工程流体力学课后习题

工程流体力学课后习题

F

ig.3-35 Problem 3.19

3.20 As shown in Fig.3-36, water flows out from a big container and into another small container. Suppose that the free surface elevations of the two containers keep unchanged, find the velocity ve at the outlet.

如图3-36所示，大容器中的水由小孔流出，流入另一盛水小容器。若两容器的水面高度保持不变，求小孔流出的速度ve。

(

) Fig.3-36 Problem 3.20

3.21 A Pitot tube is submerged in a prismatic pipeline, which is shown as in Fig.3-37. If the density of the fluid inside the pipeline is ?, and that in the U-tube is ?’, the elevation difference in the U-tube is ?h, find the velocity in the pipeline.

一皮托管置于等截面的管路中，如图3-37所示。U形管内流若管内流体的密度为?，

体的密度为?’，液面高度差为?h，求管流速度。(

)

Fig.3-37 Problem 3.21 3.22 As shown in Fig.3-38, transport water from container A to container B by means of a siphon. If the volume flow rate is 100m3/h, H1=3m, z=6m, and neglect the head loss, find the diameter of the siphon and the vacuum value in the upper part of the siphon.

如图3-35所示，利用虹吸管把水从容器A引到容器B。已知体积流量为100m3/h，H1=3m，z=6m，不计水头损失，求虹吸管的

管径，以及上端管中的真空值。 Fig.3-38 Problem 3.22 (0.068m，5.89?104Pa)

3.23 A water sprinkler is shown as in Fig. 3-39, the lengths of its two arms are l1=1m and l2=1.5m respectively, if the diameter of the nozzle is d=25mm, do not take the frictional moment into account, find the rotating speed n.

洒水器如图3-39所示，两臂长分别为l1=1m、l2=1.5m，若喷口直径d=25mm，

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工程流体力学课后习题

每个喷口的流量qv=3L/s，不计摩擦阻力矩，求转速n。(44.9 r/min)

Fig. 3-39 Problem 3.23 3.24 A symmetrical sprinkler is shown as in Fig. 3-40. The rotating radius is R=200mm, ?=450, the nozzle diameter is d=8mm, the total flow rate is qv=0.563L/s, if the frictional moment is 0.2N?m, find the rotating speed n. And what is the magnitude of the moment needed to hold the sprinkler at rest while it is in operation?

对称洒水器如图3-40所示。旋转半径 Fig. 3-40 Problem 3.24 R=200mm，?=450，喷口直径d=8mm，总

流量qv=0.563L/s，若已知摩擦阻力矩为0.2N?m，求转速n。若喷水时不让其旋转，应受到多大的力矩？(103 r/min，0.441 N?m)

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工程流体力学课后习题

Problems

1.1 The velocity field of a rotational flow is given by

Find the average angular rotating velocity at point (2,2,2).

已知有旋流动的速度场为

求在点（2,2,2）处平均旋转角速度。(?x=0.5，?y=?2，?z=?0.5)

1.2 Determine whether the following flow field is rotational flow or irrotational flow.

确定下列流场是有旋运动还是无旋运动：

(1) (2)

( (1)有旋，(2)无旋)

4.3 The velocity distribution of a flow field is described by v=x2yi?xy2j Is the flow irrotational?

流场的速度分布为

v=x2yi?xy2j

该流动是否无旋？(有旋)

4.4 For a certain incompressible, two-dimensional flow field the velocity component in the y direction is given by vy=x2+2xy

Determine the velocity component in the x direction so that the continuity equation is satisfied.

某一不可压缩平面流场在y方向的速度分量为 vy=x2+2xy

确定x方向的速度分量，以满足连续性方程。(vx=?x2+C)

4.5 For a certain incompressible flow field it is suggested that the velocity components are given by the equations

vx=x2y vy=4y3z vz=2z Is this a physically possible flow field?

某一不可压缩流场流场的速度分量由下列方程给出

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vvxxv

工程流体力学课后习题

vx=x2y vy=4y3z vz=2z 试问该流场在物理上是否可能？(不可能)

4.6 It is known that streamlines are concentric circles, and velocity distribution is 已知流线为同心圆族，其速度分布为

Find the velocity circulation along circle x2+y2=R2, where the radiuses of the circle are

(1) R=3；(2) R=5；(3) R=10 respectively.

求沿圆周x2+y2=R2的速度环量，其中圆的半径R分别为 (1) R=3；(2) R=5；(3) R=10。

((1) 18?/5，(2) 10?，(3) 10? )

4.7 Assume there is a vortex of ?=?0 locating at point (1，0), and another vortex of ?=-?0 at point (-1，0). Find the velocity circulation along the following routes: (1) x2+y2=4； (2) (x-1)2+y2=1；

(3) Square of x= ?2，y= ?2； (4) Square of x= ?0.5，y= ?0.5.

设在点(1，0)处置有?=?0的旋涡，在点(-1，0)处置有?=-?0的旋涡。试求下列路线的速度环量：

(1) x2+y2=4； (2) (x-1)2+y2=1；

(3) x= ?2，y= ?2的方形框；

(4) x= ?0.5，y= ?0.5的方形框。( (1) 0，(2) ?0，(3) 0，(4) 0 )

4.8 For incompressible fluid, determine if there exist stream functions in the following flow fields, where K is a constant.

对于不可压缩流体，试确定下列流场是否存在流函数？式中K为常数。 (1) vx=Ksin(xy)，vy=-K sin(xy)

(2) vx=Kln(xy)，vy=-Ky/x ( (1) 不存在，(2) 存在)

4.9 Demonstrate the following planar flow of an incompressible fluid

?satisfies continuity equation, and is a potential flow, then find the potential function.

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工程流体力学课后习题

试证明以下不可压缩流体平面流动

满足连续性方程，是有势流动，并求势函数。( ?=x2/2+x2y?y2/2?y3/3)

4.10 A velocity field is given by vx=x2y+y2，vy=x2?xy2，vz=0，questions： (1) If there exist stream function and potential function?

(2) Find the expressions of stream function and potential function if they exist. 给定速度场vx=x2y+y2，vy=x2?xy2，vz=0，问： (1) 是否存在流函数和势函数？ (2) 如果存在，求其具体表达式。

((1)存在流函数，不存在势函数；(2) ?=x2y2/2+y2/3?x2/3) 4.11 The velocity potential in a certain flow filed is ?=4xy

Determine the corresponding stream function. 某流场的速度势为

?=4xy 求相应的流函数。( ?=2x2?2y2)

4.12 The velocity potential for an incompressible, planar flow is ?=x2?y2+x Find its stream function.

不可压缩流体平面流动的势函数为 ?=x2?y2+x 试求流函数。( ?=2xy+y) 4.13 The stream function for an incompressible, planar flow is

?=xy+2x?3y

Find the potential function.

不可压缩流体平面流动的流函数为 ?=xy+2x?3y 试求势函数。( ?=(x2?y2)/2?3x?2y)

4.14 Demonstrate the following two flow fields are identical:

(1) the potential function is ?=x2+x ?y2 (2) the stream function is ?=2xy+y 证明下列两个流场是相同的。 (1) 势函数 ?=x2+x ?y2 (2) 流函数 ?=2xy+y

4.15

Given the velocity distribution of a flow field as

vx=Ax+By

vy=Cx+Dy

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vx

工程流体力学课后习题

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.

将2?106N/m2 的压强施加于初始体积为1,000cm3的水上，计算加压后水的体积。

(999.1cm3)

1.2 As shown in Fig.1-9, in a heating system there is a dilatation water tank. The whole volume of the water in the system is 8m3. The largest temperature rise is 500C and the coefficient of volume expansion is ?v=0.0005 1/K, what is the smallest cubage of the water bank?

如图1-10所示，一采暖系统在顶部设一膨胀水箱，系统内的水总体积为8m3，最大温升500C，膨胀系数?v=0.005 1/K，求该水箱的最小容积？

(0.2m3) Fig. 1-9 Problem 1.2

1.3 When the increment of pressure is 50kPa, the density of a certain liquid is 0.02%. Find the bulk modulus of the liquid.

