閉氣體；(2)圓柱體左邊是自由液 面剛好與柱頂平齊的水。設兩種情況下圓柱 體的右邊與頂部為標準大氣壓。(1) Fx=130.5kN，Fz=35kN ； Fx=68.1kN，Fz=100.5kN)aProblem 2.172.17 The cross section of a tank is as shown in the figure. BC is a cylindrical surface with r=6m, and h=10m. If the tank contains gas at a pressure of 8kPa,

18、 determine the magnitude and location of the horizontal and vertical force comp onents act ing on un it width of tank wall ABC.圖示為一容器的剖面，BC是半徑r=6m的圓柱面。 容器高h=10m。如果容器裝有壓強為8kPa的氣體， 求作用在容器壁ABC上單位寬度的水平分力與 鉛直分力的大小與作用位置。rotate(Fx=80kN，Fz=48kN)2.18 Find the minimum value of z for which the gate in the figu

19、re will coun terclockwise if the gate is: (a) recta ngular 5m high by 4m wide; (b) tria ngular, 4m base as axis, height 5m. n eglect frict ion in beari ngs.Problem 2.18當下述情況時，求使圖示閘門沿逆時針方向轉動的z的最小值：(a)閘門為高5m、寬4m的矩形；(b)閘門為上底4m (轉軸)、高5m的三角形。(a) z=307.5m, (b)305m)2.19 A curved surface is formed as a quar

20、ter of a circular cyli nder with R=0.75m, asshow n in the figure. The cyli nder surface is w=3.55m wide (out of the pla ne of the figure toward the reader). Water standstill to the right of the curved surface to a depth of H=0.65m. Determi ne(1) The magn itude of the hydrostatic force on the surface

21、.(2) The direct ion of the hydrostatic force.Problem 2.19一曲面由半徑為R=0.75m的四分之一的圓柱體組成，如圖所示。圓柱面寬w=3.55m (垂直于圖形平面)。曲面右側靜水深度H=0.65m。試求：(1) 作用于曲面上靜水壓力的大小；(2) 靜水壓力的方向。(Fx=7357N, Fz=6013N)2.20 As shown in the diagram, there is a cylinder with diameter D=4m and length L=12m in water. The depth of water on the

22、 right and left side of the cylinder are 4m and 2m respectively. Find the magnitude and directi on of the force on the cyli nder exerted by water.Problem 2.204m和2m。求水對圓柱體如圖所示，直徑D=4m、長L=12m的圓柱體放于水中，圓柱體左右兩邊水的深度分別為 的作用力的大小與方向。(Fx=706kN，Fz=1579kN)2.21 As shown in the figure, determine the pivot location

23、 y of the rectangular gate, so that the gate will just ope n.如圖所示，求閘門剛好開啟時轉軸的位置 y為多少。（y=0.44m）Problems3.1 A two-dime nsion al, i ncompressible flow field is give n byFind the velocity and acceleratio n at point (1,2).二維不可壓縮流動由確定。試求點(1, 2)處的速度與加速度。(Vx=5, Vy=-30； ax=75, ay=150)3.2 Suppose velocity dis

24、tribution of a flow field is given byFind:(1) the expression of local acceleration; (2) the acceleration of the fluid particle at poi nt (1,1) when t=0.設流場的速度分布為求：（1）當地加速度的表達式；（2）t=0時在點（1，1 ）處流體質點的加速度。（1） Wx/：t=4, ：vy/ft=0； （2） ax=3, a/=-1）3.3 The velocity comp onents ofield isDeterm ine the streaml

25、i ne equati on thr一流場的速度分量為oint (x,yt0.確定在t=t0時刻通過點（X0,y0）的流線方程。3.4 A two-dime nsional velocity field is givWhat is the streamline equation in this flow field?已知二維速度場，求流線方3.5 It is known the velocity field is+C=0)(x1+t=cy)Try to find the streamline equation已知速度場g through poi1, 1).1，1）的流線方程。(x =2，5-z

26、=2z)I3.6 An oil transportation pipeline, the velocity at the section of diameter 20cm is 2m/s, what is the velocity and mass flow rate at the sect ion of diameter 5cm? The3density of the oil is 850kg/m .有一輸油管道，在內徑為20cm的截面上流速為2m/s,求在另一內徑為5cm 的截面上的流速以及管內的質量流量。油的密度為850kg/m3。(32m/s, 53.4kg/s)3.7 In a pi

27、peline of inner diameter 5cm, the mass flow rate of air is 0.5kg/s, pressure at a certa in is 5 105Pa, the temperature is 10(C. Fi nd the average air flow velocity on this sect ion.在內徑為5cm的管道中，流動空氣的質量流量為0.5kg/s，在某一截面上壓強為5 105Pa,溫度為1000C。求該截面上氣流的平均速度。(54.5m/s)3.8 The velocity distributio n of an in c

28、ompressible fluid isTry to deduce the expressi on of/z by adopti ng con ti nuity equati on.已知一不可壓縮流體的速度分布為 用連續方程推導出Vz的表達式。(vz=-z(2x+2y+z+1)+c(x,y)3.9 As show n in Fig. 3-25, water flows steadily in to a two-dime nsio nal tube at a uniform velocity v. Since the tube bends an angle of 90 , velocity di

