Resistance Coefficient K for Sudden Expansion-Contraction

The losses through these fitting are generally evaluated by first obtaining

ß = d2 / d1

Important Note:

the resulting K values as tabled below are based on the flow velocity in the larger pipe,

if the flow velocity in the small pipe is used to evaluate the head loss then the K values tabled below should be multiplied by 

( ß)^4 = (d2 / d1) ^4

Head loss (h):

h_expansion(he) = Ke*(v2)^2 / (2*g)

h_contraction(hc) = Kc*(v2)^2 / (2*g)

v2= Average velocity (m/s) of water in small pipe

g =  Constant of gravity 9.8 m/s^2

Table of Ke & Kc against β = d2 / d1

β	Ke	Kc
0.15	1887.42	965.43
0.2	576	300
0.25	225	120
0.3	102.23	56.17
0.35	51.31	29.24
0.4	27.56	16.41
0.45	15.51	9.72
0.5	9	6
0.55	5.32	3.81
0.6	3.16	2.47
0.65	1.87	1.62
0.7	1.08	1.06
0.75	0.6	0.69
0.8	0.32	0.44
0.85	0.15	0.27
0.9	0.06	0.14
0.95	0.01	0.06
1	0	0

Ref : http://www.roymech.co.uk/Related/Fluids/Fluids_Pipe.html

Trash rack (or screen) losses

By Ahmad Suhendra

A screen is always required at the entrance of a pressure pipe . The function of screen (trash rack) is :

• keep debris away from the entrance to the outlet works where the debris will not clog the critical portions of the structure;
  
• capture debris in such a way that relatively easy removal is possible;

The flow of water through the rack also gives rise to a head loss. Though usually small, it can be calculated by a formula due to Kirchmer .

ht = [Kt * (t / b)^(4 / 3) * (Vo ^2 * Sin α )] / (2 * g)

ht = Screen head loss (m)
Kt = Resistance coefficient
t = Bar thickness (mm)
b = Width between bars (mm)
Vo= Approach velocity (m/s)
g = Gravitational constant (9.8 m/s^2)
α = Angle of inclination from horizontal


Ref :
ESHA (European Small Hydropower Association),”Layman’s Handbook on How To Develop a Small Hydro Site,”2nd ed, 1998 http://www.scribd.com/doc/8885765/Layman-Handbook-for-hydro-electric-power-plants

http://www.knoxcounty.org/stormwater/pdfs/vol2/3-3-5%20Trash%20Racks%20and%20Safety%20Grates.pdf

The microhydro plant

By Manfred Mornhinweg (manfred@ludens.cl)

My little paradise has a stream that provides enough water flow and head to run a small turbine, to provide electricity to my home. While writing this, the microhydro plant is being implemented, and here are some photos of the process.

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Walsh River Micro-Hydro Turbine Contruction Guide

Prepared by Max Enfield, December 2007, revised March 2010

These notes are intended as a guide to those wishing the construct a Banki-crossflow turbine like that were previously available and used in the Walsh River Micro-Hydro Systems. The focus of the notes is on construction details, rather than design.

The Walsh River Micro-Hydro System derived its name from the Walsh River in Far North Queensland, where the prototype system was installed. The system concept was developed and prototyped in 1991 by Jerry Jeffress and features the integration of custom made Banki-crossflow turbines, with Baldor DC generators and AERL Hydromax DC:DC step down controllers. It can also be used to pump water, indeed it has been used to pump water and generate electricity simultaneously.

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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

Calculation of flood spillway

By Ahmad Suhendra

Flood spillway was designed based on the excess water and high water in the channel carrier (head race)

Example :

Flood Spillway will be made on a channel that has a water depth of 0.691 m, with a normal discharge (Q normal) of 0.6 m^3/sec. What is the length of Flood spillway?

Spillway length (L spillway) is obtained by using the equation of calculating Weir and must be able to pass through if the flow (Q spillway) in a state of excess but not based on the flood peak.

Dicharge Coefficient (Cd)
Profile of Crest Weir	μ- factor	Cd=2.953 μ
Board, sharp edge	0.49-0.51	1.44 - 1.51
Board, round edge	0.50-0.55	1.48 - 1.62
Round overfall	0.65-0.73	1.92 - 2.16
Sharp edge,	0.64	1.89
Rounded	0.75	2.21
Roof Shaped	0.79	2,33

Standard Weir equations:
Q = Cd * L weir * (h over the top )^1.5
In this case :

• L spillway = L weir
• Q spillway = Q minor flood - Q normal = Cd * L spillway * ( h over the top)^1.5

There are some values of  Discharge Coefficient  (Cd) and in this calculation the value of Cd was taken 1.6 (Board, the round edge)

Then :

• L spillway = (Q minor flood – Q normal) / (Cd * ( h over the top)^1.5 )

To increase the water on the head race taken a number of around 20% of normal conditions and is considered as a minor flood (small flood).

• Q minor flood = 1.2 * 0.6 = 0.72 m^3/sec
• h minor flood = 1.2 * h = 1.2 x 0.691 = 0.829 m
• h over the top = 0.829 - 0.691 = 0.138 m
• Q spillway = 0.72 - 0.6 = 0.12 m3/sec
• L spillway = ( 0.12) / (1.6 * 0.138 ^1.5) = 1.46 m

Loss coefficients for pipe bends are commonly used in MHP

The losses in figure as shown left , vary according to the R/D ratio and the deflection angle of the bend. An R/D ratio of six results in the lowest head loss, although only a slight decrease is indicated for R/D ratios greater than four. As the fabrication cost of a bend increases with increasing radius and length, there appears to be no economic advantage in using R/D ratios greater than five.

Ref:
BURIED STEEL PENSTOCKS SECOND EDITION 1998
Published by Construction Marketing Committee, AMERICAN IRON AND STEEL INSTITUTE
In cooperation with and editorial collaboration by STEEL PLATE FABRICATORS ASSOCIATION, INC

Generator Selection

Generators must be sized to handle their load based on the continuous KW, kilowatt load, and KVA, kilovoltamp load, and the worst case starting load KW + KVA. They must be derated for temperature and elevation. They are sized also on whether they are continuous or standby use. The following steps are used to obtain information:

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ref:

• http://www.fs.fed.us/database/acad/elec/greenbook/24_generator_selection.pdf
• http://www.teachnet.ie/torourke/Physicswebsite/electromagnetism.htm