Lecture2_Solution

1/62

建工学院土木系Dept. of Civil Engineering

Autumn 2008

Solution to Lecture 2

Dr. Shao Weiyun

Dept. of Civil Engineering

Email:shaowy@https://www.sodocs.net/doc/1a18943752.html,

2/62

建工学院土木系Dept. of Civil Engineering Autumn 2008

2.10

The basic elements of a hydraulic press are shown in Fig. P2.10.The plunger has an area of 1 in.2, and a force, F 1, can be applied to the plunger through a lever mechanism having a mechanical advantage of 8 to 1. If the large piston has an area of 150 in.2, what load, F 2, can be raised by a force of 30 lb applied to the lever? Neglect the hydrostatic pressure variation.

3/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.16A U-tube manometer is connected to a closed tank as shown in Fig. P2.16. The air pressure in the tank is 0.50 psi and the liquid in the tank is oil (γ= 54.0 lb/ft3). The pressure at point A is 2.00 psi. Determine: (a) the depth of oil, z , and (b) the differential reading, h , on the manometer.

4/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.21?The inverted U-tube manometer of Fig. P2.21 contains oil (SG = 0.9) and water as shown. The pressure

differential between pipes A and B , pA ?pB , is ?5 kPa. Determine the differential reading, h .

5/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.22? A piston having a cross-sectional area of 0.07 m2 is located in a cylinder containing water as shown in Fig. P2.22. An open U-tube manometer is connected to the cylinder as shown. For h 1 = 60 mm and h

= 100 mm, what

is the value of the applied force, P , acting on the piston? The weight of the piston is negligible. 6/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.36? A rectangular gate having a width of 5 ft is located in the sloping side of a tank as shown in Fig. P2.36. The gate is hinged along its top edge and is held in position by the force P.Friction at the hinge and the weight of the gate can be neglected . Determine the required

value of P.

7/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.46A thin 4-ft-wide, right-angle gate with negligible mass is free to pivot about a frictionless hinge at point O , as shown in Fig. P2.46. The horizontal portion of the gate covers a 1-ft-diameter drain pipe which contains air at atmospheric pressure. Determine the minimum water depth, h , at which the gate will pivot to allow water to flow into the pipe.

8/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.49?Water backs up behind a concrete dam as shown in Fig. P2.69. Leakage under the foundation gives a pressure distribution under the dam as indicated. If the water depth, h , is too great, the dam will topple over about its toe (point A ). For the dimensions given, determine the maximum water depth for the following widths of the dam: ?= 20, 30, 40, 50, and 60 ft. Base your analysis on a unit length of the dam.

The specific weight of the concrete is 150 lb/ft3.

9/62

建工学院土木系Dept. of Civil Engineering

Autumn 2008

10/62

建工学院土木系Dept. of Civil Engineering Autumn 2008

2.50

? A 4-m-long curved gate is located in the side of a reservoir containing water as shown in Fig. P2.50. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate. Will this force pass through point A ? Explain.

11/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.51?The air pressure in the top of the 2-liter pop bottle shown in Video V2.4and Fig. P2.51 is 40 psi, and the pop depth is 10 in. The bottom of the bottle has an irregular shape with a diameter of 4.3 in. (a)If the bottle cap has a diameter of 1 in. what is the magnitude

of the axial force required to hold the cap in place? (b)Determine the force needed to secure the bottom 2 in. of the bottle to its cylindrical sides. For this calculation assume the effect of the weight of the pop is negligible. (c)By how much does the weight of the pop increase the pressure 2 in. above the bottom? Assume the pop has the same specific weight as that of water.

12/62

建工学院土木系

Dept. of Civil Engineering Autumn 2008

2.56? A closed tank is filled with water and has a 4-ft-diameter hemispherical dome as shown in Fig. P2.56. A U-tube manometer is connected to the tank. Determine the vertical force of the water on the dome if the differential manometer reading is 7 ft and the air pressure at the upper end of the manometer is 12.6 psi.

13/62

建工学院土木系Dept. of Civil Engineering Autumn 2008

2.57

?Three gates of negligible weight are used to hold back water in a channel of width b as shown in Fig. P2.57. The force of the gate against the block for gate (b) is R.

Determine (in terms of R ) the force against the blocks for the other two gates. 14/62

建工学院土木系Dept. of Civil Engineering

Autumn 2008

15/62

建工学院土木系Dept. of Civil Engineering

Autumn 2008

2.59?The homogeneous wooden block A of Fig. P2.83 is 0.7 m by 0.7 m by 1.3 m and weighs 2.4 kN. The concrete block B (specific weight = 2

3.6 kN/m3) is suspended from A by means of the slender cable

causing A to float in the position indicated. Determine the volume of

B.16/62

建工学院土木系Dept. of Civil Engineering Autumn 2008

2.61

?An inverted test tube partially filled with air floats in a plastic water-filled soft drink bottle as shown in Video V2.5and Fig. P2.61. The amount of air in the tube has been adjusted so that it just floats. The bottle cap is securely fastened. A slight squeezing of the plastic bottle will cause the test tube to sink to the bottom of the bottle. Explain this phenomenon.