24 CENTRE OF PRESSURE. 



f f/iy dx dy 



y = ^r- -, (6) 



I I h dxdy 



If we take for the axis of y the line of intersection EH, 

 of the plane with the surface of the fluid, and denote the 

 inclination of the plane to the horizon by 0, we have 



PK = PM sin PMK, 

 or, h = x sin 6 ; 



which in (5) and (6) give us, 



f fx* dx dy 



-T- -. 



/ I x dxdy 

 f fxy dx dy 



-rr- - 



/ I x dxdy 



(8) 



COB. 1. If the axis of x be taken so that it will be sym- 

 metrical with respect to the immersed plane, the pressures 

 on opposite sides of this axis will obviously be equal, and 

 the centre of pressure will be on this axis, or y = 0. 



COE. 2. Since (7) and (8) are independent of it ap- 

 pears that the centre of pressure is independent of the incli- 

 nation of the plane to the horizon, so that if a plane area be 

 immersed in a fluid, and then turned about its line of inter- 

 section with the surface of the fluid as a fixed axis, the 

 centre of pressure will remain unchanged. 



REM. The position of the centre of pressure is of great 

 importance in practical problems. It is often necessary to 

 know the exact effect of the pressure exerted by fluids 

 against the sides of vessels and obstacles exposed to their 



