§ 194. Angle which the Guide-Blades make with the Circumference of the Wheel.—At the moment the water enters the wheel, the radial component of the velocity is ui, and the velocity is vi. Hence, if γ is the angle between the guide-blades and a tangent to the wheel
γ = sin−1 (ui/vi).
This angle can, if necessary, be corrected to allow for the thickness of the guide-blades.
| Fig. 196. |
§ 195. Condition determining the Angle of the Vanes at the Inlet Surface of the Wheel.—The single condition necessary to be satisfied at the inlet surface of the wheel is that the water should enter the wheel without shock. This condition is satisfied if the direction of relative motion of the water and wheel is parallel to the first element of the wheel vanes.
Let A (fig. 196) be a point on the inlet surface of the wheel, and let vi represent in magnitude and direction the velocity of the water entering the wheel, and Vi the velocity of the wheel. Completing the parallelogram, vri is the direction of relative motion. Hence the angle between vri and Vi is the angle θ which the vanes should make with the inlet surface of the wheel.
§ 196. Example of the Method of designing a Turbine. Professor James Thomson’s Inward Flow Turbine.—
| Let H = the available fall after deducting loss of head in pipes and channels from the gross fall; Q = the supply of water in cubic feet per second; and η = the efficiency of the turbine. |
The work done per second is ηGQH, and the horse-power of the turbine is h.p. = ηGQH/550. If η is taken at 0.75, an allowance will be made for the frictional losses in the turbine, the leakage and the friction of the turbine shaft. Then h.p. = 0.085QH.
The velocity of flow through the turbine (uncorrected for the space occupied by the vanes and guide-blades) may be taken