22 OF THE AGGREGATE PRESSURE OF FLUIDS 



Let A B c D represent a vertical section of a mass or collection of 

 quiescent fluid, contained by the walls or embankments indicated by 

 the shaded boundary ; and let A B E F be the horizontal surface of the 

 fluid, with which one side of the immersed rectangle is supposed to be 

 coincident. 



Now, suppose abdc, to be the immersed rectangle, and draw 

 the diagonal b d; then are a b d and bdc 

 the triangles, into which the parallelogram 

 abed is divided by the diagonal b d, and 

 for which the pressures are required to be 

 investigated. 



Draw the diagonal a c, which divide into 

 three equal portions in the points m and n > 

 then are m and n respectively the centres of gravity of the constituent 

 triangles a b d and bdc. 



Through the points m and n, and parallel to a d or b c, the immersed 

 sides of the figure, draw me and nf meeting a b perpendicularly in 

 the points e and/; then, through the points e and /thus determined, 

 and in the plane of the fluid surface, draw er and/s respectively 

 perpendicular to ab; then are the angles mer and nfs equal to 

 one another, and each of them is equal to the angle which the plane 

 of the immersed parallelogram makes with the surface of the fluid. 



From m and n, the centres of gravity of the triangles a b d and 

 b d c, demit the lines m r and n s respectively perpendicular to e r and 

 fs; then are rm and sn the perpendicular depths of the centres of 

 gravity. 



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

 / = ad or be, the immersed or downward length, 

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



triangle abd, 

 S ~ sn, the perpendicular depth of the centre of gravity of the 



triangle bdc, 



D ac or ba, the diagonal of the parallelogram, 

 ty~mer, or nfs, the inclination of the plane to the surface of 



the fluid, 



Pzz the whole pressure on the parallelogram abed, 

 p m the pressure on the triangle abd, 

 ythe pressure on the triangle bdc, 

 and s the specific gravity of the fluid. 



Then, because the parallelogram abed is rectangular, the triangle 



