EXAMPLES. 25 



action, in order to adjust the dimensions of the latter, so 

 that they may be strong enough to resist this pressure. 

 Examples are furnished us in the construction of reservoirs, 

 in which large quantities of water are collected and retained 

 for purposes of irrigation, the supply of cities and towns, or 

 to drive machinery, and of dykes to protect low districts 

 from being inundated by seas and lakes and rivers in times 

 of freshets. 



EXAMPLBS. 



1. Find the centre of pressure of a rectangle vertically 

 immersed, and having one side parallel to the surface of the 

 fluid, and at a given distance below it. 



Let a and b be the distances of the bottom and top of the 

 rectangle from the surface of the fluid, and d the width ; 

 take the intersection of the plane of the rectangle with the 

 surface of the fluid for the axis of y, and the middle point 

 of this side for the origin, the axis of x bisecting the rectan- 

 gle. Then from (7) we have, 



pa p\d pa 



I J x*dxdy I x*dx 



pa p\d pa 



I I xdxdy I xdx 



- 3 2 _ J2 



COB. If the upper side of the rectangle is in the surface 

 of the fluid, b = 0, and therefore we have 



x = fa, 



or the centre of pressure of a vertical rectangle, one side 

 being in the surface of the fluid, is two-thirds the height of 

 the rectangle below the surface of the fluid. The value of 

 y is evidently zero. 



