48 EXAMPLES. 



32. The lighter of two fluids, whose densities are as 2 : 3, 

 rests on the heavier, to a depth of 4 in. A square is im- 

 mersed in a vertical position, with one side in the upper 

 surface. Determine the side of the square in order that the 

 pressures on the portions in the two fluids may be equal. 



Ans. | (l + VTo) in. 



33. Find the centre of pressure of a semi-parabola, the 

 extreme ordinate coinciding with the surface of the fluid. 



[Let LBF (Fig. 20) be the semi-parabola ; let BF = a, 

 and LF = b, and suppose to be the centre of pressure, 

 OG being parallel to LF.] Ans. FG = +a ; GO = ^b. 



34. A quadrant of a circle is just immersed vertically in 

 a liquid, with one edge in the surface, as in Ex. 3, Art. 16. 

 Find the centre of pressure when the density varies as the 

 depth. 



Taking the edge in the surface for the axis of y and the 

 vertical edge for the axis of x, we find 



- _ 32a - _ 16a 



~15^r ; = 157r* 



35. The total breadth of a water passage closed by a pair 

 of flood-gates is 10 ft. and its depth is 6 ft. ; the hinges are 

 placed at one foot from the top and bottom. Find the 

 pressure upon the lower hinge when the water rises to the 

 top of the gates, Ans. 4218 Ibs. 



36. If we suppose everything to be the same as in Ex. 2, 

 Art 20, except that the height of the wall is determined by 

 the condition that the wall just sustain the pressure when 

 the water rises to the top, what is the height of the wall ? 



Ans. 6.96 ft. 



37. A wall of masonry, a section of which is a rectangle, 

 is 10 ft. high, 3 ft. thick, and each cubic foot weighs 100 

 Ibs. Find the greatest height of water it will sustain with- 

 out being overturned. Ans. 



