1/62
建工学院土木系Dept. of Civil Engineering
Autumn 2008
Solution to Lecture 3
2/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.1
The velocity field of a flow is given by , where x , y , and z are in feet. Determine the fluid speed at the origin (x = y = z = 0) and on the x axis (y = z = 0).
3/62
建工学院土木系
Dept. of Civil Engineering Autumn 2008
3.6? A velocity field is given by V = x ?+ x (x ?1)(y + 1)?, where
u and v
are in ft/s and x and y are in feet. Plot the streamline that passes through x = 0 and y = 0. Compare this streamline with the streakline through the origin. 4/62
建工学院土木系
Dept. of Civil Engineering Autumn 2008
3.6
5/62
建工学院土木系
Dept. of Civil Engineering Autumn 20083.12
?Determine the acceleration field for a three-dimensional flow with velocity components u = ?x , v = 4x 2y 2, and w = x ?y .
6/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.14
?The velocity of air in the diverging pipe shown in Fig. P4.17 is given by V 1 = 4t ft/s and V 2 = 2t ft/s, where t is in seconds. (a)Determine the local acceleration at points (1) and (2). (b)Is the average
convective acceleration between these two points negative, zero,or
positive? Explain.
7/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.40
Water flows from the faucet on the first floor of the building shown in Fig. P3.14 with a maximum velocity of 20 ft/s. For steady inviscid flow, determine the maximum water velocity from the basement faucet and from the faucet on the second floor (assume each floor is 12 ft tall).
8/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.47
?Water flows from a large tank of depth H , through a pipe of length L ,
and strikes the ground as shown in Fig. P3.47. Viscous effects are negligible. Determine the distance h as a function of θ.
9/62
建工学院土木系
Dept. of Civil Engineering Autumn 2008
3.47
10/62
建工学院土木系
Dept. of Civil Engineering Autumn 2008
3.49?Water flows steadily downward through the pipe shown in Fig. P3.25. Viscous effects are negligible, and the pressure gage indicates the pressure is zero at point (1). Determine the flowrate and the pressure at point (2).
11/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.59
?Water is siphoned from the tank shown in Fig. P3.39. The water barometer indicates a reading of 30.2 ft. Determine the maximum value of h allowed without cavitation occurring. Note that the pressure of the vapor in the
closed end of the barometer equals the vapor pressure. 12/62
建工学院土木系Dept. of Civil Engineering Autumn 2008
3.64
?Water flows through a converging–diverging nozzle as shown in Fig. P3.45. Determine (a)the volumetric flowrate, Q , through the nozzle and (b)the height, h , of the water in the Pitot tube inserted into the
free jet. Viscous effects are negligible.
13/62
建工学院土木系
Dept. of Civil Engineering Autumn 2008
3.94?An automatic boat bailer is shown in Fig. P3.88. The “bump”on the bottom of the hull is designed to increase the velocity at point (1) to approximately 1.2V 0, where V 0 is the velocity of the boat through the water. If the pressures at (1) and (2) are essentially equal, what minimum velocity is needed to initiate the bailing action?
14/62
建工学院土木系Dept. of Civil Engineering
Autumn 2008