34 EXAMPLES. 



3 (a + ft) 





EXAMPLES. 



1. The total breadth of a flood-gate is 2b feet, and the 

 depth is a feet ; the hinges are placed at d feet from the 

 respective extremities of the gate ; required the pressure 

 upon the lower hinge. 



Let AB represent the height of the gate, 

 D and E the hinges, and C the centre of 

 pressure of the water. The pressure of the 

 water upon each half of the gate = \a?bw ; 

 and since the pressure of the water at C is 

 supported by the hinges D and E, we have, 

 by the equality of moments with respect 

 toD, Fifl ' M 



Pressure on E x DE = Pressure on C x DC ; 



but DE = a 2d, and DC = f a d ; 



.*. Pressure on E (a 2d) = \a*bw (f# d) ; 



atbiv (2a 3d) 



.: Pressure on E = / - ' 

 6 (a 2d) 



2. A brick wall, with rectangular cross-section, 12 ft 

 high and 3 ft. thick, sustains the pressure of water against 

 one of its faces. Find the height to which the water may 

 rise without overthrowing the wall, each cubic foot of the 

 wall weighing 112 Ibs. 



Ans. 8.34 ft., or within 3.66 ft. of the top of the wall. 



3. A brick wall, whose cross-section is a right-angled tri- 

 angle, weighs 120 Ibs. per cubic foot, and sustains the 

 pressure of water against its vertical face ; its height is 



