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blackstreet23
 one year ago
A cylindrical tank lying on its side is filled with liquid weighing 50lb/ft^3. Find the work required to pump all the liquid to a level 1 ft above the top of the tank.The diameter of the tank is 4 feet.The depth of the tank is 10 feet. NOTE: Please remember the tank is lying on its SIDE, it's NOT upright. A hint my professor gave is that the answer should be a number multiplied by pi. I'm not really sure where my slice goes and how to set up my integral because it's not upright.
blackstreet23
 one year ago
A cylindrical tank lying on its side is filled with liquid weighing 50lb/ft^3. Find the work required to pump all the liquid to a level 1 ft above the top of the tank.The diameter of the tank is 4 feet.The depth of the tank is 10 feet. NOTE: Please remember the tank is lying on its SIDE, it's NOT upright. A hint my professor gave is that the answer should be a number multiplied by pi. I'm not really sure where my slice goes and how to set up my integral because it's not upright.

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blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0I found a picture of it in that website

phi
 one year ago
Best ResponseYou've already chosen the best response.1The work to lift x lbs up y ft is x*y ftlbs Each thin "plate" is lifted from its "y" to y=3 and the distance is 3y the weight of the place is density * volume or in this case 50 lbs/ft^3 * 2*x*10*dy ft^3 and it is lifted 3y feet thus \[ \int_{2}^2 50\cdot 2 \cdot x \cdot 10 \cdot (3y) \ dy \] because we are integrating over y, replace x with the equivalent \[ x= \sqrt{4y^2} \] we have \[ 1000 \int_{2}^2 \sqrt{4y^2}\ (3y) \ dy \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1to integrate that, write it as two separate integrals the first one requires some kind of trig substitution the second is more straightforward.

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0I do not understand how you found the width :s

phi
 one year ago
Best ResponseYou've already chosen the best response.1a cylinder has a circle as its base and (in this case) a height of 10 tip the cylinder on its side, and look at its base (a circle) I put the circle with radius 2 (i.e. diameter/2) at the origin the equation of a circle at the origin is x^2 + y^2 = r^2 follow?

phi
 one year ago
Best ResponseYou've already chosen the best response.1if we solve for x, we get \[ x = \sqrt{4y^2} \] if we take the positive value for the square root, then for a given y , we have found the point on the circle on the right side of the origin, in other words, the distance from the yaxis to the circle on its right side. double that value to get the entire width of the "plate"

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0Thanks a lot !! Sorry I didn't answer before I have been busy.
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