29、stribution at the outlet becomes.Assu ming the width hof the tube is con sta nt, find con sta nt C.求常數Co ( C=v/3)。設通道寬度h3.10 Water is flowing in a r shown in Fig. 3-26. Two Pitot tub stacked and connected to a mano meter containing a fluid gravity 0.82. Fi nd va and vb.水在河道中流動，如圖differ of spe3-26所示

30、兩個重疊的皮托管與一裝有比重為0.8的流體的壓差計連接。試求va及vb。(vA=1.212m/s, vb =1.137m/s)Fig.roblem 3.9Fig. 3-26LT?如圖3-25所示，水以均勻速度v 定常流入一個二維通道，由于通道彎 曲了 90，在出口端速度分布變為3.11 As show n in Fig. 3-27, a pipe of diameter 1m is in stalled horiz on tally, of which a part bends an angle of 30. Oil of specific gravity 0.94 flows in side

31、 the pipe with a flow rate of 2m3/s. Assume pressure in the pipe is uniform, the gauge pressure is 75kPa, find the horizontal force exert ing on the elbow pipe.直徑為1m的水平裝置的管Fig. 3-27 Problem 3.11道有一段30的彎管，如圖3-27所示。管內比重為0.94的油以2m3/s的流量流動。設彎管內壓強均勻，表壓為75kPa,求彎管受到的水平力。(Fx=8.64kN, Fy=31.9kN)3.12 The heigh

32、t of the mercury column in U-tube is 60mm, as shown in Fig. 3-28. Assume the diameter of the conduit is 100mm, find the volume flow rate of water through the conduit at secti on A.如圖3-28所示，U形管內汞柱高度 為60mm。設排水管的直徑為100mm， 求在截面A處通過排水管的體積流量。(0.0314m3/s)Fig. 3-28 Problem 3.120dd.vJFig. 3-29 Problem 3.133.

33、13 A no zzle is conn ected at one end of a water pipe, as show n in Fig. 3-29. The outlet diameter of the water pipe is d1=50mm, and that of the nozzle is d2=25mm. The no zzle and the pipe are connected by four bolts. The gauge pressure at inlet of the no zzle is 1.96 10 Pa, volume flow rate is30.00

34、5m /s, try to find the tension applied on each bolt.在水管的端部接有噴嘴，如圖 3-29所示。水管出口直徑d1=50mm， 噴嘴出口直徑d2=25mm。噴嘴與 管之間用四個螺栓連接。噴嘴入口 處的表壓為1.96 105Pa,流量為0.005m3/s，求每個螺栓所受到的拉力。(86.75N)3.14 A cen trifugal pump draws water from a well, as shown in Fig.3-30. Assume the inner diameter of the slouch is d=150mm, volum

35、e flow 3rate is q=60 m /h, and the vacuum value at point A where the slouch and the pump are conn ected4is pv=4 10 Pa. Neglect head loss, what is the sucti on height Hs of the pump?Fig. 3-30 Problem 3.14離心式水泵從井里抽水，如圖3-30所示。 設吸水管內徑d=150mm,流量為qv=60 m3/h, 吸水管與水泵接頭處A點的真空值為 pv=4 104Pa。不計水頭損失，求水泵的吸水高 度 Hs

36、。(4.03m)3.15 As shown in Fig.3-31, an oil of specific gravity 0.83 rushes towards a vertical plate at velocity v=20m/s, find the force n eeded to support the plate.如圖3-31所示，相對密度為0.83 的油水平射向直立的平板，已知v=20m/s， 求支撐平板所需的力F。(652N)Fig.3-31 Problem 3.15Fig. 3-32 Problem 3.163.16 A horiz on tal jet flow with

37、volume flow rate q v0 rushes towards an in cli ned plate at velocity v 0, as show n in Fig. 3-32. Neglect the effects of gravity and impact loss of the fluid, the pressure and velocity of the jet flow rema in the same after it splits into two distributaries. Find the formulas of the two distributari

38、es flow rate qv1and qv2, and the force acting on the plate.如圖3-32所示，一股速度為v。、體 積流量為qv0的水平射流，射到傾斜的光 滑平板上。忽略流體撞擊的損失和重力 的影響，射流的壓強與速度在分流后也 沒有變化，求沿板面向兩側的分流流量 qv1與qv2的表達式，以及流體對板面的 作用力。3.17 As shown in Fig.3-33, a cart carry ing an in cli ned smooth plate moves at velocity v against a jet flow, the velocity

39、 , flow rate and density of the jet flow are vo, qv ,and respectively. Ig nore the friction between the cart and ground, what is the power W n eeded for driv ing the cart?如圖3-33所示，帶有傾斜光滑平 板的小車逆著射流方向以速度 v運動， 射流的速度和流量分別為V0和qv，射 流的密度為6不計小車與地面的摩擦 力，求推動小車所需的功率W。( )p1iB2 mA4 m13 ID1D 22QCFig. 3-34 Problem

40、 3.183.18 A crooked pipe stretches out from a big container, as shown in Fig. 3-34, the diameter of the pipe is 150mm, and that of the no zzle is 50mm. If n eglect the head loss, try to find the flow rate of the pipe, and pressures at point A, B, C, and D.從一大容器引出一彎曲的管道如圖 3-34所示，管徑為 150mm，噴嘴直徑為 50mm，不計水頭損失，求管的輸水流量， 以及A、B、C、D各點的壓強。(0.0174m3/s, 68.2、-0.47、-20.1