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 αv=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αv=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 αv=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 αl=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αv=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αl=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

ν=3⨯10-5m2/s and ρ=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ν=3⨯10-5m2/s、ρ=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 (μ=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(μ=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？