PRESSURE UPON BOTH SIDES OF A SURFACE. 33 



or, more 



simply, h = \ (a + b) ~ + d L, (5) 



IV i 



and the dam will move or not according as 

 h >or 



COR. If the embankment is rectangular, <7 = and 

 b = a, and (5) becomes 



h = 2a -^ //. 

 w, 



20. Pressure upon Both Sides of a Surface. If 



a plane surface is subjected on both sides to the pressure of 

 a fluid, the two resultants of the pressures on the two sides 

 have a new resultant, which, as they act in opposite direc- 

 tions, is obtained by subtracting one from the other. 



Let AB be a flood-gate with the 

 water pressing on both sides of it, to 

 determine the resultant pressure, and 

 the centre of pressure. Let AB = a, 

 the depth of the water on one side ; 

 DB = b, the depth of the water on 

 the other side ; P = the resulting 

 pressure on the gate ; and w t = the 

 weight of a cubic foot of water. Then ///7 lFig.' 



P = pressure on AB pressure on DB ; 



... P = t(a-P) Wl . (1) 



Now let and C t be the centres of pressure of the sur- 

 faces AB and DB, and C 2 the point to which the resultant 

 pressure P, is applied. Then, taking moments with respect 

 to A, and putting AC g = z, we have 



P x z = pressure on AB x AC pressure on DB x AC, 

 x \a ^w^ (a $b). 



