20 EXAMPLES. 



expanse of sea outside which will affect the pressure, but the 

 height of the surface of the sea. 



EXAMPLES. 



1. If a cubical vessel be filled with a liquid, find the ratio 

 of the pressures against the bottom and one of its sides. 



The area of the surface pressed, in each case, is the same, 

 but the depth of the centre of gravity of the bottom is twice 

 that of the centre of gravity of the side ; therefore the ratio 



is 2 : 1. 



i 



2. Find the pressure on the internal surface of a sphere 

 when filled with water. 



Let a=. the radius of the sphere; then the area of the 

 surface = 4rr 2 , and the depta of the centre of gravity of 

 the surface below the surface of* the water = a ; therefore, 

 calling the pressure P, we have, from (5), 



p = 



which is three times the weight of the water. 



3. A rectangle is immersed with two opposite sides hori- 

 zontal, the upper one at a depth c, and its plane inclined at 

 an angle to the horizontal. Find the whole pressure on 

 the plane. 



[Let a be the horizontal side, and b the other side.] 



Am. Pressure = gpab (c -f - sin 0). 



4. If a cubical vessel is filled with water, and each edge 

 of the vessel is 10 ft, find the pressure on the bottom and 

 on a side, a cubic foot of water weighing 62 Ibs. 



A j Pressure on bottom = 62500 Ibs. 

 ( Pressure on side = 31250 Ibs. 



5. A rectangular surface, 10 ft. by 5 ft, is immersed in 

 water with its ehort sides horizontal, the upper side being 



