1. Open Channel Hydraulics
Environmental Hydrology
Lecture 12

2. Winooski Falls, Photo by Jim Westphalen

3. Conditions of flow In space In time
Uniform flow – no change in velocity, width, depth with distance
Non-uniform flow – velocity, width, depth can change (gradually varying, rapidly varying)
In time
Steady flow – no change in flow with time
Unsteady flow – flow changes with time

4. Forces operating on open channels
Driving force: w sinq q w
Resisting force: friction

5. Metrics of flow conditions
Reynolds Number (Re) – ratio of inertial forces to viscous forces
Re = v R u
Re < 500 laminar flow
500 < Re < 2000 transition
Re > 2000 turbulent flow
where:
v = average velocity
R = “characteristic depth” (i.e. hydraulic radius)
u = kinematic viscosity

6. Metrics of flow conditions
Froude Number (Fr) – ratio of inertial forces to gravity forces
Fr = v
√g y
Fr < 1 subcritical flow
Fr = 1 critical flow
Fr > supercritical flow
where:
V = average velocity
g = acceleration due to gravity (9.81m/sec2, 32.2 ft/sec2)
y = flow depth

7. Nash Stream at Whitcomb Peak. Image Source: Cohostrail.org

8. Uniform Open Channel Flow
Continuity equation
Resistance equations
Energy & momentum equations
Connecticut River at East Haddam.
Image Source: Franklin Academy

9. Continuity Inflow 3 A 3 Outflow 1 A’ 2
Section AA’
Image source: Andy Ward
Inflow – Outflow = Change in Storage

10. Continuity Flow or Discharge (Q) = V x A 3 where:
V = average flow velocity at cross section (ft/sec, m/sec)
A = cross sectional area (ft2, m2) 3
Section AA’
Image source: Andy Ward

11. velocity profile in a river
Depth-averaged velocity is above the bed at about 0.4 times the depth

12. “resistance” in the channel
Particle size distribution
Ward & Trimble, Fig 7.3

13. Julius Ludwig Weisbach
Antoine Chezy
( )
Henri Darcy
( )
Henri Emilie Bazin
( )
Robert Manning ( )
Julius Ludwig Weisbach
( )

14. Resistance Manning’s equation where: v = velocity (ft/sec*)
R = wetted cross-sectional area/perimeter (ft*)
S = slope (ft/ft*)
n = Manning’s roughness coefficient
* 1.49 is conversion factor for English units, use 1 if v, R, and S are in SI units

15. Ward & Trimble, Table 7.1

16. Resistance Darcy Weisbach equation where: v = velocity (m/s)
g = gravitational constant (9.81m/s2)
R = wetted cross-sectional area/perimeter (m)
S = slope (m/m)
f = Darcy-Weisbach friction factor

17. Application of resistance equations
Roughness characterization
Discharge estimation
Flood reconstruction
1995 flood in Madison Co., Va.
Image: Craig Kochel

18. Potential and Kinetic Energy in Open Channels
Velocity head
Pressure of fluid column
(P = rgy = gy) y1 y2
Elevation above datum
Total head (H) = Z + P/g + v2/2g
Bernoulli equation

19. Specific Energy Specific energy (E) = y + v2/2g
See also Ward & Trimble, Fig 8.1
Specific energy (E) = y + v2/2g

20. Hydraulic Jump “Meatgrinder” – So. Fork American River
Image source: Greg Pasternack, UC Davis