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(a) Show how to derive the following formula for the work required to pump all the water out of the tank: W = 8pg 5y - y° dy (Note that the water has to be pumped a height of 2m above the top of the tank). (b) Evaluate the integral to find the work required in J. You can leave p and g as constants.

(a) Show how to derive the following formula for the work required to pump all the water out of the tank: W = 8pg 5y - y° dy (Note that the water has to be pumped a height of 2m above the top of the tank). (b) Evaluate the integral to find the work required in J. You can leave p and g as constants.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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2. A triangular tank with the dimensions shown in the diagram below (on the left) is full of water. - 3 m → Zm 2 m 3 m 1 Sm 8 m 8m (a) Show how to derive the following formula for the work required to pump all the water out of the tank: = 8pg - y² dy 5y – (Note that the water has to be pumped a height of 2m above the top of the tank). (b) Evaluate the integral to find the work required in J. You can leave p and g as constants. (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured above on the right). Compute the work needed to pump all of the water out of this tank (again, to a height of 2m above the top). (d) Compare your answers to parts b) and c). Why does it make sense that one requires more work, even though the total volume of water displaced is the same?
Transcribed Image Text:2. A triangular tank with the dimensions shown in the diagram below (on the left) is full of water. - 3 m → Zm 2 m 3 m 1 Sm 8 m 8m (a) Show how to derive the following formula for the work required to pump all the water out of the tank: = 8pg - y² dy 5y – (Note that the water has to be pumped a height of 2m above the top of the tank). (b) Evaluate the integral to find the work required in J. You can leave p and g as constants. (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured above on the right). Compute the work needed to pump all of the water out of this tank (again, to a height of 2m above the top). (d) Compare your answers to parts b) and c). Why does it make sense that one requires more work, even though the total volume of water displaced is the same?
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