流体力学课后作业

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？

((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？

(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)

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

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。

(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

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

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.

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.

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

(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

0.5

标平面上半部确定任一驻点的位置。( ?s=?/2，rs=(m/4?))

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。

(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)

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

3

Fr相等，测得模型上的流量为0.19m/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。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，108kN)

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？ (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有关，导出流速的表达式。(

)

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. 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)

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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