1268

THEORY AND PRACTICE OF ENGINEERING.

Book II.

the fly-wheel. The crank moves more slowly when at these points, and more rapidlyin its other positions, from which there is inequality of motion in the axis.

The Fly-wheel is a necessary part of the machinery, where perfectly steady and uniformmotion is the object: it consists of a large wheel with a heavy rim, usually formed of iron,is attached to the axis on which the crank turns, and revolves along with it ; by itsweight it acts as a drag on the engine, and prevents its motion being too rapid, and theimpetus it acquires from its weight, it carries on the machinery with the usual or graduallydecreasing force, when the proportion of the resistance to the power becomes augmented,and the engine has a tendency to move slowly ; its heavy rim absorbs any surplus forcewhich it acquires, and yields it again when required; it is a reservoir which collects theintermitting currents and sends forth a constant and regular stream.

To proportion the rim of the fly-wheel, multiply *40 times the pressure of the pistonin pounds, by the radius of the crank in feet, and divide this product by the cube ofthe radius of the fly-wheel in feet, and by the number of its revolutions per minute; thisresult will give the area of the rim of the fly-wheel in inches; the number of the horse-power multiplied by 200 will be the greatest pressure on the piston. "When the velocity ofthe fly-wheel exceeds 12 feet at the rim per second, its arms should be of wrought-iron,and a velocity of 33 feet per second at the rim is the extreme velocity that should be givenat any time; with cast-iron rims, the velocity should not exceed 13 feet per second, thatthey may be perfectly safe. The proportions of the fly-wheel are derived from the laws ofrotary motion, and are found by adding the time, the radius corresponding to the angularvelocity of the exterior ring of the wheel; and comparing with the force of gravity to obtainthe co-efficient, it is,

32 P. drt

— , 2 - = nV -

bx*

P here is the mean quantity the moving force varies in its intensity«in excess above theresistance, and t the time in which that variation takes place; r, the velocity, and nr, thegreatest variation of velocity ; d, the leverage the force P acts with ; and r, the radiuscorresponding to the velocity v; and 6, the weight of the fly, acting at the distance x fromthe axis: the weight of the rim being always at the extremity of the radius; x = r t andthe equation becomes,

32 P. dt

When the weight of the rim is great, it acquires a great momentum with little increase ofangular velocity, or it loses a considerable momentum with a small diminution of thatvelocity ; and the greater the angular velocity of the axis of the fly is, the greater will beits equalising power, all other things being equal: variation of velocity is inversely as thevelocity of the rim.

To measure the useful Effect of an Engine. — The most convenient method is by the meansof friction : if the rim of a brake-wheel on the engine shaft of a given diameter, be pressedwith a force exactly equal to the effect of the engine at its working speed, then the frictionbeing ascertained, which this pressure produces, the power of the engine may be found bymultiplying the friction by the velocity of the rubbing surface.

Let A B be a lever, tightened by a friction strap, which passes round the shaft or wheelC ; the lever being stopped at the point D till the friction be equal to the power of theengine when all other work is thrown ^

off; then, while the engine is in b .. - - -- —-- — \

motion, place at E a weight sufficientto retain the lever in its horizontalposition : to obtain the power, mul-tiply the length F C in feet, by theweight placed at E in pounds, thenumber of revolutions per minute

6

Fig 2038.

made by C, and 6*2832 ; the result will he the number of pounds raised in a minute one foothigh, which divided by 33,000 gives the horse-power. Suppose l be the leverage theweight w acts with, r the radius of the wheel or shaft c, the friction f the velocity o,

l w

the revolution of c per minute n; then f v equals the power, and f = —, and v = 6 *2832 r n ;

consequently, vf=6'2832lwn, the power in pounds raised one foot, when / is in feet andw in pounds.

The jyortable Condensing Engine. — The cylinder is supported by a cast-iron frame,and two eccentric wheels on the crank-shaft give motion to the levers by connecting rods:the lever works the cold-water pump by a rod, while the beam, by means of slings, worksthe air and hot-water pumps. On the cross rail is a guide to confine the air-pump rod toa vertical motion : the condenser surrounds the air-pump, and is again surrounded by