工程流體力學(xué)課后習(xí)題

1、.工程流體力學(xué)課后習(xí)題1.1 A pressure of 2´106N/m2 is applied to a mass of water that initially filled a 1,000cm3 volume. Estimate its volume after the pressure is applied. 將2´106N/m2 的壓強(qiáng)施加于初始體積為1,000cm3的水上，計(jì)算加壓后水的體積。(999.1cm3)1.2 As shown in Fig.1-9, in a heating system there is a dilatation water ta

2、nk. The whole volume of the water in the system is 8m3. The largest temperature rise is 500C and the coefficient of volume expansion is av=0.0005 1/K, what is the smallest cubage of the water bank?如圖1-10所示，一采暖系統(tǒng)在頂部設(shè)一膨脹水箱，系統(tǒng)內(nèi)的水總體積為8m3，最大溫升500C，膨脹系數(shù)av=0.005 1/K，求該水箱的最小容積？(0.2m3) Fig. 1-9 Problem 1.21.

3、3 When the increment of pressure is 50kPa, the density of a certain liquid is 0.02%. Find the bulk modulus of the liquid.當(dāng)壓強(qiáng)增量為50kPa時(shí)，某種液體的密度增加0.02%。求該液體的體積模量。( 2.5´108Pa)1.4 Fig.1-10 shows the cross-section of an oil tank, its dimensions are length a=0.6m, width b=0.4m, height H=0.5m. The diam

4、eter of nozzle is d=0.05m, height h=0.08m. Oil fills to the upper edge of the tank, find:(1) If only the thermal expansion coefficient av=6.5´10-41/K of the oil tank is considered, what is the volume Fig.1-10 Problem 1.4of oil spilled from the tank when the temperature of oil increases from t1=

5、-200C to t2=200C?(2) If the linear expansion coefficient al=1.2´10-51/K of the oil tank is considered, what is the result in this case?圖1-10為一油箱橫截面，其尺寸為長(zhǎng)a=0.6m、寬b=0.4m、高H=0.5m，油嘴直徑d=0.05m，高h(yuǎn)=0.08m。由裝到齊油箱的上壁，求：(1) 如果只考慮油液的熱膨脹系數(shù)av=6.5´10-41/K時(shí)，油液從t1=-200C上升到t2=200C時(shí)，油箱中有多少體積的油溢出？(2) 如果還考慮油箱的

6、線膨脹系數(shù)al=1.2´10-51/K，這時(shí)的情況如何？(1)2.492´10-3m3 (2)2.32´10-3m3)1.5 A metallic sleeve glides down by self weight, as shown in Fig. 1-11. Oil of n=3´10-5m2/s and r=850kg/m3 fills between the sleeve and spindle. The inner diameter of the sleeve is D=102mm, the outer diameter of the spin

7、dle is d=100mm, sleeve length is L=250mm, its weight is 100N. Find the maximum velocity when the sleeve glides down freely (neglect air resistance). Fig. 1-11 Problem 1.5有一金屬套由于自重沿垂直軸下滑，如圖 1-11所示。軸與套間充滿了n=3´10-5m2/s、r=850kg/m3的油液。套的內(nèi)徑D=102mm，軸的外徑d=100mm，套長(zhǎng)L=250mm，套重100N。試求套筒自由下滑時(shí)的最大速度為多少(不計(jì)空氣阻力

8、)。(50 m/s)1.6 The velocity distribution for flow of kerosene at 200C (m=4´10-3N·s/m2) between two walls is given by u=1000y(0.01-y) m/s, where y is measured in meters and the spacing between the walls is 1 cm. Plot the velocity distribution and determine the shear stress at the walls.在200C

9、時(shí)，煤油(m=4´10-3N·s/m2)在兩壁面間流動(dòng)的速度分布由u=1000y(0.01-y) m/s確定，式中y的單位為m，壁面間距為1cm。畫(huà)出速度分布圖，并確定壁面上的剪應(yīng)力。(4´10-2Pa)1.7 As shown in Fig.1-12, the velocity distribution for viscous flow between stationary plates is given as follows: Fig. 1-12 Problem 1.7If glycerin is flowing (T=200C) and the pressu

