The inward flow reaction turbine having radial discharge an outlet is known as Francis Turbine, After the name of J.B.Francis who was an american engineer who in the beginning designed inward radial flow reaction type of turbine.

In modern Francis turbine, the water enters the runner of turbine in the radial direction at outlet and leaves in the axial direction at the inlet of runner.

Hydraulic efficiency will be,

$n_h = \frac{V_{w1 u1}}{gH}$

Important relations for Francis Turbines:

1] The ratio of width of the wheel to its diameter is given as $n = \frac{B_1}{D_1}$

(n = 0.10 to 4.0)

2] The ratio of flow is given as,

$= \frac{vf_1}{\sqrt{2gH}}$ and varies from 0.15 to 0.30

3] The speed ratio,

$= \frac{u_1}{\sqrt{2gH}}$ varies from 0.6 to 0.9