Pelton wheel 3.0 m diameter operates under the following conditions: N...
Pelton Wheel Performance Analysis
Given Data
- Net available head, H = 300 m
- Rotational speed, N = 400 r.p.m.
- Co-efficient of velocity = 0.98
- Blade friction coefficient = 0.95
- Blade angle = 165o
- Diameter of the jet, d = 25 cm
- Mechanical Efficiency = 90%
Inlet and Outlet Velocity Diagrams
The inlet and outlet velocity diagrams for Pelton Wheel can be drawn as follows:
- Inlet Velocity Diagram: The absolute velocity of the jet is V and the blade velocity is U. The angle between the jet and blade is α. The relative velocity of the jet is W.
- Outlet Velocity Diagram: The absolute velocity of the jet is V' and the blade velocity is U'. The angle between the jet and blade is β. The relative velocity of the jet is W'.
Power Developed
The power developed by Pelton Wheel can be determined using the following formula:
Power developed = (mass flow rate) x (head)
The mass flow rate can be determined using the following formula:
mass flow rate = (π/4) x d^2 x V x ρ
Where, ρ is the density of water.
The head can be determined using the following formula:
head = (V^2 - V'^2)/(2g)
Where, g is the acceleration due to gravity.
Using the given data, we can determine the power developed by Pelton Wheel.
Hydraulic Efficiency
The hydraulic efficiency of Pelton Wheel can be determined using the following formula:
Hydraulic efficiency = (Power developed)/(Power supplied)
The power supplied can be determined using the following formula:
Power supplied = (mass flow rate) x (head + losses) x g
Where, losses include frictional losses and losses due to leakage.
Using the given data, we can determine the hydraulic efficiency of Pelton Wheel.
Specific Speed
The specific speed of Pelton Wheel can be determined using the following formula:
Specific speed = (N√Q)/(H^0.75)
Where, Q is the flow rate in m^3/s.
The dimensional specific speed can be converted to non-dimensional specific speed by dividing it by (gH)^(1/2).
Using the given data, we can determine the dimensional and non-dimensional specific speed of Pelton Wheel.