10、re gradient dp/dx is 1.6kN/m3, what is the velocity and shear stress at a distance of 12 mm from the wall if the spacing By is 5.0 cm? What are the shear stress and velocity at the wall?如圖1-12所示，兩固定平板間粘性流動(dòng)的速度分布由 給出。如果流體為甘油(T=200C) 且壓強(qiáng)梯度dp/dx為1.6kN/m3，間距By為5.0 cm，距平板12mm處的速度與剪應(yīng)力為多少？平板處的剪應(yīng)力與速度為多少？(u12

11、=0.59m/s；12=20.8N/m2；u0=0；0=40.4N/m2)1.8 What is the ratio of the dynamic viscosity of air to that of water at standard pressure and T=200C? What is the ratio of the kinematic viscosity of air to water for the same conditions?在標(biāo)準(zhǔn)大氣壓、T=200C時(shí)，空氣與水的動(dòng)力粘度之比為多少？同樣條件下它們的運(yùn)動(dòng)粘度之比又為多少？(mA/mW=0.0018；nA/nW=15.1)

12、1.9 The device shown in Fig. 1-13 consists of a disk that is rotated by a shaft. The disk is positioned very close to a solid boundary. Between the disk and boundary is viscous oil.(1) If the disk is rotated at a rate of 1 rad/s, what will be the ratio of the shear stress in the oil at r=2cm to Fig.

13、 1-13 Problem 1.9the shear stress at r=3cm?(2) If the rate of rotation is 2 rad/s, what is the speed of oil in contact with the disk at r=3cm?(3) If the oil viscosity is 0.01 N·s/m2 and the spacing y is 2mm, what is the shear stress for the condition noted in (b)? 圖1-13所示裝置由繞一根軸旋轉(zhuǎn)的圓盤構(gòu)成。圓盤放置在與固體

14、邊界很近的位置。圓盤與邊界間為粘性油。(1) 如果圓盤的旋轉(zhuǎn)速率為1 rad/s，問(wèn)半徑為r=2cm與r=3cm處的剪應(yīng)力之比為多少？(2) 如果旋轉(zhuǎn)速率為2 rad/s，r=3cm處與圓盤接觸的油層的速度為多少？(3) 如果油的粘度為0.01 N·s/m2 、且間距y為2mm，(b)情況下的剪應(yīng)力為多少？(1) 2:3；(2) 6cm/s；(3) 0.3Pa)1.10 As shown in Fig. 1-14, a cone rotates around its vertical center axis at uniform velocity. The gap between t

15、wo cones is d=1mm. It filled with lubricant which m=0.1Pa·s. In the Figure, R=0.3m, H=0.5m, Fig. 1-14 Problem 1.10w=16 rad/s. What is the moment needed to rotate the cone?如圖1-14所示，一圓錐體繞豎直中心軸等速旋轉(zhuǎn)，錐體與固定的外錐體之間的隙縫d=1mm，其中充滿m=0.1Pa·s的潤(rùn)滑油。已知錐體頂面半徑R=0.3m，錐體高度H=0.5m，當(dāng)旋轉(zhuǎn)角速度 w=16 rad/s 時(shí)，求所需要的旋轉(zhuǎn)力矩。(

16、39.6N·m)2.1 Two pressure gauges are located on the side of a tank that is filled with oil. One gauge at an elevation of 48m above ground level reads 347 kPa. Another at elevation 2.2m reads 57.5 kPa. Calculate the specific weight and density of the oil.兩個(gè)測(cè)壓計(jì)位于一充滿油的油箱的一側(cè)。一個(gè)測(cè)壓計(jì)高于地面的位置高度為48m，讀數(shù)57.

