Flow Regimes &Open Channel Hydraulics
Understanding the relationship between Manning's equation, the Froude number, and flow regimes is essential for effective drainage system design.
Manning's Equation
Developed by Irish engineer Robert Manning in 1889, Manning's equation remains the most widely used formula for calculating open channel flow velocity. Its empirical nature makes it practical for engineering applications while maintaining reasonable accuracy across a wide range of conditions.
Velocity Form
V = (1/n) × R2/3 × S1/2
- VMean flow velocity (m/s or ft/s)
- nManning's roughness coefficient (dimensionless)
- RHydraulic radius = A/P (cross-sectional area / wetted perimeter)
- SChannel slope (m/m or ft/ft)
Discharge Form
Q = (1/n) × A × R2/3 × S1/2
The discharge form extends velocity to volumetric flow rate by multiplying by the cross-sectional area (A).
Unit Note: In SI units, the equation is used as shown. For U.S. customary units, multiply by 1.486 to account for unit conversion.
Common Manning's n Values
Smooth Surfaces
- Glass, plastic0.009-0.011
- Finished concrete0.011-0.013
- PVC pipe0.009-0.011
Intermediate
- Unfinished concrete0.014-0.017
- Corrugated metal0.022-0.026
- Cast iron0.012-0.015
Natural Channels
- Clean earth0.018-0.025
- Gravel bottom0.025-0.035
- Heavy vegetation0.050-0.120
The Froude Number
Named after William Froude (1810-1879), the Froude number is a dimensionless parameter that characterizes the ratio of inertial forces to gravitational forces in open channel flow. It serves as the primary criterion for classifying flow regimes.
Fr = V / √(g × D)
Where D is the hydraulic depth (A/T, area divided by top width)
Fr < 1
Subcritical
Fr = 1
Critical
Fr > 1
Supercritical
Understanding Flow Regimes
Subcritical Flow
Fr < 1Characteristics
- Tranquil, slow-moving flow
- Flow depth greater than critical depth
- Gravitational forces dominate inertial forces
- Surface waves can travel upstream
Control & Applications
- Downstream control: Conditions at the outlet determine flow
- Ideal for most drainage applications
- Good sediment transport characteristics
- Stable, predictable behavior
Critical Flow
Fr = 1Characteristics
- Transitional state between regimes
- Minimum specific energy for given discharge
- Maximum discharge for given specific energy
- Wave celerity equals flow velocity
Engineering Significance
- Inherently unstable: Small perturbations cause regime changes
- Used for flow measurement (weirs, flumes)
- Indicates system is at capacity threshold
- Consider upsizing if occurring frequently
Supercritical Flow
Fr > 1Characteristics
- Rapid, shooting flow
- Flow depth less than critical depth
- Inertial forces dominate gravitational forces
- Surface waves cannot travel upstream
Design Considerations
- Upstream control: Inlet conditions govern flow
- High erosion potential - requires protection
- May require energy dissipation structures
- Common on steep slopes or constrictions
The Hydraulic Jump
When flow transitions from supercritical to subcritical, a hydraulic jump occurs. This phenomenon involves a sudden rise in water surface accompanied by significant energy dissipation through turbulence.
The conjugate depth relationship, derived from momentum principles, allows engineers to predict the downstream depth after a hydraulic jump:
y₂/y₁ = ½ × (√(1 + 8Fr₁²) - 1)
Where y₁ is the upstream (supercritical) depth, y₂ is the downstream (subcritical) depth, and Fr₁ is the upstream Froude number.
Energy Loss in Hydraulic Jumps
ΔE = (y₂ - y₁)³ / (4 × y₁ × y₂)
The energy loss increases dramatically with the Froude number. This makes hydraulic jumps useful for:
- Energy dissipation at spillways
- Stilling basin design
- Aeration and mixing
- Flow regime control
Academic References
Primary Texts
Open-Channel Hydraulics
Chow, V.T. (1959). McGraw-Hill.
The definitive reference on open channel flow, covering uniform flow, gradually varied flow, and rapidly varied flow in comprehensive detail.
Open Channel Flow
Henderson, F.M. (1966). Macmillan.
Excellent treatment of theoretical foundations with practical engineering applications.
Open Channel Hydraulics
Sturm, T.W. (2001). McGraw-Hill.
Modern textbook integrating computational methods with classical hydraulics.
Online Resources
FHWA HEC-22: Urban Drainage Design Manual
Federal Highway Administration
Comprehensive guide for urban stormwater drainage system design.
USBR Engineering Monograph No. 25
U.S. Bureau of Reclamation
Hydraulic design of stilling basins and energy dissipators.
Open Channel Flow Resistance
Yen, B.C. (2002). Journal of Hydraulic Engineering.
Comprehensive review of resistance coefficients in open channel flow.
Historical Papers
On the Flow of Water in Open Channels and Pipes
Manning, R. (1891). Transactions, Institution of Civil Engineers of Ireland.
The original paper presenting Manning's equation.
The Theory of Stream Lines
Froude, W. (1868). Transactions INA.
Foundation work on similitude and the dimensionless number bearing his name.
Apply These Concepts
Use our Flow Calculator to analyze flow regimes and hydraulic parameters for your specific channel conditions.