Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
The ends of a water trough have the shape of the region bounded by the graphs of y = x2 and y = 4 with x and y both measured in...Question
The ends of a water trough have the shape of the region bounded by the graphs of y = x^2 and y = 4 with x and y both measured in feet. To what depth must the trough be filled with water so that the force exerted by the water on either end of the trough is 779.423 lb? (Density of water is 62.5 lb per cubic foot).
Answers
bee
please help if possible !
questioner
What'd you get?
anon
3.528 feet
Paulie
Let h be the water level
Each small slice of area from one end of parabola to the other end = 2*sqrt(y) dy
Pressure exerting on small slice = density * (h-y) ; h-y is the depth of water from the surface.
So, F = 62.5 integral of (h-y) 2*sqrt(y) dy from 0 to h
F = 125 (2/3*h*y^3/2 - 2/5*y^5/2) from 0 to h
Substitue F with 779.423
h = 3.528 ft.
Each small slice of area from one end of parabola to the other end = 2*sqrt(y) dy
Pressure exerting on small slice = density * (h-y) ; h-y is the depth of water from the surface.
So, F = 62.5 integral of (h-y) 2*sqrt(y) dy from 0 to h
F = 125 (2/3*h*y^3/2 - 2/5*y^5/2) from 0 to h
Substitue F with 779.423
h = 3.528 ft.