Hydrostatic Force 

Trapezoidal Dam 

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

Introduction 

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 the 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 

The water behind a trapezoidal dam (with dimensions in feet 25 by 15 by 15 by 15 with the longest edge the uppermost) is 10 feet deep. Find the total hydrostatic force on this structure if water weighs /.  

 

If is measured positive upwards from the bottom of the dam, deduce from Figure 1 that a horizontal strip at depth has area . 

Solution 

 

 

 

Figure 1: View of the trapezoidal dam. 

 

 

 

To deduce that the horizontal strip has area  

 

 

 

observe that  

 

 

which implies 

 

so 

 

 

and 

 

 

The force on the horizontal strip of area is the product of the pressure and so the total force on the dam is given by integral  .  

 

Step	Result
Form the integral representing the total hydrostatic force.    Use the definite integral template in the Expression palette to enter the definite integral needed in the expression for the force.        Evaluate the integral.    Right-click and select Evaluate.	(3.1)

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