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September 22, 2014

September 22, 2014

Posted by **hussain** on Sunday, January 30, 2011 at 10:35pm.

- calculus -
**MathMate**, Sunday, January 30, 2011 at 11:23pmYou will need to set up the expression for the pressure, and then proceed to integrate the expression throughout the height of the door.

We also have to assume that the door is at the*base*of the dam, and that the base of the triangular door is at the bottom of the dam.

We will denote elevation from the bottom of the dam by y, so that the water level is at y=15-3=12m.

The width w of the triangular door is diminishing with h, such that at y=0, w=3, and at y=top of the door h= 3√3/2, w=0.

Thus the width as a function of height is

w(y)=3(h-y)/h (in m) for 0<y<h

The hydrostatic pressure at an elevation y from the bottom is p(y)=ρg(H-y) (in N/m²)

The total hydrostatic force on a horizontal strip of door of height dy is therefore p(y)*w(y)dy

The total hydrostatic force for the whole door

= ∫pressure&dA

= ∫p(y)*w(y)dy for y=0 to h.

I get 425230 N. (to the nearest 10 N)

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