Open Channel Flow Analysis Tool

Open Channel Flow Analysis Tool - Worksheet

Manning's & Specific Energy Principles

1. Flow Conditions
Calculation Mode
Design Discharge (Q)		m³/s
-+
Water Depth (y)		m
-+
Channel Slope (S)		m/m
-+
Manning's Roughness (n)

2. Channel Geometry
Channel Shape
Bottom Width (B)		m
Bottom Arc Radius (R)		m
Side Slope (z:1 H:V)		-
Shape Factor (c) where T = c·√y		m^0.5
Internal Diameter (D)		m
Berm Elevation (y_b)		m
Berm Width (ea side)		m
Embankment Level		m

* Normal depth (y_n) is the depth of uniform, steady flow where gravity perfectly balances friction. Critical depth (y_c) represents the depth of minimum specific energy.

Hydraulic Properties at Normal Depth
Normal Depth (y_n)	Critical Depth (y_c)	Velocity (V)	Froude No. (F_r)	Specific Energy (E)	Flow Area (A)	Top Width (T)	Wetted Perim (P)
0.00 m	0.00 m	0.00 m/s	0.00	0.00 m	0.00 m²	0.00 m	0.00 m
Flow Regime State		SUBCRITICAL

Channel Cross-Section

Specific Energy Curve (y vs E)

Rating Curve (y vs Q)

Flow Scenario Analysis
Scenario	Discharge (m³/s)	y_n (m)	y_c (m)	Velocity (m/s)	Froude (F_r)	Regime

Theoretical Background

1. Manning's Equation (Steady Uniform Flow):
Calculates Normal Depth (y_n) where gravity balances friction.
Q = (k / n) · A · R^2/3 · S^1/2 (k = 1.0 for Metric, 1.486 for Imperial)
R = A / P (Hydraulic Radius)
2. Froude Number & Critical Depth (y_c):
Critical depth occurs when specific energy is minimized and F_r = 1.0.
F_r = V / √(g · D_m)
D_m = A / T (Hydraulic Depth)
3. Specific Energy (E):
The total energy head relative to the channel bottom.
E = y + V² / 2g
4. Geometric Properties (Area A, Perimeter P, Top Width T):

Rectangular:
A = B · y P = B + 2y T = B

Triangular:
A = z · y² P = 2y · √(1 + z²) T = 2z · y

Trapezoidal:
A = B·y + z·y² P = B + 2y · √(1 + z²) T = B + 2z·y

Circular (Partial Full):
θ = 2·arccos(1 - 2y/D) A = (D²/8)·(θ - sin(θ)) P = (D/2)·θ T = D·sin(θ/2)

Parabolic:
T = c · √y A = (2/3) · T · y P ≈ T + 8y² / (3T)

Round-Bottom Trapezoidal:
y_t = R(1 - cosθ), θ = atan(1/z) if y ≤ y_t: Circular segment if y > y_t: A = A_t + T_t(y-y_t) + z(y-y_t)²

Compound Berm (for y > y_b):
A = A_base + (T_base+2W_b)·(y-y_b) + z·(y-y_b)² P = P_base + 2W_b + 2(y-y_b)·√(1+z²) T = T_base + 2W_b + 2z·(y-y_b)

5. Reference Design Guidelines:

Typical Manning's n

Plastic / Glass	0.010
Concrete (Finished)	0.012
Brickwork / Masonry	0.015
Earth (Clean, straight)	0.020
Earth (Winding, weedy)	0.025 - 0.035
Gravel / Cobble bed	0.030 - 0.040
Natural Stream (Clean)	0.030
Stream (Heavy Brush)	0.070 - 0.100

Max Permissible Velocity (V)

Material	m/s	ft/s
Fine Sand	0.45	1.5
Sandy Loam	0.50	1.7
Silt Loam	0.60	2.0
Firm Clay / Loam	0.75	2.5
Gravel / Cobbles	1.50	5.0
Soft Shale / Rock	1.80	6.0
Concrete / Asphalt	3.0+	10.0+

Typical Longitudinal Slopes (S)

Large Unlined	0.0001 - 0.0003
Small Unlined	0.0002 - 0.0005
Lined Canals	0.0005 - 0.002+

Minimum Velocity (Non-silting)

Prevent siltation	0.6 - 0.9 m/s
Prevent weed growth	≥ 0.75 m/s
Design Dilemma: If Min Velocity > Max Permissible, unlined earth is not viable. Solution: Line the channel to safely increase max limits.

Recommended Side Slopes (z:1)

Material	z (Horizontal)
Hard Rock (Intact)	0.25 - 0.50
Concrete Lined	1.00 - 1.50
Stiff Clay / Peat	1.00 - 1.50
Firm Earth / Loam	1.50 - 2.00
Loose Sandy Soil	2.00 - 3.00
Porous Sand / Gravel	3.00 - 4.00

Minimum Freeboard Guidelines

Condition / Flow	Metric (m)	Imperial (ft)
Unlined Earth Canals
Q < 0.5 m³/s	0.30	1.0
Q = 0.5 - 3.0 m³/s	0.45	1.5
Q > 3.0 m³/s	0.60+	2.0+
Lined Canals
Small / Shallow	0.15 - 0.30	0.5 - 1.0
Large / Deep	0.30 - 0.60	1.0 - 2.0
USBR Rule: Freeboard ≈ √(c · y) or 5-30% of y