California State University, Sacramento                     CE 135 HYDRAULICS LABORATORY

Department of Civil Engineering

PELTON WHEEL TURBINE

REFERENCE:

Daugherty, R. L., and J. B. Franzini, 1977, FLUID MECHANICS WITH ENGINEERING APPLICATIONS. 7th Ed., McGraw Hill Book Co. Chap. 14 and 15

          Internet site:

                     Http:inventors.about.com/library/inventors/bl_lester_pelton.htm

American Society of Civil Engineers, Sacramento Section, 1976, HISTORIC CIVIL ENGINEERING LANDMARKS Of Sacramento and Northern California, p. 29: THE WHEEL THE WON THE WEST. TA 24. C2 A5 (Reference)

US Army Corps of Engineers, 1985, HYDROPOWER, EM 1110-2-1701, Office of Chief of Engineers, Dept. of Army, Washington, D.C.

Turbines Convert Fluid Power to Mechanical Power

Machines that work on fluids are pumps, blowers,
   compressors
Machines on which fluids work are turbines
Much of the same basic theory & similarity parameters work
   for both pumps & turbines
The most comman turbines are reaction and impulse turbines

There are many types of reaction turbines
  Most common in Central Valley are Francis & Kaplin types

Impulse turbines
  The turbine in Hydraulics Lab is a Pelton wheel
      developed in the Sacramento Valley by Lester A. Pelton
      high-velocity jet directed at buckets
      normally used in conditions of low flow and high head

Pelton came to California for the gold rush
     Became a carpenter and millwright
        served his apprenticeship in Knight’s Foundry
Gold miners used water jets to blast the gold deposits from
     the hillsides (placer mining)
Pelton experimented with ways to make the jets that the
     miners used work as turbines
Splash from one blade of turbine striking next blade
     slowed down turbine
Pelton devised a blade to split the flow so it went off the
     side instead bouncing back

Pelton wheel turbine in our lab is basically the same as he
     devised

The Prony Brake

[To measure power that might go to a power network]
Invented in 1821 by French engineer Gaspard Prony
Applies an adjustable load torque to output shaft of a prime mover (e.g. our turbine)
Power output is dissipated as heat in the braking material
Power output = torque * rotation speed,

Efficiency of Turbine = P₀/P_w

        P₀ = Tω = 2πTN/60 in common English units


T = Torque on the shaft (ft-lbf)
ω = angular velocity (rad./sec.)
N = revolutions per minute
P_w = γQh = γQh/550 in common English units
γ = specific weight of water (lbf/ft3)
Q = flow rate (cfs)
h = energy head (ft)

Power transfer from the water to the turbine wheel is a momentum transfer
Depends on the relative velocities between the fluid and the wheel
Too fast, the water velocity is too low for significant momentum transfer
Too slow, shaft speed is so slow that the power output is decreased


Theoretically, the optimum is when speed of bucket is half the speed of water jet
                u = πDN/60
                V = (2gh)^0.5
             φ = u/V is a dimensionless speed factor
        In practice, the maximum efficiency φ just less than 0.5

PELTON WHEEL EXPERIMENTAL PLAN

EQUATIONS INVOLVED

     Basic Equations

        n_S = N*P^0.5/h^1.25 = N(wQh_t/550)^0.5/h_t^1.25

            = (w/550)^0.5 N Q^0.5 / h^0.75

 

        v = (2gh_t)^0.5     u = φv = πDN/60 and η = u/v

     Thus, For Water

        Q = 3.75E-4 (n_S D/φ)² h_t^0.5

        For a Pelton wheel, n_S ranges from about 2 to 8; so use 5

                as a central value

                     φ ranges about 0.43 to 0.48; so use 0.45

        Our Pelton wheel has D = 1 ft, so Q = 0.0463 h_t^0.5

        Optimal efficiency points should be near

For h=	30	40	50	60	feet
Q	0.25	0.30	0.34	0.37	cfs
N	400	436	488	534	rpm

PELTON WHEEL EXPERIMENT

GENERAL APPROACH

     Select a Value For h_t

        Use range of Q & N above & below likely optimum points

 

Note: If pipe at pressure gage is 4 in. diameter, then for

                Q = 0.4 cfs, you have v²/2g = 0.33 ft.

           At this value, we can neglect this for planning the total

                 head for the sample data.

CALCULATIONS DURING THE EXPERIMENT

     Primary objective of calculations is to assure that you have

                the most efficient point included.

        Power: Input P_w = γQ h_t = 62.4 Q h_t

                Output P_o = 2πNT/60 = L F_w N 2π/60

 

        Efficiency: P_o / P_w = k F_w N / Q

                with k = 2π L / 60 γ h_t = 0.002517/h_t