are only a few inches across, and can be used to tap power from mountain streams having flows of a few gallons per minute. Some of these systems use household plumbing fixtures for water delivery. These small units are recommended for use with or more of head, in order to generate significant power levels. Depending on water flow and design, Pelton wheels operate best with heads from , although there is no theoretical limit. Design rules The specific speed parameter is independent of a particular turbine's size. Compared to other turbine designs, the relatively low specific speed of the Pelton wheel, implies that the geometry is inherently a "low gear" design. Thus it is most suitable to being fed by a hydro source with a low ratio of flow to pressure, (meaning relatively low flow and/or relatively high pressure). The specific speed is the main criterion for matching a specific hydro-electric site with the optimal turbine type. It also allows a new turbine design to be scaled from an existing design of known performance. (dimensionless parameter), where: = Frequency of rotation (rpm) = Power (W) = Water head (m) = Density (kg/m3) The formula implies that the Pelton turbine is geared most suitably for applications with relatively high hydraulic head H, due to the 5/4 exponent being greater than unity, and given the characteristically low specific speed of the Pelton. Turbine physics and derivation Energy and initial jet velocity In the ideal (frictionless) case, all of the hydraulic potential energy (Ep = mgh) is converted into kinetic energy (Ek = mv2/2) (see Bernoulli's principle). Equating these two equations and solving for the initial jet velocity (Vi) indicates that the theoretical (maximum) jet velocity is Vi = . For simplicity, assume that all of the velocity vectors are parallel to each other. Defining the velocity of the wheel runner as: (u), then as the jet approaches the runner, the initial jet velocity relative to the runner is: (Vi − u). The initial velocity of jet is Vi Final jet velocity Assuming that the jet velocity is higher than the runner velocity, if the water is not to become backed-up in runner, then due to conservation of mass, the mass entering the runner must equal the mass leaving the runner. The fluid is assumed to be incompressible (an accurate assumption for most liquids). Also, it is assumed that the cross-sectional area of