当压强增量为50kPa时，某种液体的密度增加0.02%。求该液体的体积模量。( 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 diameter 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 ?v=6.5?10-41/K of the oil tank is

considered, what is the volume Fig.1-10 Problem 1.4

of oil spilled from the tank when the temperature of oil increases from t1=-200C to t2=200C?

(2) If the linear expansion coefficient ?l=1.2?10-51/K of the oil tank is considered, what is the result in this case?

图1-10为一油箱横截面，其尺寸为长a=0.6m、宽b=0.4m、高H=0.5m，油嘴直径d=0.05m，高h=0.08m。由装到齐油箱的上壁，求：

(1) 如果只考虑油液的热膨胀系数?v=6.5?10-41/K时，油液从t1=-200C上升到 t2=200C时，油箱中有多少体积的油溢出？

(2) 如果还考虑油箱的线膨胀系数?l=1.2?10-51/K，这时的情况如何？

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工程流体力学课后习题

((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 ?=3?10-5m2/s and ?=850kg/m3 fills between the sleeve and spindle. The inner diameter of the sleeve is D=102mm, the outer diameter of the spindle 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

有一金属套由于自重沿垂直轴下滑，如图 1-11所示。轴与套间充满了?=3?10-5m2/s、?=850kg/m3的油液。套的内径D=102mm，轴的外径d=100mm，套长L=250mm，套重100N。试求套筒自由下滑时的最大速度为多少(不计空气阻力)。 (50 m/s)

1.6 The velocity distribution for flow of kerosene at 200C (?=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时，煤油(?=4?10-3N?s/m2)在两壁面间流动的速度分布由u=1000y(0.01-y) m/s确定，式中y的单位为m，壁面间距为1cm。画出速度分布图，并确定壁面上的剪应力。 (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 1.7

If glycerin is flowing (T=200C) and the pressure 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?

如图1-12所示，两固定平板间粘性流动的速度分布由

给出。如果流体为甘油(T=200C) 且压强梯度dp/dx为1.6kN/m3，间距By为5.0 cm，距平板12mm处的速度与剪应力为多少？平板处的剪应力与速度为多少？

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工程流体力学课后习题

(u12=0.59m/s；τ12=20.8N/m2；u0=0；τ0=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?

在标准大气压、T=200C时，空气与水的动力粘度之比为多少？同样条件下它们的运动粘度之比又为多少？ (?A/?W=0.0018；?A/?W=15.1)

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. 1-13 Problem 1.9 the 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)?

图1-13所示装置由绕一根轴旋转的圆盘构成。圆盘放置在与固体边界很近的位置。圆盘与边界间为粘性油。

(1) 如果圆盘的旋转速率为1 rad/s，问半径为r=2cm与r=3cm处的剪应力之比为多少？

(2) 如果旋转速率为2 rad/s，r=3cm处与

圆盘接触的油层的速度为多少？ (3) 如果油的粘度为0.01 N?s/m2 、且间距y为2mm，(b)情况下的剪应力为多少？ ((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 two cones is ?=1mm. It filled with lubricant which

?=0.1Pa?s. In the Figure, R=0.3m, H=0.5m, Fig. 1-14 Problem 1.10 ?=16 rad/s. What is the moment needed to rotate the cone?

如图1-14所示，一圆锥体绕竖直中心轴等速旋转，锥体与固定的外锥体之间的隙缝?=1mm，其中充满?=0.1Pa?s的润滑油。已知锥体顶面半径R=0.3m，锥体高度H=0.5m，当旋转角速度 ?=16 rad/s 时，求所需要的旋转力矩。 (39.6N?m)

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工程流体力学课后习题

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.

两个测压计位于一充满油的油箱的一侧。一个测压计高于地面的位置高度为48m，读数57.5 kPa。另一个位置高度为2.2m，读数347kPa。计算油的重度与密度。(?=6.32kN/m3,?=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 the shells apart?

两半球壳完美密闭在一起，内压减至20 kPa，内径15 cm，外径15.5 cm。如果大气压强为100 kPa，求要将半球拉开所需的力为多少。(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 free surface of the oil.

如图所示，密闭容器中油的密度为800 kg/m3，其下方为水。如果h1=300mm, h2=500mm, 及 h=400mmHg，求油的自由

表面上的压强。(46.1kPa) Problem 2.3 2.4 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 pressure. If hv=2m, what is the pressure inside of container A?

如图，一根管子一端与一抽空的容器相连，另一端插入暴露于大气的水池中。如hv=2m，容器内的压强是多少？(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 specific weight of sea water.

一测压计置于海平面下，如果在自由表面下300m深处测压计的读数为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

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工程流体力学课后习题

pressure at points a, b and c in water. (see attached figure)

如果当地大气压的绝对压强为98.1 kPa，求水中a、b 及 c 点的相对压强。（见附图）(Pa=68.6kPa，Pb=31.3kPa，Pc=-29.4kPa)

Problem 2.6

2.7 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 ?1=800kg/m3 and that of mercury as ?3=13 600kg/m3. Compute the height H(cm) of the mercury column in the U-tube.

圆柱形容器的活塞上作用一5788N的力，容器内充有水和油。当水柱高h2=50cm时，油柱高h1=30cm。容器直径d=40cm，油的密度?1=800kg/m3，水银密度?3=13 600kg/m3。求U形管内的汞柱高H(cm) 。(14.07cm)

Problem 2.7

2.8 According to the diagram, a closed tank contains water that has a 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?

如图所示，一密闭容器内盛有自由表面相对 Problem 2.8 压强为po=- 44.5kN/m2的水。

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工程流体力学课后习题

(1) 求距离h；

(2) 水面下0.3m处的M点 的压强为多少？

(3) M点相对于基准面1-1的测压管水头是多少？ (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.

一竖直的U形管安装在以匀加速度a=0.5m/s2作直线运行的车罩上，长度L=500mm。求U形管内两自由液面的高度差。 (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 ? with the horizontal plane and the equation of water pressure p at the free surface?

如图所示，一盛水的开口容器以加速度a=3.6m/s2沿30o的斜面运动。求自由液面与水平面的夹角?，并写出水的压强p的分布方程。

(?=15o，p=pa+?gh)

Problem 2.10

2.11 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. 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) 如图所示，闸门宽2m，重500kg，绕铰链H转动。闸门重心在距右端1.2m处且高于H 0.9m。问铰链H上方水深x为多少时，闸门

将关闭？（忽略铰链摩擦及闸门的厚度）(1.25m) Problem 2.11

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工程流体力学课后习题

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 can automatically open around point O?

一1米高的平板闸门在O点处用铰链连接，且可绕铰链转动（见附图）。O点的高度为a=0.4m。水深多少时，闸门将自动开启？ (h=1.33m)

Problem 2.12

2.13 As shown in the diagram, a closed tank forming 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 on a tank wall as a function of height, (c) the location of the center of pressure by water on the tank wall.

如图所示，一密闭立方体水箱装了一半的水，求：(a) 箱底的绝对压强；(b) 将流体对一侧箱壁的作用力表示为高度的函数；

(c) 水对箱壁的压力中心位置。 Problem 2.13 (17.8kPa，F=2h(8000+0.5?gh)，2/3)

2.14 A circular sluice gate of diameter d=1m is submerged in water as shown in the figure. The slant angle ?=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 rotate upward about axis a (neglect friction at axis a).

如图所示的一直径d=1m圆形闸门淹没于水中。倾角?=60o，淹深hc=4.0m，闸门重FG=1kN。求使闸门绕a轴向上转动的铅直力T的大小。(230kN)

Problem 2.14

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工程流体力学课后习题

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, what torque applied to the shaft through N is required to hold the gate closed?

图示闸门M绕N轴转动。如a=33m、 b=13m、d=20m且与图形垂直的宽度为3m，要使闸门关闭，需要施加多大的力矩在转轴上？(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 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 atmospheric pressure conditions exist to the right and top of the cylinder.

