v_(ri) = u_i cosec [theta];
or, as this is only a small term, and [theta] is on the average 90°,
we may take, for the present purpose, v_(ri) = u_i nearly.
Inserting these values, and remembering that for an axial flow turbine
V_i = V_o, [h] = 0, and the fall d in the wheel is to be
added,
_ _
| / V_i² / u_o² \ u_i² \ |
v_i = c_v[root] | 2g ( H - ---- ( 1 + ---- ) + ---- - d ) |.
|_ \ 2g \ V_o² / 2g / _|
For an outward flow turbine,
_ _
| / V_i² / u_o² \ u_i² \ |
v_i = c_v[root] | 2g ( H - [h] - ---- ( 1 + ---- ) + ---- ) |.
|_ \ 2g \ V_i² / 2g / _|
For an inward flow turbine,
_ _
| { V_i² / u_o² \ u_i² } |
v_i = c_v[root] | 2g { H - ---- ( 1 + ---- ) + ---- } |.
|_ { 2g \ V_i² / 2g } _|
§ 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 u_i, and the velocity is v_i. Hence, if
[gamma] is the angle between the guide-blades and a tangent to the
wheel
[gamma] = sin^(-1) (u_i/v_i).
This angle can, if necessary, be corrected to allow for the thickness
of the guide-blades.
[Illustration: 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
v_i represent in magnitude and direction the velocity of the water
entering the wheel, and V_i the velocity of the wheel. Completing the
parallelogram, v_(ri) is the direction of relative motion. Hence the
angle between v_(ri) and V_i is the angle [theta] 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._--