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Pelton Impulse Water Turbine Design Formulas

Pump Engineering and Design
Machine Design and Engineering
Hydraulics and Pneumatics

Pelton Impulse Water Turbine Design Formulas

This is a water turbine in which the pressure energy of the water is converted wholly to kinetic energy in one or more jets which impinge on buckets disposed around the periphery of a wheel. The jet is almost completely reversed in direction by the buckets and a high efficiency is attained. Formulae are given for the optimum pipe size to give maximum power, and for the jet size for maximum power (one jet).

Pelton Wheel with Drop
Pelton Wheel with Drop

Pelton Water Turbine Forces
Pelton Water Turbine Forces

Symbols used:
θ = bucket angle
H = available head
Htot = total head
Hf = friction head
D = mean diameter of bucket wheel
Dp = pipe diameter
d = jet diameter
ρ = water density
g = gravity
f = pipe friction factor
L=length of pipe
ηh = hydraulic efficiency
ηm = maximum efficiency at ( r = 0.5 )
N = wheel speed
Cv =jet velocity coefficient
Q = flow through jet
U = mean bucket speed
V = jet velocity
Vp = pipe velocity
ηo = overall efficiency


Available head H = (Htot - Hf)
Shaft power P = pgHηo
Jet velocity V = Cv (2gH)0.5
Mean bucket speed U = πDN
Flow through jet Q = πd2V/4
Hydraulic efficiency ηh = 2r (1 - r) (1 + k cosθ)
where: r = U/V, θ = bucket angle (4-7°)
k = friction coefficient (about 0.9)

Maximum efficiency (at r = 0.5):
ηm(max) = ( 1 + k cosθ ) / 2

Overall efficiency
ηo = ηhηm

Maximum power when: Hf = Htot / 3 = ( 4fLVp2 ) / ( 2gFp )

Optimum size of supply pipe
Dp = [ ( f L Q2 ) / Htot ] 1/5 Approximately

Jet size for maximum power d = [ Dp5 / ( 8 F L )]1/4

Pelton Turbine Angular Forces and wheel speed
Pelton Turbine Angular Forces and wheel speed

Reference:

Mechanical Engineering Data Book, Butterworth Heinemann, Carvill, James 2003

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