Friday

November 28, 2014

November 28, 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)

**Answer this Question**

**Related Questions**

Fluid Mechanics - a masonry dam 7m high has a top width of 1.5 metres and bottom...

math - The spring runoff from melting snow from a certain region is being ...

Calculus II - A cone-shaped water reservoir is 20 ft. in diameter and 20 ft. ...

Physics - A hand-pumped water gun is held level at a height of 0.85 m above the ...

Science Physics - The Hoover Dam is 726 ft high. Find the potential energy of 1....

calculus - A reservoir is in the form og the frustum of a cone with upper base ...

physics - In the figure below, the fresh water behind a reservoir dam has depth ...

maths - a dam holds 13.5 megalitres of wate when full. If water flows from the ...

Math PLZ HELP!!!! - A tank that holds 4000 gallons of water will drain ...

Physic - The spout heights in the container in the figure are 15 cm, 30 cm, 45 ...