Calculating Fluid Force on Circular Plate in Water Tank

[kari82]

Find the fluid force on the circular plate shown in figure (see attachment). Assume the plates are in the wall of a tank filled with water and the measurements are given in feet.

F=w∫h(y)L(y) dy

I have that h(y)= 7-y and L(y)=2√(4-y^2). Therefore, F=2(62.4)∫(7-y)√(4-y^2) dy from y=0 to y=4. Can someone please help me find the integrate of this equation. Thanks!

 

[tiny-tim]

hi kari82!

(try using the X² icon just above the Reply box )

… Therefore, F=2(62.4)∫(7-y)√(4-y^2) dy from y=0 to y=4. Can someone please help me find the integrate of this equation. Thanks!

you have ∫ (7 - y)√(4 - y²) dy, so just split it up …

∫ 7√(4 - y²) dy can be solved by a trig substitution, and

∫ y√(4 - y²) dy is obvious!