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Hydrostatic Force: Submerged Disk

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Hydrostatic Force 

Submerged Disk 

Copyright Maplesoft, a division of Waterloo Maple Inc., 2007 



This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips.  Click on theImage buttons to watch the videos. 

This application is reusable. Modify the problem, then click the !!! button on the toolbar to re-execute the document to solve the new problem. 

Problem Statement 

Under heavy seas, the top of a circular porthole one foot in diameter is submerged under 20 ft of water. If sea water weighs Typesetting:-mrow(Typesetting:-mi(/Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(, find the total force on the port hole.  






Figure 1: View of the submerged porthole. 


From Figure 1, the area of a horizontal strip across the porthole is  




where Typesetting:-mrow(Typesetting:-mi( is 21 feet below the surface of the water.  This strip is at depth  




The hydrostatic force on this strip is  





By integrating Typesetting:-mrow(Typesetting:-mi( over the port hole, form the expression for the total force on the port hole. 


Use the definite integral template in the  Expression palette for the integral needed in the expression for total hydrostatic force.. 




Evaluate the integral. 


Right-click and select Simplifications>Assuming Positive.  




Right-click, Evaluate at a Point.Enter Typesetting:-mrow(Typesetting:-mi( into the field, click Ok.. 




Typesetting:-mrow(Typesetting:-msubsup(Typesetting:-mo(Typesetting:-mrow(Typesetting:-mi(`+`(`-`(`*`(196.3495408, `*`(`^`(r, 3)))), `*`(4123.340358, `*`(`^`(r, 2))))Typesetting:-mrow(Typesetting:-mi(1006.291397 


Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft.