Fluid Force

1. Fluid Pressure (Definition)

   We define the fluid pressure P to be equal to the weight density w times the depth of the fluid h.  

   P = wh

   Pascal's Principal

   The pressure is equal in all directions

   Since Pressure = force/area we have 
   

   F = PA

   
   

2. Force on a Submerged Rectangular Sheet

   Suppose that a glass sheet lies parallel to and five feet below the surface of a lake has dimensions 2 by 3. Then the total pressure on the sheet is

   P = wh = (62.4)(5) = 312

   The total force on the plate is

   PA = (312)(6) = 1872
   

3. Force on a Vertical Surface

   Example :  A 3x2 square window on the new Disney Cruise liner is to be built so that top of the window is four feet below the surface of the water.  What total force will the window be subjected to?  

   Solution:  We take horizontal cross sections.  Letting y be the distance from the top of the window to the cross section, we have

   DF = 62.4(4 + y)(D A) = 62.4(4 + y)(3)(Dy)

   Hence the total force is

   

   In general:  
   

    

   Exercises:

   1. In the VIP suite, the glass window is in the shape of an equilateral triangle with diagonal length 2 such that the top of the triangle is submerged 5 feet below the water.  What total force will this window be subjected to? 

   2. A radius 2 feet circular portal is vertically submerged so that its center is 20 feet below the surface of the water.  Find the total force of the water on the portal.