求下述流体对图示圆柱体所施加的水平与铅直方向的分力。(1)圆柱体左边是压强为35kPa的密闭气体；(2)圆柱体左边是自由液面刚好与柱顶平齐的水。设两种情况下圆柱

体的右边与顶部为标准大气压。 Problem 2.16 ((1) Fx=130.5kN，Fz=35kN；(2) Fx=68.1kN，Fz=100.5kN)

2.17 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, determine the magnitude and location of the horizontal and vertical force components acting on unit width of tank wall ABC. 图示为一容器的剖面，BC是半径r=6m的圆柱面。容器高h=10m。如果容器装有压强为8kPa的气体，求作用在容器壁ABC上单位宽度的水平分力与铅直分力的大小与作用位置。

(Fx=80kN，Fz=48kN) Problem 2.17

2.18 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.

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工程流体力学课后习题

Problem 2.18

当下述情况时，求使图示闸门沿逆时针方向转动的z的最小值：(a) 闸门为高5m、宽4m的矩形；(b) 闸门为上底4m（转轴）、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 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 一曲面由半径为R=0.75m的四分之一的圆柱体组成，如图所示。圆柱面宽w=3.55m（垂直于图形平面）。曲面右侧静水深度H=0.65m。试求：

(1) 作用于曲面上静水压力的大小； (2) 静水压力的方向。 (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 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.

如图所示，直径D=4m、长L=12m Problem 2.20

的圆柱体放于水中，圆柱体左右两边水的深度分别为4m 和 2m。求水对圆柱体的作用力的大小与方向。

(Fx=706kN，Fz=1579kN)

2.21 As shown in the figure, determine the pivot location y of the rectangular gate, so that the gate will just open.

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工程流体力学课后习题

如图所示，求闸门刚好开启时转轴的位置y为多少。(y=0.44m)

Problem 2.21

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工程流体力学课后习题

Problems

3.1 A two-dimensional, incompressible flow field is given by

Find the velocity and acceleration at point (1,2).

二维不可压缩流动由

确定。试求点（1，2）处的速度

与加速度。(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.

设流场的速度分布为

。求：（1）当地加速度的

表达式；（2）t=0时在点（1，1）处流体质点的加速度。

((1) ?vx/?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. 一流场的速度分量为

确定在t=t0时刻通过点(x0,y0)的流线方程。(x2?y?Aty+C=0)

3.4 A two-dimensional velocity field is given by

What is the streamline equation in this flow field? 已知二维速度场

3.5 It is known the velocity field is

Try to find the streamline equation passing through point（2，1，1）.

已知速度场

vx，求流线方程。(x1+t=cy)

，求通过点（2，1，1）的流线方程。

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工程流体力学课后习题

(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 section of diameter 5cm? The density of the oil is 850kg/m3.

有一输油管道，在内径为20cm的截面上流速为2m/s，求在另一内径为5cm的截面上的流速以及管内的质量流量。油的密度为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 average air flow velocity on this section.

在内径为5cm的管道中，流动空气的质量流量为0.5kg/s，在某一截面上

压强为5?105Pa，温度为1000C。求该截面上气流的平均速度。(54.5m/s)

3.8 The velocity distribution of an incompressible fluid is

，

Try to deduce the expression of vz by adopting continuity equation.

已知一不可压缩流体的速度分布为

用连续方程推导出vz的表达式。(vz=-z(2x+2y+z+1)+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.

如图3-25所示，水以均匀速度v定常流入一个二维通道，由于通道弯曲了900，在出口端速度分布变为

，

。试

。设通道宽度h为常数， Fig. 3-25 Problem 3.9

求常数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.

水在河道中流动，如图3-26所示。两个重叠的皮托管与一装有比重为0.82

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工程流体力学课后习题

的流体的压差计连接。试求vA 及 vB。

(vA=1.212m/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 75kPa, find the horizontal force exerting on the elbow pipe.

直径为1m的水平装置的管 Fig. 3-27 Problem 3.11 道有一段300的弯管，如图3-27

所示。管内比重为0.94的油以2m3/s的流量流动。设弯管内压强均匀，表压为75kPa，求弯管受到的水平力。(Fx=8.64kN，Fy=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 is 100mm, find the volume flow rate of water through the conduit at section A.

如图3-28所示，U形管内汞柱高度为60mm。设排水管的直径为100mm，

求在截面A处通过排水管的体积流量。

(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, and 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.

在水管的端部接有喷嘴，如图3-29所示。水管出口直径d1=50mm，

喷嘴出口直径d2=25mm。喷嘴与 Fig. 3-29 Problem 3.13 管之间用四个螺栓连接。喷嘴入口

处的表压为1.96?105Pa，流量为0.005m3/s，求每个螺栓所受到的拉力。(86.75N)

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工程流体力学课后习题

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 is pv=4?104Pa. Neglect head loss, what is the suction height Hs of the pump?

离心式水泵从井里抽水，如图3-30所示。设吸水管内径d=150mm，流量为qv=60 m3/h，吸水管与水泵接头处A点的真空值为pv=4?104Pa。不计水头损失，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.

如图3-31所示，相对密度为0.83

的油水平射向直立的平板，已知v0=20m/s，求支撑平板所需的力F。(652N)

Fig.3-31 Problem 3.15 3.16 A horizontal jet flow with volume flow rate qv0 rushes towards an inclined plate at velocity v0, as shown in Fig. 3-32. Neglect the effects of gravity and impact loss of the fluid, the pressure and velocity of the jet flow remain the same after it splits into two distributaries. Find the formulas of the two distributaries’ flow rate qv1and qv2, and the force acting on the plate.

如图3-32所示，一股速度为v0、体积流量为qv0的水平射流，射到倾斜的光滑平板上。忽略流体撞击的损失和重力的影响，射流的压强与速度在分流后也没有变化，求沿板面向两侧的分流流量qv1与qv2的表达式，以及流体对板面的

作用力。 Fig. 3-32 Problem 3.16

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工程流体力学课后习题

(

)

3.17 As shown in Fig.3-33, a cart carrying an inclined smooth plate moves at velocity v against a jet flow, the velocity , flow rate and density of the jet flow are v0, qv，and ? respectively. Ignore the friction between the cart and ground, what is the power W needed for driving the cart?

如图3-33所示，带有倾斜光滑平板的小车逆着射流方向以速度v运动，射流的速度和流量分别为v0和qv，射流的密度为?，不计小车与地面的摩擦

力，求推动小车所需的功率W。 Fig.3-33 Problem 3.17

(

)

3.18 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 nozzle is 50mm. If neglect the head loss, try to find the flow rate of the pipe, and pressures at point A, B, C, and D.

从一大容器引出一弯曲的管道如图3-34所示，管径为150mm，喷嘴直径为50mm，不计水头损失，求管的输水流量，以及A、B、C、D各点的压强。

(0.0174m3/s，68.2、-0.47、-20.1、38.8kPa) Fig. 3-34 Problem 3.18

3.19 A Venturi flowmeter is installed bias as shown in Fig.3-35, diameter at the inlet is d1, and diameter at the throat is d2, try to deduce its flow rate expression.

文丘里管流量计倾斜安装如图3-35所示，入口直径为d1，喉部直径为d2。试推导出其流量的计算公式。

(

q)

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工程流体力学课后习题

If the flow is incompressible and irrotational, find

(1) What relationship should coefficients A、B、C、D satisfy? (2) The stream function of the flow field. 已知流场的速度分布为

vx=Ax+By vy=Cx+Dy 若流体不可压缩，且流动无旋，试问

(1) 系数A、B、C、D应满足怎样的关系？ (2) 求流场的流函数。

( (1) A=?D，B=C；(2) ?=B(y2?x2)/2+Axy )

4.16 There is a fixed point vortex of circulation ? and distance a to a stationary wall. Find the velocity potential function of the flow and pressure distribution on the wall.

有一环量为?的固定点涡，离一静止壁面的距离为a。试求流动的速度势和 壁面上的压强分布。 (

，

)

4.17 Given the velocity of an incompressible planar potential flow as vx=3ax2?3ay2, vx=vy=0 at point (0，0), find the volume flowrate passing the connecting line of points (0，0) and (0，1).

