An example of force on a curved sluice gate with fluid both above and below the gate.
A 1.5m long cylinder, radius 1m, lies as shown in the figure. It holds back oil of relative density 0.8. If the cylinder has a mass of 2250 kg find
a) the reaction at A b) the reaction at B
Horizontal force RH = projection of vertical plane
Reaction at A = -RH = 0.5 x rgH2 x Length
= 0.5 x 0.8 x 103 x 9.81 x 22 x 1.5
= 23544 N, to the left
Vertical force = Reaction at B
RV = Force due to weight of fluid, DCE, above (down)
+ Force due to fluid below BD (upward)
+ Force due to weight of cylinder
Force of fluid above = area of sector
DCE x length x rg
Force from below = area of real or imaginary fluid above BD
= area of BDEC x length x rg
Taking downward as positive
RV = 0.8 x 103x9.81 x(11 - pr2/4) x 1.5
- 0.8 x103 x9.81 x( 11 + pr2/4) ) x 1.5
+ 22509.81
= 2526 -
= 3580 N
Reaction at B = 3580 N, vertically up
The resultant and angle of application
are given by:
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