Consider a cylindrical tank that has a height of 12 m and a radius of 5 m. Recall that if the tank is full of water12then| 25xpg(15 - y)dy equals the work required to pump all the water out of the tank, through an outflowpipe that is 15 m above the bottom of the tank. Revise this work integral for the following scenario. (Do notevaluate the integrals.)The work required to empty the tank through an outflow pipe at the top of the tank.If D(y) is the distance a horizontal slice must be lifted, what is D(y) when the outflow pipe is at the top of thetank?D(y) =|

Answered: Consider a cylindrical tank that has a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a cylindrical tank that has a height of 12 m and a radius of 5 m. Recall that if the tank is full of water
12
then
| 25xpg(15 - y)dy equals the work required to pump all the water out of the tank, through an outflow
pipe that is 15 m above the bottom of the tank. Revise this work integral for the following scenario. (Do not
evaluate the integrals.)
The work required to empty the tank through an outflow pipe at the top of the tank.
If D(y) is the distance a horizontal slice must be lifted, what is D(y) when the outflow pipe is at the top of the
tank?
D(y) =|

Expert Solution

Step 1Find the weight of slice:

Assume the height from the bottom to the slice is y and the remaining height from slice to above the tank is $15 - y$ and similarly, the remaining height of the tank from slice to top of the tank is (12-y). Calculate the weight of the slice to find the work done of the flow.

$\begin{array}{rcl} w & = & v o l u m e \times ρ g \\ = & (π r^{2} d y) \times ρ g \\ = & π \times 5^{2} \times d y \times ρ g \\ = & 25 π ρ g d y \end{array}$

Here, $ρ$ is the density and g is the acceleration due to gravity.

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