182 EXAMPLES. 



8. A hemisphere is filled with water. Find the time of 

 emptying it (1) through an orifice in its vertex, and (2) 

 through an orifice in its base. 



A H < m 



-/I /to. I -M 



9. A rectangular orifice is 3 feet wide and 1 feet high, 

 and the lower edge is 2 feet below the level of the water. 

 Find the quantity discharged in 1 second. 



Ans. 43.7 cubic feet. 



10. An orifice in the form of an isosceles triangle, with 

 its vertex in the surface of the water has a base of 1 foot 

 which is horizontal, and an altitude of 6 inches. Find the 

 quantity discharged in 1 second. Ans. 1.135 cubic feet. 



11. If the orifice in Ex. 10 has its vertex downwards and 

 its base 6 inches below the surface of the water, and hori- 

 zontal, find the quantity discharged in 1 second. 



Ans. 1.632 cubic feet. 



12. If a vessel, when filled with,, water to the depth of 4 

 feet, weighs 350 Ibs., and if it be drawn upwards by a weight 

 P of 450 Ibs., as in Fig. 46, find the velocity of efflux 

 through an orifice in the bottom. Ans. 17.02 feet. 



13. If the vessel (Fig. 47), which is filled with water, 

 makes 100 revolutions per minute, and if the orifice is 

 2 feet below the surface of the water at the centre, and at a 

 distance of 3 feet from the axis XX', find the velocity of 

 efflux. Ans. 33.4 feet. 



14. Find the times in which the surface of water con- 

 tained in a vessel, formed by the revolution of the curve 

 y 4 = a*x about the axis of x, will descend through equal 

 distances h, the water issuing through a small orifice in the 

 vertex, and the axis vertical. 



Ans. 



15. Water issues through a small orifice 16^ feet below 

 the surface of the liquid. If the area of the orifice is 0.1 of 



