Page:Lowell Hydraulic Experiments, 4th edition.djvu/89

	computed; — its several values are given in inches, in column 1;— to compute the value of ${\textstyle O}$ in feet, ${\textstyle R'}$ must be taken in feet.
${\textstyle \omega =}$	the angular velocity. In experiment 30, the velocity of the outside of the wheel was 19.711 feet per second, and the radius of the outside of the wheel is 4.669 feet, consequently, $$\omega ={19.711 \over 4.669}=4.2217.$$
${\textstyle AH=}$	the volume of that part of the space between two adjacent buckets, included between the outside of the wheel and the radius ${\textstyle R'}$; — its several values are given in column 9.
${\textstyle Q''=}$	the quantity of water discharged, per second, by each orifice in the wheel. In experiment 30, we have, by table VI, the total quantity discharged ${\textstyle =112.996}$ cubic feet per second, and as there are forty orifices, we have $${112.996 \over 40}=2.8249.$$

In figure 2, plate IX., the buckets and guides are drawn to a scale one fourth the full size;—the radius of the are $AB=R=56.028$ inches. To find the limit of the stream on the side $BC$, the arcs $IF$, $KH$, etc., $NC$, are drawn with the radii 55 inches, 54 inches, etc., 47.922 inches;— the arcs $EF$, $GH$, etc., $OC$, being taken from column 10, equal to 0.415 feet, 0.796 feet, etc., 2.748 feet; the points $B$, $F$, $H$, etc., $C$, being connected by suitable lines, determine the limit of the stream on that side. The limit of the stream on the other side is found by making the arcs $FL=EI,\ HM=CGK,\ {\text{etc}}.,\ CD=ON$;—the points $A,L,M,\ {\text{etc}}.,\ D$, being connected by suitable lines, determine the limit of the stream on that side.

By an examination of figure 2, it will be seen, that the section of the stream just after it has entered the wheel, is sensibly greater than the section of the stream as it leaves the guides, and that, consequently, if the stream flowed according to the hypothesis, there must have been a sudden change in the velocity of the water, causing a shock, which, according to the common theory, implies a loss of power. This indicates a defect in the design; nevertheless, the success attending this first essay, on a large scale, of a centre-vent water-wheel, in which due regard has been paid to accuracy of construction and perfection of workmanship, guided by such light as the present imperfect theories can afford, ought to encourage us to hope, that, when it has received the same degree of attention as the turbine, it will not be much behind that celebrated motor, in its economical use of water.