已知不可压缩平面势流的速度分布为 vx=3ax2-3ay2，在(0，0)点上vx=vy=0，试求通过(0，0)、 (0，1)两点连线的体积流量。( qv=a )

4.18 A two-dimensional flow field is formed by adding a source at the origin of the coordinate system to the velocity potential ?=r2cos2?

Locate any stagnation points in the upper half of the coordinate plane. (0????) 一二维流场是在速度势?=r2cos2?上于坐标原点处叠加一点源而形成。试在坐标平面上半部确定任一驻点的位置。( ?s=?/2，rs=(m/4?)0.5)

4.19 The stream function for a two-dimensional, incompressible flow field is given by the equation

?=2x-2y

where the stream function has the units of m2/s with x and y in meter.

(1) Sketch the stream function for this flow field, indicate the direction of flow along the streamlines;

(2) Is this an irrotational flow field?

(3) Determine the acceleration of a fluid particle at the point x=1m and y=2m. 二维不可压流场的流函数为

?=2x-2y 式中x、y的单位为m，流函数单位为m2/s。

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工程流体力学课后习题

(1) 做出流线分布图，标明流线方向； (2) 流动是否无旋？

(3) 确定点(1,2)处流体质点的加速度。 ( (1) ?=2x?2y，(2) 无旋，(3) a=0)

4.20 The stream function for the flow of a nonviscous, incompressible fluid in the vicinity of a corner (see Fig. 4-27) is

?=2r4/3sin(4?/3). Determine an expression for the pressure gradient along the boundary ?=3?/4.

一无粘不可压流体在如图4-27所示的转角附近流动的流函数为?=2r4/3sin(4?/3)，

试确定沿边界?=3?/4的压强梯度表达式。 Fig. 4-27 Problem 4.20

(

)

4.21 Two sources are located at points (1，0) and (-1，0)，their source strength are all 4?，find the velocity at points (0，0)、 (0，1)、 (0，-1)、(1，1).

位于(1，0)和(-1，0)之两个点源，其源强度均为4?，试求在(0，0)、 (0，1)、

(0，-1)、(1，1)处的速度。

( vx=vy=0；vx=0，vy=2；vx=0，vy=?2；vx=4/5，vy=12/5)

4.22 A source with strength 20m2/s is located at point (-1，0)，another source with strength 40m2/s is located at point (2，0). Given the pressure at the coordinate base point of the overlapped flow field is 100Pa，the fluid density is 1.8kg/m3，find the velocity and pressure at point (0，1) and (1，1).

强度为20m2/s的点源位于(-1，0)，强度为40m2/s的点源位于(2，0)，已知叠加流场在坐标原点处的压强为100Pa，流体的密度为1.8kg/m3，求在点(0，1)和点(1，1)处的速度与压强。

(

?p)

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工程流体力学课后习题

Problems

5.1 A 1:25 scale model of an airship is tested in water at 200C. If the airship travels 5m/s in air at atmospheric pressure and 200C, find the velocity for the model to achieve dynamic similitude. Also, find the ratio of the drag force on the prototype to that on the model. The densities of water and air at these conditions are 1000kg/m3 and 1.2kg/m3 respectively. The corresponding dynamic viscosities of water and air are 10-3N?s/m2 and 1.81?10-5 N?s/m2。 一比尺为1:25的飞艇模型在200C的水中实验。如果飞艇是在200C、大气压力下的空气中以5m/s的速度飞行，为了达到动力相似，求模型的速度。并求原型与模型的阻力之比。已知在实验条件下水与空气的密度分别为1000kg/m3 及 1.2kg/m3，相应的动力粘度为10-3N?s/m2 与 1.81?10-5 N?s/m2。(8.29m/s，0.273) 5.2 A scale model of a pumping system is to be tested to determined the head losses in the actual system. Air with a specific weight of 0.085kg/m3 and a viscosity of 3.74?10-7 m2/s is used in the model. Another fluid with a specific weight of 62.4kg/m3 and a viscosity of 2.36?10-5m2/s is used in the prototype. The velocity in the prototype is 2m/s. A practical upper limit for the air velocity in the model to avoid compressibility effects is 100m/s. Find the scale ratio for the model and the ratio of the pressure losses in the prototype to those in the model. 对一抽送系统的缩小模型进行实验以确定原型的水头损失。原型所使用的空气重度为0.085kg/m3 、粘度为3.74?10-7 m2/s。另一种重度为62.4kg/m3、粘度为2.36?10-5m2/s的流体用于原型实验。原型速度为2m/s。为了避免压缩性效应，模型中空气流速的实际上限为100m/s。求模型的比尺与原型及模型中压强损失比尺。(0.294) 5.3 To study the flow of a spillway with a model of the length scale ratio kl=1:20. It is known that Fr of the prototype and model are equal, flowrate of the model is measured as 0.19m3/s. Find the flowrate of the prototype.

用模型研究溢流道的流动，采用的长度比例系数kl=1:20，已知原型与模型的Fr相等，测得模型上的流量为0.19m3/s。求原型上的流量。(339m3/s)

5.4 The kinematic viscosity of a fluid in the prototype is ?=15?10-5m2/s, the length scale ratio of the model is 1:5, if let Fr and Eu be the decisive similitude numbers, what is the kinematic viscosity of the fluid in the model ?

原型中流体的运动粘度?=15?10-5m2/s，模型的长度比例系数为1:5，如以Fr和Eu作为决定性的相似准数，模型流体的运动粘度?m应为多少？(1.34?10-5m2/s) 5.5 The sloshing of oil in a tank is affected by both viscous and gravitational effects. A 1:4 scale model of oil with a kinematic viscosity of 1.1?10-4 m2/s is to be used to study the sloshing. Find the kinematic viscosity of the liquid to be used in the model. 油在容器中的晃荡受到粘性与重力的影响。用一比尺为1:4的模型来研究运

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工程流体力学课后习题

动粘度为1.1?10-4 m2/s的油的晃荡。求模型中液体的运动粘度。(1.37?10-5m2/s) 5.6 A wind-tunnel test is performed on a 1: 20 scale model of a supersonic aircraft. The prototype aircraft flies at 480m/s in conditions where the speed of sound is 300m/s and the air density is 1.0kg/m3. The model aircraft is tested in a wind-tunnel in which the speed of sound is 279m/s and the air density is 0.43kg/m3. The drag force on the model is 100N. What speed must the flow in the wind-tunnel be for dynamic similitude, and what is the drag force on the prototype?

对一比尺为1:20的超音速飞机模型进行风洞实验。原型飞机在音速为300m/s、密度为1.0kg/m3的空气中以480m/s的速度飞行。模型飞机在音速为279m/s、密度为0.43kg/m3的空气中进行风洞实验。测得模型的阻力位100N。

108kN) 为达到动力相似，风洞的流速应为多少？原型上的阻力是多少？(446m/s，

5.7 A ventilation pipe of diameter 1m and average flowing velocity 10m/s. Model test is performed on a water pipe of diameter 0.1m, what is the velocity in the water pipe to achieve dynamic similitude? Suppose the pressure and temperature of air and water are all 101kPa and 200C.

