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308-12-16 - 12 A gate having the shape shown is located in...

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12. A gate having the shape shown is located in the vertical side of an open tank containing water. The gate is mounted on a horizontal shaft. (a) When the water level is at the top of the gate, determine the magnitude of the fluid force on the rectangular portion of the gate above the shaft and the magnitude of the fluid force on the semicircular portion of the gate below the shaft. (b) For this same fluid depth, determine the moment of the force acting on the semicircular portion of the gate with respect to an axis which coincides with the shaft. (c) Clearly sketch the hydrostatic pressure distribution on the vertical gate. Shaft 6 m 3 m Fluid Side view of gate Rectangular part F rect =ρgAh c =(999)(9.807)(6)(6)(3)=1058097 N Semicircular part ) m 3 ( π 3 4 m 6 R π 3 4 m 6 h c + = + = =7.273 m I xc =0.1098R 4 N 007344 1 ) 273 . 7 ( (3) π 2 1 7) (999)(9.80 gAh ρ F 2 c semi = = = m 359 . 7 ) 273 . 7 ( ) 3 ( 2 π 0.1098(3) m 273 . 7 Ay I y y 2 4 c xc c semi = + = + = Moment acting on semicircular part M=F semi (y semi -6 m)=(1007344)(7.359-6) M=1369483 N·m =1.37 MN·m 13. A 3-m long curved gate is located in the side of a reservoir containing water as shown. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate for a gate radius of R=2 m and a fluid depth of 6 m.
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