3. Toolbox Reynolds Number Relative roughness Darcy Equation HP Equation
Moody Chart

4. More Toolbox Explicit equation Hazen- Williams Hydraulic radius
HW Coefficient

5. Hazen-Williams
Empirical: equation fitted to data on water at 60oF, pipe diameter >2in., water velocity < 10fps
Water works primary use
V = 1.318CHWRH0.63S0.54 (USCS)
CHW – roughness coefficient
RH – hydraulic radius
S – energy gradient

7. Friction Pipe – Darcy Equation Minor losses Fittings Valves
Special purpose components

8. Minor Losses
Head loss: streamline separation
Loss coefficient

9. Minor Losses Fittings Valves P loss due to change in Direction
Velocity

11. Loss Coefficient

12. Loss Coefficients
K = 0.5
K = .07
For 60o
K = 1.0
K = 0.3

13. Minor losses Equivalent length hf = f (Le/D)(V2/2g)
Wide-open gate valve: K = 10
Wide-open gate valve: Le = 340

14. Minor Losses Inlet/exit Expansion/ contraction Bends/elbows Valves
Globe
Needle
Gate
Ball
Check
Butterfly
Diaphram

15. Loss Coefficient
hL = K V2/2g

16. Type of Component or Fitting
Minor Loss Coefficient - ξ -
Tee, Flanged, Dividing Line Flow
0.2
Tee, Threaded, Dividing Line Flow
0.9
Tee, Flanged, Dividing Branched Flow
1.0
Tee, Threaded , Dividing Branch Flow
2.0
Union, Threaded
0.08
Elbow, Flanged Regular 90o
0.3
Elbow, Threaded Regular 90o
1.5
Elbow, Threaded Regular 45o
0.4
Elbow, Flanged Long Radius 90o
Elbow, Threaded Long Radius 90o
0.7
Elbow, Flanged Long Radius 45o
Return Bend, Flanged 180o
Return Bend, Threaded 180o
Globe Valve, Fully Open 10
Angle Valve, Fully Open 2
Gate Valve, Fully Open
0.15
Gate Valve, 1/4 Closed
0.26
Gate Valve, 1/2 Closed
2.1
Gate Valve, 3/4 Closed 17
Swing Check Valve, Forward Flow
Ball Valve, Fully Open
0.05
Ball Valve, 1/3 Closed
5.5
Ball Valve, 2/3 Closed
200
Diaphragm Valve, Open
2.3
Diaphragm Valve, Half Open
4.3
Diaphragm Valve, 1/4 Open 21
Water meter 7

19. Minor Losses
Equivalent length
LE/D fT

20. Images & examples References
Mechanics of Fluids, 3rd Edition, Potter & Wiggert, Brooks & Cole
Applied Fluid Mechanics, 6th Edition, Mott, Prentice Hall
Engineering Fluid Mechanics, 5th Edition Crowe, & Roberson, Wiley
Fluid Mechanics Cengel & Cimbala McGraw Hill