直径为1m的空气管道，平均流速为10m/s，现用直径为0.1m的水管进行模

200C。 型实验，为了动力相似，水管中的流速应为多大？设空气和水均为101kPa、

(6.73 m/s) 5.8 In order to predict the drag on a smooth, streamlined object flying in air, a model is designed to test in water. It is known that the length of the prototype is 3m, flies in air at a speed of 10 m/s. The designing length of the model is 50cm, what is the velocity of water? If the drag on model is measured as 15N, what is the drag on the prototype? Suppose the pressure and temperature of the prototype and model are all 101kPa and 200C. 为了预测一光滑流线型物体在空气中的飞行阻力，设计一模型在水中实验。已知原型的长度为3m，以10 m/s的速度在空气中飞行。模型的长度设计为50cm，水流的速度应为多少？若测得模型受到的阻力为15N，原型受到的阻力将是多少？设原型、模型均处于101kPa、200C。(4 m/s，4.05N) 5.9 The height of an automobile is 1.5m, travels in air 200C at a speed of 108km/h. Air in model test is 00C and its flowing velocity is 60m/s. Find the height of the model. If the front resistance in model test is measured as 1300N, what is the front resistance on the prototype automobile when running ? 汽车高度为1.5m，速度为108km/h， 行驶在200C的空气中，模型实验的空气为00C，气流速度为60m/s。求模型试验汽车的高度。如果在模型实验中测得正面阻力位1300N，求实物汽车行驶时的正面阻力是多少。(0.654m，1586N) 5.10 The surface tension of pure water is 0.073N/m, and the surface tension of soapy water is 0.025N/m. If a pure water droplet breaks up in an airstream that is moving at 10m/s, at what speed would the same size soapy water droplet break up? 纯净水的表面张力为0.073N/m，肥皂水的表面张力为0.025N/m。如果纯净水滴在10m/s的气流中破裂，问尺寸相同的肥皂水滴的破裂气流速度为多少？

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工程流体力学课后习题

(5.85 m/s) 5.11 A 1:49 scale model of a ship is tested in a water tank. The speed of the prototype is 10m/s. The purpose of the test is to measure the wave drag on the ship. Find the velocity of the model and the ratio of the wave drag on the prototype to that on the model. 一比尺为的船模在水池中实验。原型中的速度为10m/s。实验的目的是测定作用在船上的波浪阻力。求模型的速度，及原型与模型的波浪阻力比值。 (1.43 m/s，1.18?105) 5.12 A Venturi tube with diameter D1=300mm and d1=150mm is used to measure the flowrate of oil of kinematic viscosity ?1=4.5?10-6m2/s and density ?1=820kg/m3. The flowrate Q1 is 100L/s. Use water of kinematic viscosity ?2=1?10-6m2/s and a 1:3 model to perform the test. (1) What must the water flow rate Q2 be for dynamic similarity? (2) If the head loss hf2 is measured at 0.2m and the pressure difference ?p2 at 1.0 bar in the model test, find the real head loss and pressure difference of the prototype. 一直径为D1=300mm 及 d1=150mm的文丘里管用于测量运动粘度为?1=4.5?10-6m2/s、密度为?1=820kg/m3的油的流量。流量Q1 为100L/s。用运动粘度为?2=1?10-6m2/s的水、比尺为1:3的模型进行实验。

(1) 为了达到动力相似，水的流量Q2为多少？

(2) 如果模型实验测得水头损失hf2为0.2m、压差?p2为1.0 bar，求原型的水 头损失与压差为多少。?

5.13 The flowrate qv of a fluid passing through a horizontal capillary pipe has relationship with the diameter d, dynamic viscosity ? and pressure gradient ?p/l, derive the expression of the flowrate.

流体通过水平毛细管的流量qv与管径d、动力粘度?、压强梯度?p/l有关，试导出流量的表达式。(

)

5.14 A small ball travels at a constant velocity in an incompressible viscous fluid, the drag is related with the diameter of the ball, velocity v, the density ? of the fluid, and the dynamic viscosity ?. Find the expression of the drag.

小球在不可压缩粘性流体中等速运动时，阻力FD与小球的直径d、运动速度v、流体密度?、动力粘度?有关，试推导出阻力的表达式。(

)

5.15 The outlet velocity v of an orifice is related with the orifice diameter d, fluid density ?, dynamic viscosity ? and hydrostatic head ?p, derive the expression of the outlet velocity.

设孔口出流的速度v与孔口直径d、流体密度?、动力粘度?以及静压头?p有

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工程流体力学课后习题

关，导出流速的表达式。(

)

5.16 The velocity of a sphere depends on the sphere diameter, sphere density, fluid density, fluid viscosity, and gravitational acceleration：

Find a nondimensional form for the velocity. 一球体的速度与球体的直径、球体的密度、流体的密度、流体的粘度及重力加速度有关： 试导出速度的无量纲表达式。(

5.17 The pressure drop in a smooth horizontal pipe in a turbulent, incompressible flow depends on the pipe diameter, pipe length, fluid velocity, fluid density, and dynamic viscosity:

Find a nondimensional relationship for the pressure drop. 一水平放置光滑管道内不可压缩流体的湍流压降与管道直径、管长、流体速度、流体密度及动力粘度有关： 求压降的无量纲关系式。(

5.18 A small ball is dropped into a large tube containing an incompressible, viscous liquid. Experimental results show that the resistance force FD acted on the ball is related to the diameter D, velocity of the ball v, the fluid density ?, and viscosity ? of the fluid. Derive an expression for the resistance force FD. 一小球掉入盛有不可压缩的粘性液体的大管道中。实验结果表明，作用在小球上的阻力FD与小球的直径D、速度v、流体的密度?及粘度?有关。导出阻力FD的表达式。(FD=k?D2v2f(Re)) 5.19 Experimental results show that the flowrate qv across an orifice meter is related to the pressure difference ?p between the upstream and downstream sides of the orifice, diameter D of the pipe, viscosity ? and density ? of the fluid. Using the Buckingham ? theorem to derive an expression for the flowrate q. 实验结果表明，孔口流量计的流量qv与孔口上下游的压差?p、管道直径D、流体的粘度?及密度?有关。试用帕金汉?定理导出流量qv的表达式。

v?t?tp)

)

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工程流体力学课后习题

(qv?kD?f(D2?p??2))

Problems

6.1 A fluid flows in round pipe of diameter d=15mm at velocity v＝14m/s, determine the flow regime. In order to ensure that the flow is laminar flow, what is the maximum allowed velocity in the pipe for fluid of (1) lubricant ?＝l.0?10-4m2 /s; (2) water ?＝l.0?10-6m2 /s, and (3) air ?＝l.5?10-5m2 /s?

流体以v＝14m/s 的流速在直径 d＝15mm的圆管中流动，试确定流动状态。

(1) 润滑油?＝l.0?10-4m2 /s，(2) 水?＝l.0?10-6m2 若要保证流态为层流，对于流体：

/s，(3) 空气?＝l.5?10-5m2 /s，它们在管道中的最大允许速度各为多少？ ((1) 层流，15.47m/s (2) 湍流，0.155m/s (3) 湍流，2.32m/s)

6.2 Oil of density ?=740kg/m3 and dynamic viscosity ?＝4.03?10-3Pa?s flows in a horizontal round pipe of diameter d=2.54cm at an average velocity of v=0.3m/s. Calculate the pressure drop of oil along pipe of length l＝30m, and the oil velocity at place with distance of 0.6cm to pipe wall.

密度?=740kg/m3，动力粘度 ?＝4.03?10-3Pa?s的油液以平均流速v=0.3m/s流过直径 d=2.54cm的水平放置的圆管。试计算油液在l＝30m长的管道上的压强降，并计算距圆管内壁0.6cm处油液的流速。(1799Pa 0.433m/s)

6.3 The diameter and length of oil transporting pipe are d＝15cm, l＝5000m respectively, its outlet is h＝10m higher that inlet, oil transporting flowrate is qm＝15489kg/h, oil density is ?=859.4kg/m3, oil pressure at the inlet is pi＝49?104Pa, friction loss factor is ?=0.03, find the pressure pe at the outlet.

输油管的直径d＝15cm，长l＝5000m，出口端比入口端高h＝10m，输送油的流量 qm＝15489kg/h，油的密度?=859.4kg/m3，入口端的油压pi＝49?104Pa，沿程损失系数?=0.03，求出口端油压pe。(pe=3.712?105Pa)

6.4 A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length 2l, as shown in Fig.6-30. The flow in pipes is laminar and fully developed. The pressure drop for the first pipe is 1.44 times greater than it is for the second. If the diameter of the first pipe is D, determine the diameter of the second pipe.

