Hydraulics and Fluid Mechanics in ME
The specific speed of a turbine is the speed of an imaginary turbine, identical with the given turbine, which

Delivers unit discharge under unit speed
Develops unit power under unit speed
Delivers unit discharge under unit head
Develops unit power under unit head

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Hydraulics and Fluid Mechanics in ME
For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal

ratio of inertial force to force due to viscosity
ratio of inertial force to force due to gravitation
ratio of inertial force to force due to surface tension
all the four ratios of inertial force to force due to viscosity, gravitation, surface tension, and elasticity

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