CENTRE OF PRESSURE. 



urcs upon it be applied, this force would keep the surface 

 at rest. 



In the case of a liquid, it is clear that the centre of press- 

 ure of a horizontal area, the pressure on every point of 

 which is the same, is its centre of gravity ; and since the 

 pressure varies as the depth (Art. 10). the centre of pressure 

 of any plane area, not horizontal, 

 is below its centre of gravity. 



Let ABCD be any immersed 

 plane area ; take the rectangular 

 axes OX and OY, in the plane 

 of the area. Let (x, y) be any 

 point P, of the area referred to 

 these axes, and p the pressure at 

 this point, and let EH be the line 

 of intersection of the plane with 

 the surface of the fluid. Fig. 10 



Then the pressure on the element of area 



= p dx dy ; 



.'. the resultant pressure = / / p dx dy. 



Let (x, y} be the centre of pressure; then the moment of 

 the resultant pressure about OY 



xjjpdxdy\ 



and the sum of the moments of the pressures on all the ele- 

 ments of area about OY 



= ffpxdxdy. 



Therefore, since the moment of the resultant pressure is 

 equal to the sum of the moments of the component press- 

 ures (Anal. Mechs., Art. 59), we have 