流体流过两根相互连接水平放置的长度皆为l的管道，如图6-30所示。管内流动为充分发展

的层流。第一根管上的压降是第二根的1.44倍。 Fig.6-30 Problem 6.4 如第一根管的直径为D，确定第二根管的直径。

6.5 As shown in Fig. 6-31, water flows from water tank A to storage tank B through a pipe of diameter d＝25mm and length l＝10m. If the gauge pressure of the water tank is p=1.96?105Pa, H1＝lm, H2＝5m, minor loss coefficients at inlet and

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工程流体力学课后习题

outlet of the pipe are ?1=0.5 and ?4=1 respectively, for valve ?2＝4, for each elbow ?3＝0.2, friction loss factor is ?＝0.03, find the flowrate of water.

如图6－31所示，水沿直径d＝25mm，长l＝10m的管道，从水箱A流到储水箱B。若水箱中的表压强p=1.96?105Pa，H1＝lm，H2＝5m，管道入口和出口的局部损失系数分别为?1=0.5、?4=1，阀门局部损失系数?2＝4，每个弯头的局部损失系数?3＝0.2，沿程损失系数?＝0.03，试求水的流量。

(qv=2.04?10-3m3/s)

6.6 There are 250 identical brass pipes in a vapour condenser are in parallel connection, total flowrate of condensed water through the pipes is 80L/s, water kinetic viscosity of water is ?＝l.3?10-6m2/s, the Reynolds number should not be less than 15000 in order to guarantee flow regime in brass pipe

is turbulent, what is the magnitude that the inner diameter of brass pipe should not exceed? Fig.6-31 Problem 6.5

一蒸汽冷凝器，内有250根完全相同 的黄铜管并联，通过管中的冷却水的总流量为80L/s，水的粘度为?＝l.3?10-6m2/s，为保证水在黄铜管中的流态为湍流，要求管中的雷诺数不得小于15000，问黄铜管的内径不得超过多少？(d?0.021m)

6.7 Water flows in pipe of radius r0, the flow regime is laminar flow. Find the distance r to the pipe axis at where the velocity just equals the average velocity.

水在半径为r0的管中流动，流态为层流。求流速恰好等于管内平均流速的位置与管轴之间的距离r等于多大？ (

2ro ) 2

6.8 A fluid flows through a pipe of radius R with Reynolds number of 100,000. At what location, r/R, does the fluid velocity equal the average velocity?

流体以雷诺数等于100,000流过半径为R的管道。问在何处r/R流体的流速刚好等于平均流速？

6.9 A water pipe of diameter d＝25cm, length l＝300m, and absolute roughness ?＝0.25mm. If given the flowrate qv＝95l/s, kinetic viscosity ?＝l.0?10-6m2/s, what is the friction loss?

水管直径d＝25cm，长l＝300m，绝对粗糙度?＝0.25mm，已知流量qv＝95l/s，运动粘度 ?＝l.0?10-6m2 /s，求沿程损失为多少？(4.61m水柱)

6.10 Water at 800C flows through a 120mm diameter pipe with an average velocity of 2m/s. If the pipe wall roughness is small enough so that it does not

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工程流体力学课后习题

protrude through the laminar sublayer, the pipe can be considered as smooth. Approximately what is the largest roughness allowed to classify this pipe as smooth?

800C的水以2m/s的平均流速流过直径为120mm的管道。如果管壁的粗糙度很小，没有延伸到层流底层，可认为管道是光滑管。问管道是光滑管的可容许的最大粗糙度大约为多少？

6.11 As shown in Fig.6-32, neglect minor loss, to ensure fluid flowrate in the siphon is qv＝10-3m3/s, determine: (1) when H=2m, l=44m, ?＝l.0?10-4m2 /s, ?=900kg/m3, what is d for ensuring laminar flow? (2) if the limitation vacuum on section A with a distance l/2 to the pipe inlet is pv=52 920Pa, what is the maximum allowed height Zmax of the siphon above the surface of upper oil storage pool?

如图6-32所示，不计局部损失，要保证虹吸管中液体的流量为qv＝10-3m3/s，试确定：(1) 当H=2m，l=44m，?＝l.0?10-4m2 /s，?=900kg/m3时，为保证层流，d应为多少？(2)若在距管进口l/2处的A断面上的极限真空为pv=52 920Pa，虹吸管在上面贮油池油面以上的最大允许高度

Zmax为多少？ Fig. 6-32 Problem 6.11

((1) 0.055m (2) 4.97m)

6.12 Water flows in a smooth plastic pipe of 200mm diameter at a flow rate of 0.1m3/s. Determine the friction factor ? for this flow.

水以0.1m3/s的流量在直径为200mm的塑料管中流动，试确定流动的沿程损失系数?。

6.13 Water flows from a tank along a vertical pipe of l＝2m and diameter d＝4m into atmosphere, as shown in Fig. 6-?. Neglect minor loss, friction loss factor is ?=0.04, find: (1) the relationship between the pressure at pipe’s initial section area A and the water level h in the tank, and the magnitude of h when the absolute pressure at A equals atmospheric pressure; (2) the relationship of the flowrate qv and the pipe length l, and the relationship that water level h satisfies when it does not change with l.

水从水箱沿着高l＝2m，直径d＝4m的竖直管道流入大气，如图所示。不计局部损失，并且沿程损失系数

?=0.04，试求：(1)管道起始断面A的压强与箱内水位h之间的关系式，并求当h为多少时，A处的绝对压强等 Fig.6-33 Problem 6.13 于大气压强；(2)流量qv与管长l的关系，并求出在水位 h满足什么关系时，将不随l而变化？

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工程流体力学课后习题

((1) pA?pa??g(?h?d)/(??d/l) h=1m (2) qv?h?

d

?4d22gd(h?l)

d??l?

6.14 Air flows through the fine mesh gauze shown in Fig. 6-34 with an average velocity of 1.5m/s in the pipe. Determine the loss coefficient for the gauze.

空气在管道中以1.5m/s的平均流速通过如图6-34所示的细纱布。试确定纱布的损失系数。(56.7)

Fig.6-34 Problem 6.14

6.15 As shown in Fig.6-35, the heating furnace consumes heavy oil at a rate of qm=300kg/h, density and kinetic viscosity of oil are ?=880kg/m3 and ?＝25?10-6m2/s respectively, the pressurized oil tank is h＝8m above the sprayer’s axis, oil transporting pipe’s diameter is d＝25mm and length is l=30m. Find the gauge

pressure of heavy oil in front of the oil sprayer.

如图6-35所示，加热炉消耗qm=300kg/h的重油，重油的密度?=880kg/m3，运动粘度?＝25?10-6m2/s，压力油箱位于喷油器轴线以上h＝8m处，而输油管的直径d＝25mm，长l=30m。求

在喷油器前重油的表压强。( 62504Pa) Fig.6-35 Problem 6.15

6.16 Determine the pressure drop per 300m length of new 0.2m diameter horizontal cast iron water pipe when the average velocity is 1.7m/s.

确定直径为0.2m、长300m、平均流速为1.7m/s的水平放置铸铁水管上的压降。

6.17 As shown in Fig. 6-36, the lubricant consumption of the engine is qv＝0.4cm3/s, the lubricant is supplied to the lubricant housings via an oil pipe from the pressurized tank, the pipe’s diameter is d＝6mm and length is l＝5m. The density of the lubricant is

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工程流体力学课后习题

?=820kg/m3，and kinetic viscosity is ?＝15?10-6m2 /s. If the terminal pressure of the lubricant pipe equals atmospheric pressure, find the elevation h needed by the pressurized lubricant tank.

如图6-36所示，发动机润滑油的用量qv＝0.4cm3/s，油从压力箱经一输油管供给到润滑部位，输油管的直径d＝6mm，长度l＝5m。油的密度产?=820kg/m3，运动粘度?＝15?10-6m2 /s，如果输油管道终端的压强等于大气 Fig.6-36 Problem 6.17

压强，求压力油箱所需要的位置高度h。(0.095m)

6.18 An above ground reservior of diameter 9 m and depth 1.5m is to be filled from a garden hose(smooth interior) of length 30m and diameter 0.2m. If the pressure at the faucet to which the hose is attached remains at 38kPa, how long will it take to fill the pool? Water exits the hose as a free jet 1.8m above the faucet.

