18 



2. OF THE PRESSURE OF FLUIDS THAT ARE NON - ELASTIC UPON 

 RIGHT ANGLED PARALLELOGRAMS CONSIDERED AS INDEPENDENT 

 PLANES IMMERSED IN FLUIDS. 



PROBLEM III. 



33. A right angled parallelogram is immersed in a quiescent 

 fluid, in such a manner, that one of its sides is coincident with 

 the surface, and its plane inclined to the horizon in a given 

 angle : 



It is required to determine the pressure perpendicular to the 



plane, both when it is inclined to the surface of the fluid, and 



when it is perpendicular to it, the nature of the fluid, and 



consequently its specific gravity, being known* 



Let A B c D represent a vertical section of a volume of incompressible 



fluid in a state of equilibrium, of which A B E F is the surface, and 



consequently parallel to the horizon ; let a b c d be a rectangular 



plane immersed in the fluid, in such a manner that the upper side a b 



coincides with the surface, and the plane abed is inclined to the 



horizon in a given angle. 



Draw the diagonal a c, which bisect 

 in m, and through m the centre of gra- 

 vity of the parallelogram, draw mn 

 parallel to ad or be, meeting ab the 

 line of common section perpendicularly 

 in the point n. 



In the horizontal plane A BE F, and 

 through the point n, draw nr also at right angles to ab, and from 

 m the centre of gravity of the immersed plane abed, let fall the 

 perpendicular m r ; then is the angle m n r the inclination of the plane 

 to the horizon, and rm the perpendicular depth of its centre of gravity 

 below the upper surface of the quiescent fluid. 

 Put b = ab, the horizontal breadth of the immersed parallelogram, 

 / zn a d or b c, the immersed length, 

 d-=rm, the perpendicular depth of the centre of gravity, 

 mn r, the inclination of the plane to the horizon, 

 p = the pressure on the plane perpendicularly to its surface, 

 and 5 the specific gravity of the fluid. 



* By the pressure upon any plane or curvilineal surface, is always understood 

 the aggregate of all the pressures upon every point of those surfaces, estimated in 

 directions perpendicular to them at each point, no part heing lost by obliquity of 

 direction. 



