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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

(x

=2，5-z=2z)

vx，求流线方程。(x1+t=cy)

，求通过点（2，1，1）的流线方程。

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

vvv 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)

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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)

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

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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。

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Fig.3-35 Problem 3.19