vo2 = √ (vro2 + Vo2 − 2Vovro cos φ)
vi = √ (vri2 + Vo2 − 2Vivri cos θ),
(13)
equations which may be used to determine φ and θ.
| Fig. 195. |
§ 192. Condition determining the Angle of the Vanes at the Outlet Surface of the Wheel.—It has been shown that, when the water leaves the wheel, it should have no tangential velocity, if the efficiency is to be as great as possible; that is, wo = 0. Hence, from (10), cos β = 0, β = 90°, Uo = Vo, and the direction of the water’s motion is normal to the outlet surface of the wheel, radial in radial flow, and axial in axial flow turbines.
Drawing vo or uo radial or axial as the case may be, and Vo tangential to the direction of motion, vro can be found by the parallelogram of velocities. From fig. 195,
tan φ = vo / Vo = uo / Vo;
(14)
but φ is the angle which the wheel vane makes with the outlet surface of the wheel, which is thus determined when the velocity of flow uo and velocity of the wheel Vo are known. When φ is thus determined,
vro = Uo cosec φ = Vo √ (1 + uo2 / Vo2).