The total force on the plate is given by
F=w∫abxydy where
x is the length (in m) of the element of area (expressed in terms of y)
y is the depth (in m) of the element of area
w is the density of the liquid (in N m-3)
(for water, this is w = 9800 N m-3)
a is the depth at the top of the area in question (in m)
b is the depth at the bottom of the area in question (in m)
Before we can proceed, we need to find x in terms of y.
Now when x=0,y=3.5, and when x=3,y=5.
So we have: y=mx+b
x=0,y=3.5:b=3.5
x=3,y=5:5=3m+3.5=>m=0.5
y=0.5x+3.5 This gives us
x=2y−7 Hence
F=9800∫3.55(2y−7)ydy=9800[32y3−27y2]53.5==99225 N F=99225 N
Comments
The x ranges from 0 to 3, hence y ranges from 3.5 to 5. The definite integral is taken with respect to y, hence a=3.5, b=5.
how to solve for a and b? please show how. :( thanks
how did you get the value of a and b?
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