Work and Fluid Force, lifting water out of a triangular prism tankby schlynn Tags: fluid, force, intagration, work 

#1
Feb2011, 05:39 PM

P: 64

1. The problem statement, all variables and given/known data
A vertical cross section of a tank is shown. Assume the tank is 16 feet long and full of water. ([tex]\delta=62.4[/tex], and that the water is to be pumped to a height of 8 feet above the top of the tank. Find the work done in emptying the tank. The tank is a triangular prisim with base=5ft and height=8ft. 2. Relevant equations Not sure that there are any. 3. The attempt at a solution First, I am supposed to find the force of the water. It says to find the width as a function of the height, and the book is unclear how to do this very well. From what I can gather it's the height divided by half the base equals the distance to pump the water divided by W, W being the width. So I solved and got W=[tex]\frac{5}{2}\frac{5}{16}y[/tex]. And then since work is force times height, you just multiply that by the distance it has to be lifted, that's 16y. And that's your integrad, but you have a 16[tex]\delta[/tex] factor too, but you just bring that outside of your integral. After I simply the integrand and anti differentiate I got [tex]40y\frac{15}{4}y^{2}+\frac{5}{48}y^{3}[/tex] evaluated from 0 to 8, again, with the factor of 16[tex]\delta[/tex]. Fundamental theorm it and I got 132787 rounded to the nearest whole number. The answer is wrong, and I'm fairly certain I know how to do all of this except finding the width as a function of the height. The book says it has to do with similar triangles. But I don't get what they are saying. Can someone shed some light on this for me? 



#2
Feb2111, 05:00 AM

HW Helper
P: 3,309

how about using conservation of energy and consider the centre of mass's




#3
Feb2111, 12:09 PM

P: 64

Because this is a calculus 2 class, not a physics class, I don't know how to do it that way. I know how to find the centroid of an area that has uniform density, but that's not how we are supposed to do it.




#4
Feb2111, 07:05 PM

HW Helper
P: 3,309

Work and Fluid Force, lifting water out of a triangular prism tank
ok well i would find w(h)
then infinetsimal vol element dV = w(h).L.dh think of the work dW required to get this infinitesimal element to teh reuired hieght and then integrate over h its all the same thing though 



#5
Feb2111, 09:44 PM

P: 64

That's what I'm having trouble with. I can't find the infitesimal volume, I can't get the width as a function of the height. Could you walk me through it?




#6
Feb2111, 11:46 PM

HW Helper
P: 3,309

changed notation in last post
ok so you know w(0) = 5 w(8) = 0 and as its a triangle, its width will vary linearly in between... so basically you have two points (0,5) and (8,0) find the equation of the line that connects them, and that will be w(h) 


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