HYDROSTATICS 437 
237 inches respectively above the floor level, and when the pump is stopped 
these levels have changed to 39-4 inches and 17°4 inches respectively above the 
floor level. A change of 1 inch in the level of the water in the tank corresponds 
to a change of 19°3 lbs, of water in the contents of the tank. The mean gauge 
of the steam in the boiler while the pump is at work is 80 lbs. per 
square inch. Neglecting friction, find the number of ft.-lbs. of work done by 
the feed-pump. , 
5. A tank of the form of a right circular cylinder 7 feet in diameter lies with 
its axis horizontal. Find the total pressure on one end when the tank is full of 
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6. A lock gate is 35 feet wide, and the heights of the water above the bottom 
of the gate on the two sides are 26 and 13 feet respectively. Find the resultant 
pressure and the height, measured from the bottom of the gate, at which it 
acts, the weight of the water per cubic foot being 64 Ibs. [Inst.C.E. ] 
7. The width of a lock is 12 feet, and that of each gate 6} feet. If the 
height of the water be 10 feet inside the lock and 4 feet outside, find the re- 
sultant fluid pressure on each gate, and also the pressure (assumed to be acting 
symmetrically) between the two gates. [Inst.C.E. } 
8. A box in the form of a cube, of internal dimensions 1 foot, has its base 
horizontal, and is half-filled with water. One vertical side is kept in its position 
by four screws only, one at each angular point. Find the tensions in these 
screws due to the water pressure. [Inst.C.E. } 
9. In the vertical side of a tank there is a rectangular opening 2 feet high 
and 1 foot wide, the shorter sides being horizontal. This opening is covered by 
a door held by two bolts placed in the middle of the width, one 13} inches 
aboye and the other 13} inches below the centre of the door. When water 
stands in the tank at a level of 10 feet above the centre of the door, what are 
the tensions in the top and bottom bolts? What would be the best positions 
for the two bolts so that they may be subjected to the same tension, and what 
would then be the tension in each bolt ? 
10. A vertical wall, 2 feet thick and 18 feet high, weighing 124 lbs. per 
cubic foot, supports the pressure of water on one side. How high may the 
water rise without causing the resultant force on the base of the wall to pass 
more than 8 inches from the middle of the wall’s width ? [Inst.C.E.] 
11. An opening in a reservoir dam is closed by a plate 3 feet square, which 
is hinged at the upper horizontal edge ; the plate is inclined at an angle of 60° 
to the horizontal, and its top edge is 12 feet below the surface of the water. If 
this plate is opened by means of a chain attached to the centre of the lower 
e, find the necessary pull in the chain if its line of action makes an angle of 
45° with the plate. The weight of the plate is 400 lbs. [U.L.] 
12. A dock entrance, whose level floor is 24 feet below the water, has a width 
of 62 feet at the water level and 50 feet at the floor, the side walls being built 
with a straight batter. The entrance is closed by a caisson, and on one side of 
the caisson the floor is dry. Calculate the total horizontal pressure upon the 
caisson, and the height of its centre of action above the floor. Take weight of 
water as 64 lbs. per cubic foot. [Inst.C.E.] 
13. A vessel of water is weighed on a parcel spring-balance, the reading of 
which shows that the vessel and water weigh 11 lbs. A 7 Jb. iron weight is 
suspended by a fine wire from the hook of an ordinary spring-balance, and is 
lowered into the water until it is completely immersed. “ Under these conditions 
find (i.) the reading of the spring-balance from which the weight is suspended, 
(ii.) the reading of the parcel spring-balance on which the vessel stands. Give 
the reasons for any change in the readings of the balances. (Specific gravity of 
iron =7°'5.) [Inst.C.E.] 
14. A rectangular wooden barge, without a deck, is 20 feet long, 11 feet 
wide, and 3 feet deep, outside measurements, and the sides, ends, and bottom 
have a uniform thickness of 3 inches. Taking the weight of the wood at 50 lbs. 
per cubic foot, determine the position of the water line when the empty barge 
floats in water weighing 63 lbs. per cubic foot. What load, in tons, will this 
barge carry when the water-line is 2 feet from the bottom ? 
15. If the area of the horizontal section of a ship at the water line is 15,000 
square feet, and the sides are vertical where they cut the water, find the extra 
depth the ship will sink when loaded in fresh water with 750 tons of cargo. 
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