CENTRE OF PRESSURE. 23 



V JP dxd y = J J 



J J pdxdy 



ffpy dx dy 



and, similarly, y = p-jr- ~> ( 2 ) 



/ I p dx dy 



the integration extending over the whole of the area con- 

 sidered. 



If polar co-ordinates be used, a similar process will give 

 the equations, 



/ / pr 2 cos 6 dr dB 



t/ / /Q\ 



x = -- , (3) 



/ / pr dr dd 



C fpr* sin 6 dr dB 



y = J 



/ pr dr dO 



If the fluid be homogeneous and incompressible, and if 

 gravity be the only force acting on it, we have [Art. 10, 

 (7)]. 



p = 



where h (= PK) is the depth of the point P below the sur- 

 face of the fluid, K being the projection of P on this sur- 

 face, and KM being perpendicular to EH. Substituting 

 this value of p in (1) and (2), we get 



/ / hx dx dy 



-r-r - -> 



/ / h dx dy 



