Bài tập Thủy lực 2 (Tiếng Anh)

• Đăng bởi: nguyenphuocbinh
• Sinh viên
• 18/12/2019

1 (a) A rectangular culvert 2.1 m wide by 1.8 m high discharges to a river channel as in Fig. At the end of the culvert is a vertical flap gate which is hinged along its top edge, the gate having the same dimensions as the culvert. During a flood the river rises to 3.5 m above the hinge. What is the force exerted by the floodwater on the gate, and at what depth from the surface does it act? (b) A circular gate, also hinged at the top, hangs vertically at the end of a pipe discharging to the river. The gate has a radius of 0.5 m, and during a flood the hinge is 3.5 m below the water surface. What is the force exerted by the floodwater on the gate, and at what depth from the surface does it act?

[(a) 163.16 x10³N at 4.461 m; (b) 30.82 x10³N at 4.015 m]

2 A gate at the end of a sewer measures 0.8 m by 1.2 m wide. It is hinged along its top edge and hangs at an angle of 30° to the vertical, this being the angle of the banks of a trapezoidal river channel. (a) Calculate the hydrostatic force on the gate and the vertical distance between the centroid of the gate, G, and the centre of pressure, P, when the river level is 0.1 m above the top of the hinge. (b) If the river level increases to 2.0 m above the hinge, what is the force and the distance GP now? (c) Has the value of GP increased or decreased, and why has it changed in this manner?

[(a) 4.21 x 10³ N, 0.090 m; (b) 22.10 x 10³ N, 0.017 m]

3 A circular gate of 0.5 m radius is hinged so that it rotates about its horizontal diameter, that is it rotates about a horizontal line passing through the centroid of the gate. The gate is at the end of a pipe discharging to a river. Measured above the centroid of the gate, the head in the pipe is 6.0 m while the head in the river is 2.0 m. Assuming that the gate is initially vertical: (a) calculate the force

exerted by the water in the pipe on the gate, and the distance GP between the centre of the gate, G, and the centre of pressure, P; (b) calculate the force exerted by the river water on the gate, and the distance GP; (c) by taking moments about the hinge, using the results from above, determine the net turning moment on the gate caused by the two forces acting at their respective centres of pressure on opposite sides of the gate. Explain your answer.

[(a) 46 228.5 N at 0.0104 m; (b) 15 409.5 N at 0.0312 m; (c) 0 exactly, allowing for rounding errors]

4 A gate which is a quarter of a circle of radius 4.0 m holds back 2.0 m of fresh water as shown in the diagram. Calculate the magnitude and direction of the resultant hydrostatic force on a unit length of the gate.

[52.05x 10³N/m at 67.9° to the horizontal, acting upwards through the centre of curvature, C]

5 A 7500 tonne reinforced concrete lock structure has been constructed in a dry dock. The lock is 60m long by 30 m wide in plan and is shaped like an open shoe box. The side walls are 8 m high. (a) Will the lock structure float in sea water of density 1025 kg/m3, and if so, what is its draught and free-board? (b) What additional weight will be required to sink the structure onto the sea bed if the depth of water is 5.3 m, assuming the structure is watertight? (c) If the additional weight is to be provided by a blanket of sand (density 2600 kg/m3), how thick must the layer of sand be? (1 tonne =1000 kg).

[(a) yes, 4.07 m, 3.93 m; (b) >22 352 x 10³N;(c) >0.5 m]