176 OF THE PRESSURE OF UNMIXABLE FLUIDS OF DIFFERENT DENSITIES. 



The perpendicular pressure upon the horizontal base of a vessel 

 containing any number of fluids of different densities, which do not 

 mix in the vessel : 



Is equal to the area of the base, multiplied by the sum of 

 the products of the specific gravities drawn into the altitudes 

 of the several fluids . 



But the pressure upon the base, will manifestly be the same, if we 

 suppose the vessel to be filled with a fluid of uniform density, arising 

 from the composition of the densities of the several fluids according to 

 their magnitudes ; or if the magnitudes are equal, the uniform density 

 will be a medium between the several given densities. 



180. EXAMPLE. A cylindrical vessel, whose diameter is 6 and alti- 

 tude 24 inches, is filled with mercury, water and olive oil, in the 

 following proportions, viz. mercury 7, water 8, and olive oil 9 inches; 

 what is the pressure on the bottom of the vessel, the specific gravities 

 being 13598, 1000 and 915 respectively? 



Here, by the principles of mensuration, the area of the bottom of 

 the vessel containing the fluids, is 



36 X .7854 28.2744 square inches ; 

 consequently, the pressure produced by the mercury, is 



;? = 28.2744x7X13598 = 2691327.0384, 

 and in like manner, the pressure of the water, is 



p 1 = 28.2744 X8 X 1000 = 226195.2, 

 and lastly, the pressure produced by the oil, is 



p"~ 28.2744x9x915 = 232839.684 ; 



and the sum of these is manifestly the whole pressure ; hence we get 

 P =. 2691327.0384 + 226195.2 + 232839.684 z=z 3150361 .9224. 

 If the pressure as here expressed be divided by 1728, the number 

 of solid inches in a cubic foot, we shall have 



181. Again, suppose the dimensions of the vessel to remain as 

 above, and let it be filled with the same fluids in equal quantities ; 

 that is, 8 inches of mercury, 8 of water, and 8 of olive oil ; what then 

 is the pressure upon the bottom ? 



Here, by proceeding as above, we have for mercury, 

 p = 28.2744 X 8 X 1 3598 = 3075802,3296 ; 



