1144
THEORY AND PRACTICE OF ENGINEERING.
Book II.
gravitation, impulse, or pressure, which produces motion. Raising a weight to a givenheight in a given time is the measure of power ; the weight raised, multiplied by theheight, gives a product which is the measure of the power that raised it: when velocity isuniform, the space is as the velocity; then the power is proportionate either to the forcemultiplied by the velocity, or the space described ; it is unimportant whether the motionhe quick or slow if it be uniform. The original power is somewhat lessened by thefriction of the machinery and the resistance of the air, which, before the useful effect canbe obtained, must be calculated : from the velocity of the water at the instant it strikes thewheel, the height of head productive of such velocity can be deduced; then, multiplying theweight of water expended in any period of time by the height of the head, we have thepower of the water ; the sum of the weight raised by the action of the water, and thatrequired to overcome the friction and resistance, multiplied by the height to whichthe weight can be raised in a given time, the product will be the effect of the power : theproportion of the two products is that of the proportion of the power to the effect.
To determine the Velocity of the Water striking the Wheel, according to Smeaton -AMien the
wheel of a machine is put in motion by the water without any weight in the scale, sup-posing the number of turns in a minute to be 60, then 60 times the circumference of thewheel will be the space through which the water would have moved in a minute if thewheel were free from friction and resistance; the velocity is, however, greater than this,as considerable deduction must be made for friction : suppose the cord wound round thecylinder in a contrary direction to the usual method, and a weight put into the scale; thisweight will assist the wheel in turning; suppose it to be sufficient to cause the machine toturn without any water somewhat faster than 60 turns a minute, as 63 ; let the water thenbe applied, assisted by the weight, the wheel will now make 64 turns ; hence we may sup-pose that the water exerts some power in giving motion to the wheel; increase the weight,so as to make 64£ turns in a minute without water, and then try it with water as before,and if it make the same number of turns with water as without, it must be evident thatthe wheel makes the same number of turns in a minute as it would do if the wheel had nofriction, the weight being equivalent thereto ; if this were too little, the water would acce-lerate the wheel beyond the weight, and if too great, retard it; thus the water becomes theregulator of the wheel motion of the wheel, and the velocity of its circumference becomesa measure of the velocity of the water.
To find the greatest product, or maximum of effect , the weight which gives the greatestproduct being known, multiply the weight in the scale by the number of turns of thewheel; find what weight in the scale, when the cord is on the contrary side of the cylinder,will cause the wheel to make the same number of turns in one direction without water. Itis evident that the weight will be equal to all the friction and resistance taken together, andconsequently the weight of the scale added to the counterweight will be equal to the weightthat could have been raised if the machine had been without friction or resistance, which,multiplied by the height to which it actually was raised, the product will be the greatesteffect of that power. This method, however, does not give the actual resistance when themaximum power and load are upon the wheel, but only the friction from the weight of theapparatus, when moving at a velocity corresponding to the maximum. The effect wasestimated by Smeaton at considerably less than its true value.
Quantity of Water expended , or its Dynamic Effect on JVheels -The pump was so well
made, that it delivered the same quantity of water at each stroke, whether worked slowlyor quick, the length of the stroke being limited. The sluice by which the water was drawnupon the wheel was stopped at a certain height by a peg; the aperture for the effluentwater was the same, so that the exact quantity of water expended was known ; the sluicebeing drawn to the first hole.
Inches.
The water above the floor of the sluice
-
-
-
- 30
Strokes of the pump in
a minute
-
-
-
- S9£
The head raised by twelve strokes
-
-
-
- 21
Turns in
a Minute.
The wheel raised the empty scale, and made
-
-
- 80
With a counterweight 11 lbs.
8 02.
-
-
- 85
Ditto, tried with water
-
-
-
-
-
- 86
No.
Lbs
02.
Turns in a Min.
Product.
1
4
0
45
180
2
5
0
42
210
3
6
0
36J
217J
4
7
0
33J
236|
5
8
0
30
240;
maximum.
6
9
0
26J
2384
7
10
0
22
220
8
11
0
16*
1814
12
0
ceased working.