CHAPTER V. 



OF THE PRESSURE OF NON-ELASTIC OR INCOMPRESSIBLE FLUIDS 

 AGAINST THE INTERIOR SURFACES OF VESSELS HAVING THE 



; FORMS OF TETRAHEDRONS, CYLINDERS, TRUNCATED CONES, 

 &C. 



1. WHEN THE VESSEL IS IN THE FORM OF A TETRAHEDRON. 



PROBLEM XVII. 



108. Suppose a vessel in the form of a tetrahedron, or equi- 

 lateral triangular pyramid, to be filled with an incompressible 

 and non-elastic fluid : 



It is required to compare the pressure on the base with that 

 upon the sides, and also with the weight of the fluid; the base 

 of the vessel being parallel to the horizon. 



Let ABCD be the tetrahedron filled with fluid, of which ABC is the 

 base parallel to the horizon, and ABD, 

 c B D and ADC the sides or equal contain- 

 ing planes. 



From D the vertex of the figure, let fall 

 the perpendicular DP, upon the base or 

 opposite side ABC; then will DP be the 

 vertical depth of the centre of gravity of 

 the base ABC, below the horizontal plane passing through D, the 

 summit of the figure, or highest particle of the fluid. 



Bisect AD and AB, two of the adjacent edges of the figure, in the 

 points m and n\ draw the straight lines BWI and DW, intersecting 

 each other in the point r ; then is r the centre of gravity of the 

 triangular plane ABD. 



Through the point r draw rs perpendicular to DP, the altitude of 

 the vessel or pyramid; then is DS, the perpendicular depth of the 

 centre of gravity of the triangular plane ADB, below the vertex D, or 

 the uppermost particle of the fluid. 



