20 OF THE PRESSURE OF FLUIDS 



and its plane inclined to the horizon in an angle of 68 degrees; 

 required the pressure which it sustains, both in the inclined and the 

 perpendicular position ? 



In this example the area of the parallelogram is 1 8 X 3 == 54 square 

 feet, and the longer side is that which is immersed downwards in the 

 fluid; therefore, according to the rule for the oblique position, the 

 solidity of the column by which the pressure is propagated, becomes 

 3 X 18 2 X s X 1 sin. 68 = 486 X s sin. 68. 



Now, in the case of water, the specific gravity is represented by 

 unity, and by the Trigonometrical Tables, the natural sine of 68 

 degrees, is 0.92718 ; consequently, by substitution, the pressure 

 becomes 



^ = 486x .92718 = 450.60948; 



the pressure here obtained, however, is estimated in cubic feet of 

 water ; but in order to have it expressed in a more appropriate and 

 definite measure, it becomes necessary to compare it with some 

 weight ; now, it has been found by experiment, that the weight of a 

 cubic foot of water is very nearly equal to 62 1 Ibs. avoirdupois; 

 therefore, the absolute pressure upon the plane, is 



p 450.60948 X 62.5 = 28163.0925 Ibs. 



36. Let the dimensions of the plane remain as in the preceding 

 case, which condition is supposed in the example ; then, the pressure 

 on its surface, when perpendicular to the horizon, is 



p 3 x 18 X 18 X 1 X J =486 cubic feet 



of water ; but we have stated above, that the weight of one cubic foot 

 is equal to 62 \ Ibs. ; therefore, we have 



p 486 X 62^ zz 30375 Ibs. ; 



consequently, the pressures on the plane in the two positions, are to one 

 another as the numbers 450.60948 and 486, when expressed in cubic 

 feet of water ; but when expressed in pounds avoirdupois, they are as 

 the numbers 28163.0925 and 30375. 



37. If the longer side of the rectangular parallelogram were coin- 

 cident with the surface of the fluid, while its plane is obliquely inclined 

 to the horizon ; then, the formula for the pressure perpendicular to its 

 surface becomes 



p=. b*ls sin. <f>. (9). 



But if the plane of the parallelogram, instead of being inclined to 

 the horizon, or which is the same thing, to the surface of the fluid, 

 were immersed perpendicularly to it ; then, zz 90, and sin. zz 1 ; 

 hence, the formula for the pressure becomes 



p =*#**. (10). 



