(14a)
Correction of the Angle φ to allow for Thickness of Vanes.—In determining φ, it is most convenient to calculate its value approximately at first, from a value of uo obtained by neglecting the thickness of the vanes. As, however, this angle is the most important angle in the turbine, the value should be afterwards corrected to allow for the vane thickness.
Let
φ′ = tan−1 (uo / Vo) = tan−1 (Q / ΩoVo)
be the first or approximate value of φ, and let t be the thickness, and n the number of wheel vanes which reach the outlet surface of the wheel. As the vanes cut the outlet surface approximately at the angle φ′, their width measured on that surface is t cosec φ′. Hence the space occupied by the vanes on the outlet surface is
| For A, fig. 192, ntdo cosec φ B, fig. 192, ntd cosec φ C, fig. 192, nt (r2 − r1) cosec φ. |
(15)
Call this area occupied by the vanes ω. Then the true value of the clear discharging outlet of the wheel is Ωo − ω, and the true value of uo is Q/(Ωo − ω). The corrected value of the angle of the vanes will be
φ = tan [Q / Vo (Ωo − ω) ].
(16)