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

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