A right isosceles triangular plate is vertically submerged below the surface of a fluid of weight density w. The top of the plate is at the surface of the fluid. Find the fluid force on the plate in terms of w.

Question

A right isosceles  triangular plate is vertically submerged below the surface of a fluid of weight density w. The top of the plate is at the surface of the fluid. Find the fluid force on the plate in terms of w.

anonymous · Answer

|dw:1393393976084:dw|

anonymous · Answer

Uhm.... .-.

anonymous · Answer

I think the fluid force is then:
$$F = w \int\limits_{a}^{b} yf(y)~~ dy$$
is this right? :3

anonymous · Answer

Yes? :3 haha /.\

anonymous · Answer

yeah
I'd say this is physics and not math

anonymous · Answer

It's for my math class though xD

anonymous · Answer

ah
calc

anonymous · Answer

I think carrying on from what I payed attention to in class the limits for a and b would be like:
a = 0 , b= 3
and f(y) = y
so:
$$F = w \int\limits_{0}^{3} y(y) ~~dy$$
$$w \int\limits_{0}^{3} y^2~ dy$$
$$w * \left[ \frac{ 1 }{ 3 }y^3 \right]^3_0$$
$$F = 9w$$
?

wolfe8 · Answer

If I'm not going way out there, isn't that formula basically the density times the area? Hmm how did you get f(y)=y?

anonymous · Answer

f(y) = y because it is the length of the horizontal part from the water surface, if that isn't wrong..

anonymous · Answer

the length of the horizontal part is at a depth of y from the water surface* 
sorry getting sleepy >.<

wolfe8 · Answer

http://tutorial.math.lamar.edu/Classes/CalcII/HydrostaticPressure.aspx I think you need to multiply by gravity as well.

anonymous · Answer

The formula involving gravity is for hydrostatic pressure not force xD
F = (w*h)*A is the formula for fluid force..

anonymous · Answer

I'll just call up my friend and ask her what she got xD
 thanks for helping anyways :)

wolfe8 · Answer

Dang that's what I've had in mind all this time. I think it looks right to me.