EXAMPLES. 



, , a 

 pa = P; 



and the depth of the centre of gravity of the lower half 

 below the upper surface of the equal weight 



1 4 - 4 v p 

 therefore, the pressure on the lower half 



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(Besant's Hydrostatics, p. 37.) 



29. A circle is just immersed vertically in a fluid. Find 

 on which chord, drawn from the lowest 



point, the pressure is the greatest. 



[Let ADBC be the circle with radius a 

 and BC the required chord, which bisect in 

 H, and draw HK perpendicular to AB; 

 /. etc.] Ans. AK = fa. 



30. A semicircle is immersed vertically 

 in a fluid, with its diameter in the upper 



surface; find on which chord, parallel to the surface, the 

 pressure is the greatest, supposing the density of the fluid 

 to increase as the depth. 



[Let LBM (Fig. 20) be the semicircle, and DE the chord 

 on which the pressure is the greatest, and a the radius of 

 the circle. Then if the density were uniform, the pressure 

 would vary as DG x GF (Art. 15) ; but, since the density 

 varies as the depth, the pressure varies as DG x GF 2 ; 

 ' etc.] Ans. FG = oVf 



31. If LBM (Fig. 20) be a parabola, FB = J. the latns 

 rectum = 4, and the other conditions the same as in 

 Ex. 30, find FG, the depth of the chord of greatest pressure 

 below the upper surface. Ans. FG = $b. 



