Square Plate
Calculate the fluid force (in Newtons) on a square plate with a side of 5 m that is submerged at a horizontal?
angle of 60 degrees. Assume that the top edge of the late is located at the surface of the water.
helllppp! i can’t figure it out.!
remember that force = pressure x area and that the pressure generated by a fluid of density rho and depth h is rho g h
here, the depth varies from zero to a final depth of 5sin60=4.33m
let’s consider the force acting on an element of area, dA
dA has a length of 5m, and a width of dL, where L is measured along the downward sloping direction, and is related to dh (an incremental change in depth) by dL = dh/sin60, so dA=5dh/sin60
now, the pressure acting on each element is rho g h, so the total force on that element is
dF=rho g h (5dh/sin60) = (5 rho g/sin60) h dh
rho of water = 1000kg/m^3, g=9.8m/s/s
and we find dF by integrating from h=0 to h=4.33:
F=Integral[(5 rho g/sin60) h dh]
integrate between limits of 0 and 4.33, substitute values for constants, and get your answer in N
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