**Related Resources: hydraulic**

### Pelton Impluse 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 Water Turbine Forces

Symbols used:

θ = bucket angle

H = available head

H_{tot} = total head

H_{f} = friction head

D = mean diameter of bucket wheel

D_{p} = pipe diameter

d = jet diameter

ρ = water density

g = gravity

*f* = pipe friction factor

L=length of pipe

η_{h} = hydraulic efficiency

η_{m} = maximum efficiency at ( r = 0.5 )

N = wheel speed

C_{v} =jet velocity coefficient

Q = flow through jet

U = mean bucket speed

V = jet velocity

V_{p} = pipe velocity

η_{o} = overall efficiency

Available head H = (H_{tot} - H_{f})

Shaft power P = pgHη_{o}

Jet velocity V = C_{v} (2gH)^{0.5}

Mean bucket speed U = πDN

Flow through jet Q = πd^{2}V/4

Hydraulic efficiency η_{h} = 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):

η_{m}(max) = ( 1 + k cosθ ) / 2

Overall efficiency

η_{o} = η_{h}η_{m}

Maximum power when: H_{f} = H_{tot} / 3 = ( 4fLV_{p}^{2} ) / ( 2gF_{p} )

Optimum size of supply pipe

D_{p} = [ ( f L Q^{2} ) / H_{tot} ] ^{1/5} Approximately

Jet size for maximum power d = [ D_{p}^{5} / ( 8 F L )]^{1/4}

Pelton Turbine Angular Forces and wheel speed

Reference:

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

Related:

- Pelton Wheel Review
- Centrifugal Pump Cavitation Review
- Preventing Cavitation Centrifugal Pump
- Cavitation Review Centrifugal Pump
- Centrifugal Pump - Net Positive Suction Head

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