Question 9.4.5: In an inward flow reaction turbine (vertical shaft) the sum ......

Given: Sum of the pressure and kinetic heads at entrance to the spiral casing is 132 m. vertical distance between this section and the tail race level is 3.3 m.

u_1 = 33  C_{f1} = C_{f2} = 11  C_{w2} = 0 (i.e. discharge is radial)

Losses between turbine entrance and discharge from guide vanes = 4.95 m, Losses in the runner = 8.8 m         losses in draft tube = 0.88 m
Kinetic energy head rejected to the tail
race = 0.55 m

1. Inlet and outlet velocity diagrams are drawn in Fig. E9.4.5. Since H and u_1 are known, C_{w1} can be obtained by using Euler turbine equation, noting that discharge is radial.
Head utilised by runner, H = C_{w1}  u_1/g = 132 + 3.3 – (4.95 + 8.8 + 0.88 + 0.55) = 120.12

→                              C_{w1} = 35.71

From velocity triangle: \tan  α_1 = C_{f1} /C_{w1} → α_1 = 17.12°

and \tan (180 – β_1) = C_{f1}/ (C_{w1} – u_1)

→                             β_1 = 103.84°

2. Take tail race as datum and apply modified Bernoulli’s equation between entrance to turbine and exit of guide vane, we get from given data: since turbine is horizontal

132+3.3 =C_1^2/2g+p_1/w+z_1+4.95=C_1^2/2g+p_1/w+3.3+4.95,

∴  p_1/w, pressure head at runner inlet = 55.87 m

3. Similarly applying modified Bernoulli’s equation between turbine entrance and runner outlet, we get

132+3.33 =C_2^2/2g+p_2/w+z_2+H+4.95+8.8

But H = 120.12 m (determined above), C2 = Cf2 = 11 and z2 = 3.3
Substitution and simplification gives: pressure head at runner outlet, p_2/w = – 8.04  m

Negative sign shows that pressure is negative and is greater than NPSH, which means there are chances of cavitation.