Page:EB1911 - Volume 14.djvu/113

TURBINES]
101
HYDRAULICS

inward, and B with outward flow turbines. In A the' wheel vanes are fixed on each side of a centre plate keyed on the turbine shaft. The vanes are limited by slightly-coned annular cover plates. In B the vanes are fixed on one side of a disk, keyed on the shaft, and limited by a cover plate parallel to the disk. Parallel flow or axial flow turbines have the wheel as in C. The vanes are limited by two concentric cylinders. Theory of Reaction Turbines. § 190. Velocity of Whirl and Velocity of Flow.-Let acb (fig. 193) be the path of the particles of water in a turbine wheel. That path will be in a plane normal to the f axis of rotation in c radial flow turbines, and on a cylindrical n, surface in axial flow turbines. At any lb point c of the path

```I the water will have
```

" some velocity 11, in

```' ' the direction of a
```

- tangent to the path. v' That velocity may be resolved into two components, a whirling velocity w in the direction of the wheel's rotation at the point c, and a component u at right angles to this, radial in radial flow, and parallel to the axis in axial ow turbines. This second component is termed the velocity of flow. Let v., , wo, u., be the velocity of the water, the whirling velocity and velocity of flow at the outlet surface of the wheel, and vt, wg, vt the same quantities at the inlet surface of the wheel. Let a and B be the angles which the water's direction of motion makes with the direction of motion of the wheel at those surfaces. Then /Q, 1 I Fio. 193. w., =v, , cos;8; u., =v., sin B (lo) wi=v;coso.: ui=v; sin a The velocities of flow are easily ascertained independently from the dimensions of the wheel. The velocities of flow at the inlet and outlet surfaces of the wheel are normal to those surfaces. Let \$20, Q; be the areas of the outlet and inlet surfaces of the wheel, and Q the volume of water passing through the wheel per second; then vo =Q/Sb; vi =Q/91. (I I) Using the notation in fig. 191, we have, for an inward flow turbine (neglecting the space occupied by the vanes), Q., =21l'fpdo§ fl; =21l'fidi~ (120) Similarly, for an outward flow turbine, SZ., =21rr., d; SZ; ==2-zrrgd; (1211) and, for an axial flow turbine, Q.. = Qt = 1¥'(7'z2-7't2l- (120) Relative and Common Velocity of the Water and Wheel.-There is another way of resolving the velocity of th€ Waféf- LU be U10 Then the velocity of the water maype resolved into a component V, which the water has V, » in common with the C wheel, and a component of, which is the velocity of the water relatively If (Xw to the wheel. velocity of the wheel at the point c, fig. 194.