一直径为9m、水深为1.5m高于地面的水池由一根长30m、直径0.2m的橡胶软管（内部光滑）灌水。如果连接软管的龙头压强保持为38kPa，求灌满游泳池所需的时间为多少？水在高于龙头1.8m处射流流出。(32小时)

6.19 As shown in Fig. 6-37, oil pump transports oil from an open oil pool to the oil tank of gauge pressure p＝0.98 ?105Pa. it is known that oil pump’s flowrate qv＝3.14L/s, and the overall efficiency of the oil pump ?=0.8, oil density ?=800kg/m3，kinetic viscosity ?＝1.25cm2/s, oil pipe’s diameter d＝2cm, length l=2m, total minor loss coefficient ??=2, altitude difference of oil surface h＝3m. Find the power P of the oil pump.

如图6-37所示，油泵从开口油池中将油送到表压强p＝0.98 ?105Pa的油箱中。已知油泵流量qv＝3.14L/s，油泵总效率?=0.8，油的密度?=800kg/m3，运动粘度?＝

1.25cm2/s，油管直径d＝2cm，长度l=2m，总局部损失系数为??=2，油面高度差h＝3m。试求油泵的功率P。 Fig.6-37 Problem 6.19

(418.9W)

6.20 Water is to flow at a rate of 1.0m3/s through a rough concrete pipe(?=3mm) that connects two ponds. Determine the pipe diameter if the elevation difference between the two ponds is 10m and the pipe length is 1000m. Neglect minor losses.

如果两水水以1.0m3/s的流量流过一连接两水池的粗糙混凝土管(?=3mm)。

池水位差为10m、管长为1000m，确定管径。忽略局部损失。(0.748m)

6.21 Without the pump shown in Fig. 6- 38, it is determined that the flow rate is to small. Determine the power added to the fluid if the pump causes the flowrate to be doubled. Assume the friction factor remains at 0.02 in either case.

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工程流体力学课后习题

如图6-38所示，如果不加水泵，发现流量太小。要使流量翻倍，试确定水泵施加在流体上的功率为多少。设在两种情况 Fig.6-38 Problem 6.21 下沿程损失系数均为0.02。(3.7kW)

6.22 Water drains from a pressurized tank through a pipe system as shown in Fig. 6-39. The head of the turbine is equal to 116m. If the entrance effects are negligible, determine the flowrate.

水从如图6-39的压力水箱经管道系统流出。涡轮的水头为116m。如果忽略入口处的损失，试确定流量为多少。 (qv=3.71?10-2m3/s)

Fig.6-39 Problem 6.22

6.23 As shown in Fig. 6-40, centrifugal pump transports condensed water with a flowrate of 20m3/h to a boiler, the diameter of pump’s sucking pipe is d＝90cm, total length is l=8m, there is an eblow of bending diameter R＝45mm and an inflow sluice valve of minor loss coefficient ?＝5, friction loss factor is ?＝0.02, according to specification, the inlet pressure of the pump should be 0.4?105Pa, find the maximum installation height of the pump above water surface.

离心泵把凝结水以20m3/h的流量输送到锅炉中，如图6－40所示，水泵吸入管直径d＝90cm，总长度l=8m，具有一个弯曲半径R＝45mm的弯头和一进水栅阀，进水栅阀的局部损失系数?＝5，沿程损失系数?＝0.02，按规定，水泵的进口压强应为0.4?105Pa，

试求水泵在水面以上的最大安装高度h。(h=5.88m) Fig.6-40 Problem 6.23

6.24 The three tanks shown in Fig. 6-41 are connected by pipes with friction factors of 0.03 for each pipe. Determine the water velocity in each pipe. Neglect minor loss.

如图6-41所示，三个水箱由沿程损失系数为0.03的管道连接。确定各管中的流速。忽略局部损失。

(v1=1.03m/s v2=0.835m/s)

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工程流体力学课后习题

Fig.6-41 Problem 6.24

6.25 Water pump pumps water into two tanks, as shown in Fig.6-42, elevations of the water pool and water tank are H1=2m and H2＝4m respectively, inner diameter of the pipe is d1＝d2=20cm, pipe lengths are l1＝40m, l2=45m, friction factors are ?1=?2=0.02, pump’s head of delivery is Hp=20m, and neglect minor loss. Find: (1) pump’s discharge; (2) when the overall efficiency of the pump is ?=70%, how much is the power which is transmitted to the pump by the motor driving the pump?

如图6－42所示，泵将水池中的水打入两水箱，水池与水箱水面的高度各为H1=2m，H2＝4m，圆管内径d1＝d2=20cm，管长l1＝40m，l2=45m，沿程

损失系数?1=?2=0.02，泵的扬程Hp=20m，不计局部损失。试求 (1) 泵的排水量；

(2) 当泵的总效率?=70%时，带动泵的电动机输给泵的功率应为多少？ Fig.6-42 Problem 6.25

((1) 0.57m3/s (2) 159.6kW)

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工程流体力学课后习题

Problems

7.1 A thin-walled circular orifice with diameter d=10mm, head H=2m. Now the diameter of contracted section is measured as dc=8mm, the volume passing through the orifice in 32.8s is 0.01m3. Try to find the orifice’s contraction coefficient ?, discharge coefficient ?, velocity coefficient ?, and minor loss coefficient ?.

有一薄壁圆形孔口，d=10mm，水头H=2m。现测得射流收缩断面的直径dc=8mm，在32.8s的时间内经孔口的水量为0.01m3。试求孔口的收缩系数?、流量系数?、流速系数?、以及孔口局部损失系数?。 (?=0.64，?=0.62，?=0.97，?=0.06)

7.2 As shown in Fig 7-21, a thin-walled orifice with diameter d=2cm, the surface in water tank is stable, and H=2m, find (1) the orifice’s flowrate qo; (2) the flowrate of the nozzle attached on the orifice; (3) the vacuum height of the contracted section in the nozzle.

如图7-21所示，薄壁孔口出流，d=2cm，水箱水位恒定且H=2m，试求(1)孔口流量qo；(2)孔口外接圆柱形管嘴的流量qn；(3)管嘴收缩断面的真空高度hv。

(qo=1.22L/s，qn=1.61L/s，hv=1.506m) Fig. 7-21 Problem 7.2

7.3 As shown in Fig.7-22, a water tank is separated by a clapboard, in the figure d1=4cm，d2=3cm，H=3m，h3=0.5m，try to find (1) h1，h2; (2) the flowrate Q.

如图7-22所示，水箱用一带有孔的隔板

d2=3cm，H=3m，h3=0.5m，隔开，图中d1=4cm，

试求：(1)h1，h2 (2)流量Q。

((1) h1=1.06m，h2=1.44m；(2) Q=3.67L/s)

Fig. 7-22 Problem 7.3

7.4 A swimming pool with the dimension of 25m long, 10m wide, and 1.5m deep, there is a drainage hole with diameter of d=10cm on the bottom of the pool, find the time needed to empty the pool when it is fully filled.

游泳池的长、宽、深分别为25m、10m、1.5m，池底设有d=10cm的排水孔，试求游泳池装满后，放净水池所需的时间。(7.89h)

7.5 As shown in Fig.7-23, the water tank of a sprinkler has a length of l and

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工程流体力学课后习题

diameter of D, there is a drainage hole with area A on the bottom of the tank, its flowrate coefficient is ?, find the time Fig. 7-23 Problem 7.5

needed to empty the tank when it is fully loaded.

