Question

4) The flow of water from a reservoir is controlled by a 5-ft-wide L-shaped gate hinged at point A, as shown. If it is desired that the gate open when the water height is 12 ft, determine the mass of the required weight W. 8 ft Gate 15 ft 12 ft

Answer 1

Draw the schematic diagram of the configuration. 18ft 15ft 12 ft

Calculate the area of the gate. A= wh Here, w is the width of the gate and n is the height of the gate. Substitute sit for w and 124 for h. A= 5x12 = 60ft? Find the vertical distance from the top of water to centroid of dam wall.

Calculate the resultant hydrostatic force. FR = yh. A Here, r is the specific weight of water. Substitute 62.41b/h" for , 6ft for h, and 60ft for a. FR = 62.4x6x60 = 22464 lb Calculate the moment of inertia about v-axis for the gate. Substitute si for w and 124 for n. 1-(5)(12) 12 = 720ft* Calculate the location of center of pressure. y, = + a Substitute of for h., 7204 for 1«, and 60ft for A. y, =6+ 720 60x6 = 8 ft

Take algebraic sum of moments about point M,=0 Fx(S+y,)=W x AB Substitute 224641b for Fx, 3p for s, if for y, and of for AB. 22464x (3+8)=W x8 W = 30888 = 30900 16 Therefore, the required weight, W is 3090016). Calculate the mass of the weight W. m= 30900 lb 32.174 ft/s? =960.4 lbm Therefore, required mass of the weight, W is 960.4 lbm.