17、5 kPa。另一個(gè)位置高度為2.2m，讀數(shù)347kPa。計(jì)算油的重度與密度。(g=6.32kN/m3,r=644kg/m3)2.2 Two hemispherical shells are perfectly sealed together, and the internal pressure is reduced to 20 kPa, the inner radius is 15 cm and the outer radius is 15.5 cm. If the atmospheric pressure is 100 kPa, what force is required to pull

18、the shells apart?兩半球殼完美密閉在一起，內(nèi)壓減至20 kPa，內(nèi)徑15 cm，外徑15.5 cm。如果大氣壓強(qiáng)為100 kPa，求要將半球拉開(kāi)所需的力為多少。(24.5kN)2.3 As shown in the figure, there is a quantity of oil with density of 800 kg/m3, and a quantity of water below it in a closed container. If h1=300mm, h2=500mm, and h=400mmHg, find the pressure at the fre

19、e surface of the oil. 如圖所示，密閉容器中油的密度為800 kg/m3，其下方為水。如果h1=300mm, h2=500mm, 及 h=400mmHg，求油的自由表面上的壓強(qiáng)。(46.1kPa) Problem 2.32.4 According to the diagram, one end of a tube connected to an evacuated container and the other end is put into a water pool whose surface is exposed to normal atmospheric pressu

20、re. If hv=2m, what is the pressure inside of container A?如圖，一根管子一端與一抽空的容器相連，另一端插入暴露于大氣的水池中。如hv=2m，容器內(nèi)的壓強(qiáng)是多少？(81.7kPa) P Problem 2.4 2.5 A pressure gauge is placed under sea level. If the gauge pressure at a point 300m below the free surface of the ocean, it registers 309 kPa, find the average specif

21、ic weight of sea water.一測(cè)壓計(jì)置于海平面下，如果在自由表面下300m深處測(cè)壓計(jì)的讀數(shù)為309 kPa，求海水的平均重度。(1.03kN/m3)2.6 If the local atmospheric pressure is given by 98.1 kPa absolute, find the relative pressure at points a, b and c in water. (see attached figure)如果當(dāng)?shù)卮髿鈮旱慕^對(duì)壓強(qiáng)為98.1 kPa，求水中a、b 及 c 點(diǎn)的相對(duì)壓強(qiáng)。（見(jiàn)附圖）(Pa=68.6kPa，Pb=31.3kPa，P

22、c=-29.4kPa) Problem 2.62.7 There is an applied load of 5788N on the piston within a cylindrical container, in which is filled with oil and water. The oil column height is h1=30cm when the water column h2=50cm. The diameter of the container is giver as d=40cm. The density of oil is r1=800kg/m3 and th

23、at of mercury as r3=13 600kg/m3. 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(nèi)充有水和油。當(dāng)水柱高h(yuǎn)2=50cm時(shí)，油柱高h(yuǎn)1=30cm。容器直徑d=40cm，油的密度r1=800kg/m3，水銀密度r3=13 600kg/m3。求U形管內(nèi)的汞柱高H(cm) 。(14.07cm) Problem 2.72.8 According to the diagram, a closed tank contains water that has a

24、relative pressure on the water surface of po= - 44.5kN/m2.(1) What is the distance h?(2) What is the pressure at point M with 0.3m below water surface?(3) What is the piezometric head of point M relative to datum plane1-1?如圖所示，一密閉容器內(nèi)盛有自由表面相對(duì) Problem 2.8壓強(qiáng)為po=- 44.5kN/m2的水。(1) 求距離h；(2) 水面下0.3m處的M點(diǎn) 的壓

25、強(qiáng)為多少？(3) M點(diǎn)相對(duì)于基準(zhǔn)面1-1的測(cè)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 traveling in a straight-line, with a constant acceleration a=0.5m/s2. 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/s2

26、作直線運(yùn)行的車罩上，長(zhǎng)度L=500mm。求U形管內(nèi)兩自由液面的高度差。 (25.5mm) Problem 2.9 2.10 According to the diagram, an open tank containing water moves with an acceleration a=3.6m/s2, along a slope of 30o. What is the inclined angle q with the horizontal plane and the equation of water pressure p at the free surface?如圖所示，一盛水的開(kāi)

27、口容器以加速度a=3.6m/s2沿30o的斜面運(yùn)動(dòng)。求自由液面與水平面的夾角q，并寫(xiě)出水的壓強(qiáng)p的分布方程。(q=15o，p=pa+rgh) Problem 2.102.11 As shown in the figure, a gate of 2m wide, extends out of the plane of the diagram toward the reader. The gate is pivoted at hinge H, and weighs 500kg. Its center of gravity is 1.2m to the right and 0.9m above H.