如图所示，洒水车的水箱长度为l，直径为D，水箱底部有一面积为A的放水孔，其流量系数为?，求水箱装满后放空所需的时间。

2lD1.5(t? )

3?Ag0.57.6 As shown in Fig. 7-24, a siphon transports water form reservoir A to reservoir B, it is known that l1=3m，l2=5m，d=75mm，elevation difference of the two reservoirs is H=2m, the maximum superelevation is h=1.8m, frictional loss coefficient ?=0.02, minor loss coefficient: inlet ?a=0.5, bend ?b=0.2, outlet ?c=1. Find the siphon’s flowrate qv and the vacuum hv at the

maximum superelevation section. Fig. 7-24 Problem 7.6

如图7-24所示，虹吸管将A池中的

水输送到B池，已知l1=3m，l2=5m，d=75mm，两水池高度差H=2m，最大超高h=1.8m，沿程损失系数?=0.02，局部损失系数：进口?a=0.5，转弯?b=0.2，出口?c=1，试求虹吸管的流量qv以及最大超高断面的真空度hv。 (qv=14.14L/s，hv=3.10m)

7.7 As shown in Fig.7-25, water flows from enclosed container A to container B via a pipe with diameter d=25cm and length l=10m, given the relative pressure on water surface of container A as p1=2atm, surface elevation as H1=1m and H2=5m, frictional loss coefficient as ?=0.025, minor loss coefficient as: valve ?v=4.0, elbow ?b=0.3. Try to determine flowrate qv in the pipe.

如图7-25所示，水从密闭容器A，沿直径d=25mm、长l=10m的管道流入容器B，已知容器A水面的相对压强p1=2atm，水面高H1=1m，H2=5m，沿程损失系数?=0.025，局部损失系数：阀门?v=4.0，弯

头?b=0.3，试求管道中的流量qv。 Fig. 7-25 Problem 7 (qv=2.15L/s)

7.8 As shown in Fig. 7-26, water flows from an orifice with diameter of d1=30mm on the bottom of the upper tank to the lower tank, then drains into air through a circular nozzle with diameter d2=20mm. After the flow becomes stable, h1=2m, h2=3m, the reading of the manometer installed on the upper tank is p1=4.9MPa. Find the flowrate Q and surface pressure of the lower tank.

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工程流体力学课后习题

一块面积为8m?8m的矩形平板放在速度v?=3m/s的水流中，水的运动粘性系数?=10-6m2/s，平板放置的方法有两种：以长边顺着流速方向，摩擦阻力为F1；以短边顺着流速方向，摩擦阻力为F2。试求比值F1/F2。 (F1/F2=0.9080)

8.9 A high speed train runs at 200km/h, kinetic viscosity of air is ?=1.5?10-6m2/s. Each carriage of the train may be regarded as a cube of 25m long, 3.4m wide and 4.5m high. Calculate the power needed by the train with ten carriages to overcome the boundary layer resistance on the top and the two sides. Assume Rexc=5.5?105，?=1.205kg/m3.

高速列车以速度200km/h行驶，空气的运动粘性系数?=1.5?10-6m2/s。每节车厢可视为长25m,宽3.4，高4.5m的立方体。试计算为了克服十节车厢的顶部和两侧面的边界层阻力所需的功率。设Rexc=5.5?105，?=1.205kg/m3。 (P=507.3kW)

8.10 A weight of 45kN is dropped from an airplane, it is required that the velocity falling to the ground not exceed 10m/s, the weight is hanged beneath a parachute of resistance coefficient CD=2, neglect parachute weight, assume air density is ?=1.205kg/m3, find the diameter of the parachute.

有45kN的重物从飞机上投下，要求落地速度不超过10m/s, 重物挂在一张阻力系数CD=2的降落伞下面，不计伞重，设空气密度为?=1.205kg/m3，求降落伞的直径。 (D≥21.85m)

8.11 There is a rectangular thin board which is 1.5m×4.5m, drag at the velocity of 3m/s in the direction of board surface, kinetic viscosity of air is v = 1.5×10－5m2/s , the density of air is ?=1.2 kg/m3。Find resistance force along short edge and long edge respectively.

有一块 1.5 m×4.5 m 的矩形薄板在空气中以 3 m/s速度沿板面方向拖动，已知空气运动粘度为 v = 1.5×10－5 m2/s , 密度为? = 1.2 kg/m3 。试求薄板沿短边方向和长边方向运动时，各自的摩擦阻力。

8.12 A smooth, flat plate of length l=6m and width b=4m is placed in water with an upstream velocity of v=0.5m/s. Determine the boundary layer thickness and the wall shear stress at the center and the trailing edge of the plate. Assume a laminar boundary layer. 一块长l=6m、宽b=4m的光滑平板放置于来流速度v=0.5m/s的水流中。试确定边界层的厚度，以及平板中心处于尾端的壁面切应力。

8.13 A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm. Determine the boundary layer thickness at distances of 0.20, 2.0, and 20 m from the leading edge. If the upstream velocity of the flow is v=1.5m/s, determine the kinematic viscosity of the fluid. Assume laminar flow.

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工程流体力学课后习题

一粘性流体流过一块平板，离板前端1.3m处的边界层厚度为12mm，确定离板前端0.20、2.0、以及20m处的边界层厚度。如果来流速度为v=1.5m/s，试确定流体的运动粘度。设流动为层流。

8.14 A laminar boundary layer formed on one side of a plate of length l produces a drag FD. How much must the plate be shortened if the drag on the new plate is to be FD/4? Assume the upstream velocity remains the same. 在一块长为l的平板一侧形成的层流边界层所产生的阻力为FD。如果要使阻力减为FD/4，板的长度需要减少多少？假设来流速度保持不变。 (lnew=l/16)

8.15 A 12-mm-diameter cable is strung between a series of poles that are 40 m apart. Determine the horizontal force this cable puts on each pole if the wind velocity is 30m/s.

一根直径为12mm的线缆悬挂在一系列相距40m的柱子间，如果风速为30m/s，试确定线缆作用在每根柱子上的水平力为多少。 (372N)

8.16 A 200-N rock (roughly spherical in shape) of specific gravity 1.93 falls at a constant speed U. Determine U if the rock falls through (a) air; (b) water.

一块比重为1.93的200N的球形岩石以速度U匀速下降。试确定岩石下降的速度：(a) 在空气中； (b) 在水中。 (176m/s；5.28m/s)

8.17 Water flows past a flat plate that is oriented parallel to the flow with an upstream velocity of 0.5 m/s. Determine the approximate location downstream from the leading edge where the boundary layer becomes turbulent. What is the boundary layer thickness at this location?

水流以0.5 m/s的来流速度绕一块与流动方向平行放置的平板流过。试确定边界层变为湍流时的截面距前端的距离、以及该处边界层的厚度。 (1.12m，7.92?10-3m)

8.18 A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm. Determine the boundary layer thickness at distances of 0.20, 2.0, and 20 m from the leading edge. If the upstream velocity of the flow is U=1.5m/s, determine the kinematic viscosity of the fluid. Assume laminar flow. 粘性流体流过一块平板，离前端1.3m处边界层的厚度为12mm。试确定离前端0.20、2.0、及20m处的边界层厚度。如果来流速度为U=1.5m/s，确定流体的运动粘度。设流动为层流。 (?=6.65?10-6m2/s)

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工程流体力学课后习题

8.19 A laminar boundary layer velocity profile is approximated by the two straight-line segments indicated in Fig. 8-10. Use the momentum integral equation to determine the boundary layer thickness, ?=?(x), and wall shear stress, ?w=?w(x). 层流边界层的速度分布图近似于两段直线，如图8-10所示。试利用动量积分方程，确定边界层厚度?=?(x)与壁面切应力的表达式?w=?w(x)。 (??4.12?x/U ?w?4?U/(3?) )

Fig.8-10 Problem 8.19

8.20 A 38.1-mm-diameter, 0.0245-N table tennis ball is ejected vertically from the bottom of a 2-m-depth swimming pool. With what initial velocity does it rise to the surface? Assume it has reached its terminal velocity. 一直径为38.1mm、重0.0245牛顿的乒乓球从游泳池底部沿铅直方向射出。问乒乓球的初始速度为多少时，刚好上升到游泳池的表面？设乒乓球到表面时速度为零。 (v=1.06m/s)

8.21 A shortwave radio antenna is constructed from circular tubing, as is illustrated in Fig.8-11. Estimate the wind force on the antenna in a 100 km/h wind. 一短波天线由圆形管子组成，如图8-11所示。确定天线在速度为100 km/h的风中所受的风力。 (FD=180N)

Fig.8-11 Problem 8.21

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