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14. Arectangular gate 6 mx 2 m is hinged at its base and inclined at 60° to the horizontal as shown in Fig. To keep the gate in a stable position, a counter weight of 29430 N is attached at the upper end of the gate. Find the depth of water at which the gate begins to fall. Neglect the weight of the gate and also friction at the hinge and pulley. WATER SURFACE [Ans. 343 m) HINGE 3 m HINGE 80 1.5 m - Fig. 3.54 Fig. 3.55

14. Arectangular gate 6 mx 2 m is hinged at its base and inclined at 60° to the horizontal as shown in Fig. To keep the gate in a stable position, a counter weight of 29430 N is attached at the upper end of the gate. Find the depth of water at which the gate begins to fall. Neglect the weight of the gate and also friction at the hinge and pulley. WATER SURFACE [Ans. 343 m) HINGE 3 m HINGE 80 1.5 m - Fig. 3.54 Fig. 3.55

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14. A rectangular gate 6 mx2 m is hinged at its base and inclined at 60° to the horizontal as shown in Fig. 354. To keep the gate in a stable position, a counter weight of 29430 N is attached at the upper end of the gate. Find the depth of water at which the gate begins to fall. Neglect the weight of the gate and also friction at the hinge and pulley. [Ans. 343 m) WATER SURFACE HINGE 3 m HINGE 60 1.5 m Fig. 3.54 Fig. 3.55 15. An inclined rectangular gate of width 5 m and depth 1.5 m is installed to control the discharge of water as shown in Fig. 3.55. The end A is hinged. Determine the force normal to the gate applied at B to open it. [Ans. 97435.8 N] FREE WATER SURFACE 16. A gate supporting water is shown in Fig. 3,56. Find the height "k' of the water so that the gate begins to tip about the hinge. Take the width of the gate as unity. 17. Find the total pressure and depth of centre of pressure on a triangular plate of base 3 m and height 3 m which is immersed in water in such a way that plane of the plate makes an angle of 60° with the free surface. The base of the plate is paràllel to water surface and at a depth of 2 m from water GATE [Ans. 3x 3 m] - HINGE Fig. 3.56 surface, [Ans. 126.52 kN, 2.996 m]
Transcribed Image Text:14. A rectangular gate 6 mx2 m is hinged at its base and inclined at 60° to the horizontal as shown in Fig. 354. To keep the gate in a stable position, a counter weight of 29430 N is attached at the upper end of the gate. Find the depth of water at which the gate begins to fall. Neglect the weight of the gate and also friction at the hinge and pulley. [Ans. 343 m) WATER SURFACE HINGE 3 m HINGE 60 1.5 m Fig. 3.54 Fig. 3.55 15. An inclined rectangular gate of width 5 m and depth 1.5 m is installed to control the discharge of water as shown in Fig. 3.55. The end A is hinged. Determine the force normal to the gate applied at B to open it. [Ans. 97435.8 N] FREE WATER SURFACE 16. A gate supporting water is shown in Fig. 3,56. Find the height "k' of the water so that the gate begins to tip about the hinge. Take the width of the gate as unity. 17. Find the total pressure and depth of centre of pressure on a triangular plate of base 3 m and height 3 m which is immersed in water in such a way that plane of the plate makes an angle of 60° with the free surface. The base of the plate is paràllel to water surface and at a depth of 2 m from water GATE [Ans. 3x 3 m] - HINGE Fig. 3.56 surface, [Ans. 126.52 kN, 2.996 m]
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