28、 For what values of water depth x above H will the gate remain closed? (Neglect friction at the pivot point and neglect the thickness of the gate)如圖所示，閘門寬2m，重500kg，繞鉸鏈H轉(zhuǎn)動(dòng)。閘門重心在距右端1.2m處且高于H 0.9m。問(wèn)鉸鏈H上方水深x為多少時(shí)，閘門將關(guān)閉？（忽略鉸鏈摩擦及閘門的厚度）(1.25m) Problem 2.112.12 A flat 1 m high gate is hinged at point O, and

29、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 can automatically open around point O?一1米高的平板閘門在O點(diǎn)處用鉸鏈連接，且可繞鉸鏈轉(zhuǎn)動(dòng)（見(jiàn)附圖）。O點(diǎn)的高度為a=0.4m。水深多少時(shí)，閘門將自動(dòng)開(kāi)啟？(h=1.33m) Problem 2.122.13 As shown in the diagram, a closed tank forming a cube

30、 is half full of water, find: (a) the absolute pressure on the bottom of the tank, (b) the force exerted by the fluids 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(duì)壓強(qiáng)；(b) 將流體對(duì)一側(cè)箱壁的作用力表示為高度的函數(shù)；(c) 水對(duì)箱壁的壓力中心

31、位置。 Problem 2.13(17.8kPa，F(xiàn)=2h(8000+0.5rgh)，2/3)2.14 A circular sluice gate of diameter d=1m is submerged in water as shown in the figure. The slant angle a=60o, the submerged depth hc=4.0m, and the weight of the gate FG=1kN. Determine the magnitude of the vertical force T so as to make the gate rota

32、te upward about axis a (neglect friction at axis a).如圖所示的一直徑d=1m圓形閘門淹沒(méi)于水中。傾角a=60o，淹深hc=4.0m，閘門重FG=1kN。求使閘門繞a軸向上轉(zhuǎn)動(dòng)的鉛直力T的大小。(230kN) Problem 2.14 2.15 The gate M shown in the figure rotates about an axis through N. If a=33m, b=13m, d=20m and the width perpendicular to the plane of the figure is 3m, wha

33、t torque applied to the shaft through N is required to hold the gate closed?圖示閘門M繞N軸轉(zhuǎn)動(dòng)。如a=33m、 b=13m、d=20m且與圖形垂直的寬度為3m，要使閘門關(guān)閉，需要施加多大的力矩在轉(zhuǎn)軸上？(666´103kN·m) Problem 2.15 2.16 Find the horizontal and vertical components of the force exerted by fluids on the fixed circular cylinder shown in the

34、 figure, if:(1) the fluid to the left of the cylinder is a gas confined in a closed tank at a pressure of 35kPa, and (2) the fluid to the left of the cylinder is water with a free surface at an elevation coincident with the uppermost part of the cylinder. Assuming in both cases that normal atmospher

35、ic pressure conditions exist to the right and top of the cylinder. 求下述流體對(duì)圖示圓柱體所施加的水平與鉛直方向的分力。(1)圓柱體左邊是壓強(qiáng)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(shè)兩種情況下圓柱體的右邊與頂部為標(biāo)準(zhǔn)大氣壓。 Problem 2.16(1) Fx=130.5kN，F(xiàn)z=35kN；(2) Fx=68.1kN，F(xiàn)z=100.5kN)2.17 The cross section of a tank is as shown in the figure. BC is a cylindrica

