Examples and Problems Example 9-218 Force on a Quarter Cylinder Determine the ma

Question

Examples and Problems Example 9-218 Force on a Quarter Cylinder Determine the magnitude, direction, and line of action of the resultant hydrostatic force acting on the curved surface. Here I-1 m. Solution The horizontal hydrostatic force is F:-h,A 9.81(1.5)12# 14.715 kN The vertical hydrostatic force is equivalent to * F:-+-9.8/ 1' (1) +12(1) = 17.515 kN The vertical location of the horizont . 1x1, bh 12y.A = 1.555 m y, =y, +12-.15+12(1.5) 11 The horizontal location of the vertical force is obtained from x,F-R+,F where x is the horizontal distance from the vertical line passing through the area of the quarter circle and the overlying square, respectively, while F, corresponds to the total area. Hence and F, correspond to r,B +4_h1(1-41)412 (1)2 (1)|= 0.5332 m F, F14.715 +17.515-22.876 kN e-arctan(%)-50 17.5153)4 The resultant force is - The line of action is at an angle of F.

Explanation / Answer

In simple words, imagine if the circular surface/gate was not there to obstruct the path of the water, the water would have risen up on the left to the same level as it is on the right side of the vertical line through B. The volume of air which is calculated above would have been filled with water, right?

So this much amount of water weight is obstructed by the gate by applying the equal amount of force in the downward direction so that water does not rise up. In other words, water is pushing up the gate with the force equal to the weight of the water of the same volume as of the air above the surface, which it would have occupied if the gate was not there.

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