The head losses in the penstock

By Ahmad Suhendra

The various head losses which occur between reservoir and turbine are as follows:

1. Trashrack (or screen) losses

2. Entrance losses

3. Losses due to pipe friction

4. Bend losses

5. Losses in valve and fittings.

6. Losses in sudden contraction and expansion

Head loss due to installation of a trashrack
ht = [Kt* (t / b) ^ (4 / 3)* (Vo ^ 2 * Sin α)] / (2 * g)
Kt= depends upon the shape of the screen
Vo=Approach velocity (m/s)

Head loss due to entrance
he = Ke * V ^2 / (2 * g)
Ke = depends upon the shape of the intake opening
V = The average velocity of water in penstock
[Permissible velocity in Penstocks,V(m/s) =0.125 (2 g H)^0.5,
Ref : USBR (1961) (P J Bier)]

Head loss due to friction in the penstock
hf = [(10.29* n ^ 2 *Qp ^ 2) / Dp^5.333] *Lp
n = manning's roughness coefficient depends upon the type of pipe

Head loss due to the installation of the bend
hb= Kb * V^2 / (2 * g)
Kb= depends upon the shape of the bend and the condition
of the inside surface
V= The average velocity of water in penstock

Head loss due to Fitting and Valve
hv = Kv *V ^ 2 / (2 * g)
Kv= depends upon the type of fitting and valve
V= The average velocity of water in penstock

Head loss due to sudden contraction and expansion
hc = Kc *V ^ 2 / (2 * g)
Kc= depends upon the type of sudden contraction and expansion
V= The average velocity of water in small pipe(1.273 Q /Dp^2 m/s)

Total Head Loss

h_total = ht + he + hf + hb + hv + hc

Where:

• g = constant of gravity 9.8 m/s^2
• Qp = flow in penstock (m^3/s)
• Dp = inside diameter of penstock (m)
• Lp= lenght of penstock (m)
  
• k = resistance coefficient
  
• t = screen thickness (mm)
• b = width between bars (mm)
• α = angle of inclination from horizontal (deg)

Ref:

1. http://www.iaa.ncku.edu.tw/~aeromems/Mott/ch10.pdf
2. ESHA (European Small Hydropower Association),”Layman’s Handbook on How To Develop a Small Hydro Site,”2nd ed, 1998