36、l surface with r=6m, and h=10m. If the tank contains gas at a pressure of 8kPa, determine the magnitude and location of the horizontal and vertical force components acting on unit 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(yuǎn)=10m。如果容器裝有壓強(qiáng)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。 (Fx=80kN，F(xiàn)z=

37、48kN) Problem 2.172.18 Find the minimum value of z for which the gate in the figure will rotate counterclockwise if the gate is: (a) rectangular 5m high by 4m wide; (b) triangular, 4m base as axis, height 5m. neglect friction in bearings. Problem 2.18當(dāng)下述情況時(shí)，求使圖示閘門沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng)的z的最小值：(a) 閘門為高5m、寬4m的矩形；(b)

38、 閘門為上底4m（轉(zhuǎn)軸）、高5m的三角形。(a) z=307.5m，(b)305m)2.19 A curved surface is formed as a quarter of a circular cylinder with R=0.75m, as shown in the figure. The cylinder surface is w=3.55m wide (out of the plane of the figure toward the reader). Water standstill to the right of the curved surface to a depth

39、of H=0.65m. Determine (1) The magnitude of the hydrostatic force on the surface.(2) The direction 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(cè)靜水深度H=0.65m。試求：(1) 作用于曲面上靜水壓力的大?。?2) 靜水壓力的方向。(Fx=7357N，F(xiàn)z=6013N)2.20 As shown in the diagram, there is a cyl

40、inder with diameter D=4m and length L=12m in water. The depth of water on the right and left side of the cylinder are 4m and 2m respectively. Find the magnitude and direction of the force on the cylinder exerted by water.如圖所示，直徑D=4m、長(zhǎng)L=12m Problem 2.20的圓柱體放于水中，圓柱體左右兩邊水的深度分別為4m 和 2m。求水對(duì)圓柱體的作用力的大小與方向。

41、(Fx=706kN，F(xiàn)z=1579kN)2.21 As shown in the figure, determine the pivot location y of the rectangular gate, so that the gate will just open.如圖所示，求閘門剛好開(kāi)啟時(shí)轉(zhuǎn)軸的位置y為多少。(y=0.44m) Problem 2.21Problems3.1 A two-dimensional, incompressible flow field is given by Find the velocity and acceleration at point (1,2)

42、. 二維不可壓縮流動(dòng)由 確定。試求點(diǎn)（1，2）處的速度與加速度。(vx=5，vy=-30；ax=75，ay=150)3.2 Suppose velocity distribution of a flow field is given by Find:(1) the expression of local acceleration; (2) the acceleration of the fluid particle at point (1,1) when t=0.設(shè)流場(chǎng)的速度分布為。求：（1）當(dāng)?shù)丶铀俣鹊谋磉_(dá)式；（2）t=0時(shí)在點(diǎn)（1，1）處流體質(zhì)點(diǎn)的加速度。(1) ¶vx/

43、2;t=4, ¶vy/¶t=0；(2) ax=3, ay=-1)3.3 The velocity components of a flow field is Determine the streamline equation through point (x0,y0) at t=t0. 一流場(chǎng)的速度分量為確定在t=t0時(shí)刻通過(guò)點(diǎn)(x0,y0)的流線方程。(x2-y-Aty+C=0)3.4 A two-dimensional velocity field is given by What is the streamline equation in this flow fiel

44、d? 已知二維速度場(chǎng)，求流線方程。(x1+t=cy)3.5 It is known the velocity field is Try to find the streamline equation passing through point（2，1，1）.已知速度場(chǎng)，求通過(guò)點(diǎn)（2，1，1）的流線方程。(x=2，5-z=2z)3.6 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

45、 section of diameter 5cm? The density of the oil is 850kg/m3.有一輸油管道，在內(nèi)徑為20cm的截面上流速為2m/s，求在另一內(nèi)徑為5cm的截面上的流速以及管內(nèi)的質(zhì)量流量。油的密度為850kg/m3。(32m/s，53.4kg/s)3.7 In a pipeline of inner diameter 5cm, the mass flow rate of air is 0.5kg/s, pressure at a certain is 5´105Pa, the temperature is 1000C. Find the av

