42 HYDRAULICS AND ITS APPLICATIONS 



Ans. : 58,914 Ibs. ; 3,370 Ibs. ; centres of pressure 4 feet ; 1 foot from 

 lower edge. 



Single resultant 50,544 Ibs. at 4*20 feet from lower edge. 



8. A rectangular sluice gate, 5 feet broad and 6 feet deep, having its 

 upper edge at a depth of 4 feet, is inclined at 45 to the vertical and 

 admits water to an empty penstock. The sluice is lifted by a force applied 

 parallel to its plane. Determine the necessary magnitude of this force 

 if the coefficient of friction between gate and guides is '12. 



Ans.: 1,375 Ibs. 



4. A circular conduit, 6 feet diameter, which just runs full, is fitted 

 with a sluice, and it is required to balance this about a horizontal axis. 

 Show that this axis should be placed 2 feet 3 inches above the bottom of 

 the conduit. 



5. A vertical wall, 10 feet high and 3 feet thick, is exposed to water 

 pressure on one side. What is the maximum depth of water in order 

 that the lowest joint should not be anywhere under tension ? Weight of 

 masonry per cubic foot = 170 Ibs. 



Ans. : 6-26 feet. 



6. A battleship weighs 13,000 tons. On filling the ship's boats on one 

 side with water this weighing 60 tons and its mean distance from the 

 centre of the boat being 30 feet the angle of displacement of a plumb 

 line is 2 16' (tan = '0396). Determine the metacentric height for 

 rolling displacements. 



Ans. : 3 feet 6 inches. 



7. Show that a solid cylinder of length I, radius r, and specific gravity s, 

 floating with its axis vertical, is in stable equilibrium if 



r > I \/2s(l s). 



8. A single-riveted steel pipe, 30 inches internal diameter, is exposed to 

 a head of 450 feet of water. Taking /= 12,000 Ibs. per square inch, and 

 the efficiency of the joints = 60 per cent., what should be its thickness? 



Ans. : t = '407 inch = Jf inch. 



9. A cast-iron pressure pipe, 4 inches diameter, is exposed to a pressure 

 of 1,100 Ibs. per square inch. Taking /= 2,800 Ibs. per square inch, 

 what is the requisite thickness ? 



Ans. : t = 1-032 inch = 1^ inch. 



10. The mean pressure over the horizontal section of a dam is 5 tons 

 per square foot. The centre of pressure over this section is at a point 



