PRESSURE ON PLANES. 



17 



faces above their common surface are inversely pro- 

 portional to their densities* 



14. Pressure on Planes. To find the pressure on 

 a plane area in the form of a rectangle when it is 

 just immersed in a liquid, with one edge in the 

 surface, and its plane inclined at an angle 6 to the 

 vertical. 



Let ABCD be a vertical section perpendicular to the plane 

 of the rectangle ; then AB is the section of the surface of 

 the liquid, and AC (= a) is the 

 section of the rectangle, the up- 

 per edge b, of the rectangle being 

 in the surface of the liquid per- 

 pendicular to AC at A. 



Pass a vertical plane BC, 

 through the lower edge of the 

 rectangle, and suppose the fluid 

 in ABC to become solid. The weight of this solid is sup- 

 ported by the plane AC, since the pressure on BC is 

 horizontal (Art. 4). Let R be the normal pressure on the 

 plane AC ; resolving R horizontally and vertically, we have, 

 for vertical forces, 





Fig. 9 



R sin 6 = weight of ABC 



[(5) of Art. 10] 



cos 



R gpab-^a cos 0; 



(1) 



that is, the pressure on the rectangle is equal to the 

 weight of a column of fluid whose base is the rec- 



* The common barometer may be considered _as an example of this principle. 

 The air and mercury are the two fluids. If the atmosphere had the same density 

 throughout as at the surface of the earth, its height could be determined. For 

 height of mercury in barometer : height of air : : density of air : density of mer- 

 cury. As mercury is 10784 times as dense as air, the height of the atmosphere 

 would be 10784 x 30 inches, or nearly 5 miles. 