46、erage air flow velocity on this section.在內(nèi)徑為5cm的管道中，流動(dòng)空氣的質(zhì)量流量為0.5kg/s，在某一截面上壓強(qiáng)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 distribution of an incompressible fluid is ，Try to deduce the expression of vz by adopting continuity equation.已知一不可壓縮流體的速度分布為，。試用連續(xù)方程推導(dǎo)出vz的表達(dá)式。(vz=-z(2x+2y+z+1

47、)+c(x,y)3.9 As shown in Fig. 3-25, water flows steadily into a two-dimensional tube at a uniform velocity v. Since the tube bends an angle of 900, velocity distribution at the outlet becomes . Assuming the width h of the tube is constant, find constant C.如圖3-25所示，水以均勻速度v定常流入一個(gè)二維通道，由于通道彎曲了900，在出口端速度分

48、布變?yōu)?。設(shè)通道寬度h為常數(shù)， Fig. 3-25 Problem 3.9求常數(shù)C。( C=v/3)3.10 Water is flowing in a river, as shown in Fig. 3-26. Two Pitot tubes are stacked and connected to a differential manometer containing a fluid of specific gravity 0.82. Find vA and vB. 水在河道中流動(dòng)，如圖3-26所示。兩個(gè)重疊的皮托管與一裝有比重為0.82的流體的壓差計(jì)連接。試求vA 及 vB。(vA=1.2

49、12m/s，vB =1.137m/s) Fig. 3-26 Problem 3.10 3.11 As shown in Fig. 3-27, a pipe of diameter 1m is installed horizontally, of which a part bends an angle of 300. Oil of specific gravity 0.94 flows inside the pipe with a flow rate of 2m3/s. Assume pressure in the pipe is uniform, the gauge pressure is 7

50、5kPa, find the horizontal force exerting 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300的彎管，如圖3-27所示。管內(nèi)比重為0.94的油以2m3/s的流量流動(dòng)。設(shè)彎管內(nèi)壓強(qiáng)均勻，表壓為75kPa，求彎管受到的水平力。(Fx=8.64kN，F(xiàn)y=31.9kN)3.12 The height of the mercury column in U-tube is 60mm, as shown in Fig. 3-28. Assume the diameter of the conduit

51、 is 100mm, find the volume flow rate of water through the conduit at section A. 如圖3-28所示，U形管內(nèi)汞柱高度為60mm。設(shè)排水管的直徑為100mm，求在截面A處通過(guò)排水管的體積流量。(0.0314m3/s) Fig. 3-28 Problem 3.12 3.13 A nozzle is connected at one end of a water pipe, as shown in Fig. 3-29. The outlet diameter of the water pipe is d1=50mm, an

52、d that of the nozzle is d2=25mm. The nozzle and the pipe are connected by four bolts. The gauge pressure at inlet of the nozzle is 1.96´105Pa, volume flow rate is 0.005m3/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 Fig. 3-29 Problem 3.13管

53、之間用四個(gè)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(gè)螺栓所受到的拉力。(86.75N) 3.14 A centrifugal pump draws water from a well, as shown in Fig.3-30. Assume the inner diameter of the slouch is d=150mm, volume flow rate is qv=60 m3/h, and the vacuum value at point A where the slouch and the pump are connected

54、is pv=4´104Pa. Neglect head loss, what is the suction height Hs of the pump?離心式水泵從井里抽水，如圖3-30所示。設(shè)吸水管內(nèi)徑d=150mm，流量為qv=60 m3/h，吸水管與水泵接頭處A點(diǎn)的真空值為pv=4´104Pa。不計(jì)水頭損失，求水泵的吸水高度Hs。(4.03m) Fig. 3-30 Problem 3.14 3.15 As shown in Fig.3-31, an oil of specific gravity 0.83 rushes towards a vertical plate at velocity v0=20m/s, find the force needed to support the plate.如圖3-31所示，相對(duì)密度為0.83的油水平射向直立的平板，已知v0=2