流体力学课后作业

流体力学课后作业-标准化文件发布号：（9456-EUATWK-MWUB-WUNN-INNUL-DDQTY-KII

1.1 A pressure of 2106N/m2 is applied to a mass of water that initially filled

a 1,000cm3 volume. Estimate its volume after the pressure is applied.

将2106N/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。

( 2.5108Pa)

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=6.510-41/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=1.210-51/K of the oil tank is considered, what is the result in this case?

(3)

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=6.510-41/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=1.210-51/K，这时的情况如何？

(3)

((1)2.49210-3m3 (2)2.3210-3m3)

1.5 A metallic sleeve glides down by self

weight, as shown in Fig. 1-11. Oil of =310-

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).

F

ig. 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 (=410-3N 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(=410-3N 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。

(410-2Pa)

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/m 3, 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

V=

给出。如果流体为甘油(T=200C) 且压强梯度dp/dx 为1.6kN/m 3，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(u 12=0.59m/s ；τ12=20.8N/m 2；u 0=0；τ0=40.4N/m 2)

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

1.9

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)

(4) If the oil viscosity is 0.01 N s/m 2 and the spacing y is 2mm, what is the shear stress for the condition noted in (b)

(5)

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？

(4)

((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 μ=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μ=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)