Ex. 102.-The mean section of a stream is 5 ft. by 2 ft.; its mean velocity is 35 ft. per minute; there is a fall of 13 ft. on this stream, at which is erected a water-wheel whose modulus is 0·65; determine the horse-power of the wheel. Ans. 5-6 H.-P. Ex. 103.-In how many hours would the wheel in the last example grind 1000 quarters of wheat, it being assumed that each horse-power will grind 1 bushel per hour? Ans. 1428 hours. Ex. 104.-How many quarters of wheat will the same wheel grind in 72 hours? Ans. 50-41 quarters. Ex. 105.-Suppose the wheel in Ex. 102 to have replaced an undershot wheel with flat float boards, whose modulus was 0.25, determine the number of quarters of wheat each wheel will grind in 24 hours. Ans. (1) 6·5. (2)·16·8. Ex. 106.-How many cubic feet of water must be made to descend the fall per minute in Ex. 102, 3, that the wheel may grind at the rate of 3 quarters per hour? Ans. 1749.5. Ex. 107.-Given the stream in Ex. 102, 3, what must be the height of the fall to grind 1 quarters per hour; first, if the modulus of the wheel is 0-40, next, if it is 0.47, and lastly, if it is 0.65 ? Ans. (1) 37.7 ft. (2) 32 ft. (3) 23.2 ft. Ex. 108.—The mean section of a stream is 8 ft. by 1 ft.; its mean velocity is 40 ft. per minute; it has a fall of 17 ft.; it is required to raise water to a height of 300 ft. by means of a water-wheel whose modulus is 0.7; how many cubic feet will it raise per minute? Ans. 13.07 cub. ft. Ex. 109.-To what height would the wheel in the last example raise 2 cubic feet of water per minute? Ans. 1742 ft. Ex. 110.-The mean section of a stream is 13 ft. by 11 ft.: its mean velocity is 2 miles per hour; there is on it a fall of 6 ft. on which is erected a wheel whose modulus is 0.7; this wheel is employed to raise the hammers of a forge, each of which weighs 2 tons, and has a lift of 1 ft.; how many lifts of a hammer will the wheel yield per minute? Ans. 142 nearly. Ex. 111.-In the last example determine the mean depth of the stream if the wheel yields 135 lifts per minute? Ans. 1.43 ft. Ex. 112.-In Ex. 110 how many cubic feet of water must descend the fall per minute to yield 97 lifts of the hammer per minute? Ans. 2483 cub. ft. Ex. 113.-Determine how many quarters of corn the mill in Ex. 110 might be made to grind in six days if it were to work for 13 hours daily? Ans. 281-5 quarters. Ex. 114.-Down a 14 ft. fall 200 cub. ft. of water descend every minute, and turn a wheel whose modulus is 0.6. The wheel lifts water from the bottom of the fall to a height of 54 ft.; how many cubic feet will be thus raised per minute? If the water were raised from the top of the fall to the same point, what would the number of cubic feet then be? Ans. (1) 31.1 cub. ft. [Of course in the second case the number of cubic (2) 34.7 cub. ft. feet of water taken from the top of the fall being x, the number of feet that turn the wheel will be 200-x.] Ex. 115.-Water has to be raised from a mine 120 ft. deep, the whole of the water raised forms a stream with a fall of 30 ft., the machinery by which the water is raised is worked by a steam-engine of 50 horse-power, and an overshot wheel whose modulus is 0.715 turned by the stream; determine the whole number of cubic feet raised per minute? Ans. 267.8 cub. ft. Ex. 116.-In the last example if the ground allowed an exit to be made for the water 30 ft. below the mouth of the shaft (by which of course the fall is entirely lost) what must be the horse-power of the engine to raise per minute the same amount of water as before? Ans. 45-6 H.-P. 16. The work of living agents.-The efficiency of men and animals is estimated in the same manner as that of the inanimate agents already considered, viz. by the number of units of work they are capable of yielding. The number yielded under given circumstances by any particular agent must of course be determined by experiment. The results of experiment on this matter are registered in the tables that follow; they are based on similar tables given in General Morin's Aide-Mémoire. It must be borne in mind that these tables give mean results when the agent works in the best manner. It would be very possible for the agents to work with greater velocities than those assigned, but were this done they would yield a much smaller daily amount of work-compare the work done by a horse walking with that done by a horse trotting. The following table gives the useful effect of men and animals employed in the horizontal transport of burdens. The second and third columns give the useful effect, viz. the product of the weight in lbs. and the distance in feet. The reader must not mistake this for the units of work done by the agent, the agent being employed not in raising the weight, but in overcoming the passive resistances, friction, &c., which depend on the weight indeed, but are only a fraction of it. TABLE IX. USEFUL EFFECT OF AGENTS EMPLOYED IN THE * Exclusive of the weight of the barrow, truck, cart, &c. (Poncelet, Méc. Ind. p. 247.) Ex. 117.-How many men would be required to raise by means of a capstan an anchor weighing 1 ton from a depth of 30 fathoms, in 15 minutes? Ans. 9 nearly. Ex. 118.-In what time would 20 men raise the anchor in the last example? Ans. 6.4 min. Ex. 119.-Through how great a distance would 30 men raise the anchor in Ex. 117 in each minute? Ans. 42 ft. nearly. Ex. 120.-There is a well 150 ft. deep, a labourer raises water from it by a rope and pulley, how many cubic feet of water will he raise in a day? Ans. 60 cub. ft. E 121.-How many cubic feet of water would a steam-engine of 10 horse-power raise from this well in 24 hours? How many labourers would be required to do the same amount of work if they raised the water by wheeland-axles, and how many if they raised it by means of capstans? How many horses would do the same amount of work walking in whim gins? Ans, (1) 50,688 cubic feet. Ex. 122.-In how many minutes could 20 men (2) 380 labourers. (4) 56 horses. working on a capstan raise an anchor weighing 2 tons from a depth of 200 fathoms ? Ans. 85.88 min, |