Experiment: Determination of Manning’s Coefficient for Different Surfaces
Objective
To determine the Manning’s coefficient of the flume or bed of the channel with the flow of water and investigate the roughness of the bed as required for design purposes.
Scope
Using the Manning’s formula, we can investigate the roughness coefficient of different beds of the flume and the roughness of river beds. This helps in understanding the roughness when constructing open channels in the field as designed.
Apparatus Required
- Long length flume (~7-10 meters)
- Needle gauge
- Orifice meter
- Types of beds (smooth, rough, gravel)
- Measuring scale
Theory
The velocity of flow is given by Manning’s equation:
\[ V = \frac{1}{n} R^{2/3} S^{1/2} \]
Where:
- \( V \): Velocity of flow
- \( R \): Hydraulic radius
- \( S \): Bed slope
- \( n \): Manning’s roughness coefficient
Hydraulic radius:
\[ R = \frac{A}{P} \]
Wetted area:
\[ A = b \cdot d \]
Wetted perimeter:
\[ P = b + 2d \]
Discharge:
\[ Q = A \cdot V \]
Discharge through orifice:
\[ Q = C_d \cdot A \cdot \sqrt{2gh} \]
Procedure
- The pump was started, and water was allowed to flow through the flume at a certain head difference.
- The head difference and the wetted depth were observed and recorded.
- The flow of water and the depth were varied for subsequent observations.
- The procedure was repeated, and multiple readings were taken.
Observation Table
| No. of Observation |
Width of Flume (b) [mm] |
Depth of Flow (d) [mm] |
Bed Slope (S) |
Orificemeter Pressure Head Diff. (H) [mm] |
| 1 |
300 |
83 – 64 = 0.019 m |
1:400 |
680 – 590 = 0.07 m |
| 2 |
300 |
96 – 71 = 0.025 m |
1:400 |
685 – 585 = 0.10 m |
| 3 |
300 |
101 – 74 = 0.027 m |
1:400 |
790 – 650 = 0.140 m |
| 4 |
300 |
110 – 80 = 0.030 m |
1:400 |
820 – 650 = 0.17 m |
| 5 |
300 |
111 – 81 = 0.030 m |
1:400 |
890 – 725 = 0.165 m |
Calculation Table
| Discharge Head (H) [m] |
Discharge (Q) [m³/s] |
Area of Flow (A) [m²] |
Wetted Perimeter (P) [m] |
Hydraulic Radius (R = A/P) [m] |
Manning’s Coefficient (n) |
| 0.070 |
2.185 × 10⁻³ |
5.7 × 10⁻³ |
0.338 |
0.0168 |
8.55 × 10⁻³ |
| 0.100 |
2.624 × 10⁻³ |
7.5 × 10⁻³ |
0.350 |
0.0214 |
0.011 |
| 0.140 |
3.050 × 10⁻³ |
8.1 × 10⁻³ |
0.354 |
0.0228 |
0.010 |
| 0.170 |
3.405 × 10⁻³ |
9 × 10⁻³ |
0.360 |
0.0250 |
0.011 |
| 0.165 |
3.365 × 10⁻³ |
9 × 10⁻³ |
0.360 |
0.0250 |
0.011 |
Average Manning’s Coefficient
\[ \bar{n} = \frac{8.55 \times 10^{-3} + 0.011 + 0.010 + 0.011 + 0.011}{5} = 0.0103 \]
Sample Calculation
Given/Observed:
- Head Difference (H): 0.15 m
- Bed Slope (S): \( \frac{1}{400} = 0.0025 \)
- Width of Flume (B): 0.25 m
- Depth of Flow (y): 0.36 m
- Discharge (Q): \( 3.325 \times 10^{-3} \, \text{m}^3/\text{s} \)
Step 1: Area of Flow (A)
\[ A = B \times y = 0.25 \times 0.36 = 0.09 \, \text{m}^2 \]
Step 2: Wetted Perimeter (P)
\[ P = B + 2y = 0.25 + 2 \times 0.36 = 0.97 \, \text{m} \]
Step 3: Hydraulic Radius (R)
\[ R = \frac{A}{P} = \frac{0.09}{0.97} \approx 0.0928 \, \text{m} \]
Step 4: Manning’s Formula
\[ Q = \frac{A \cdot R^{2/3} \cdot S^{1/2}}{n} \]
Rearranged to solve for n:
\[ n = \frac{A \cdot R^{2/3} \cdot S^{1/2}}{Q} \]
Step 5: Substituting Values
\[ n = \frac{0.09 \cdot (0.0928)^{2/3} \cdot (0.0025)^{1/2}}{3.325 \times 10^{-3}} \]
\[ = \frac{0.09 \cdot 0.207 \cdot 0.05}{3.325 \times 10^{-3}} \]
\[ = \frac{0.0009315}{3.325 \times 10^{-3}} \approx 0.28 \]
Result
Based on the experimental data, the Manning’s coefficient (n) was determined for various flow conditions. The values ranged from 0.00855 to 0.011, and the average value of Manning’s coefficient was calculated to be approximately 0.0104.
Discussion and Conclusion
The experiment showed a consistent trend in Manning’s coefficient with increasing discharge and hydraulic radius, indicating that the channel surface offered uniform resistance to flow. Minor variations in the values of n can be attributed to practical limitations such as measurement errors, turbulence, or flow non-uniformities. The average Manning’s coefficient of 0.0104 lies within the typical range for smooth channels, confirming the validity of Manning’s equation in open channel flow analysis.
Understanding and determining the Manning’s coefficient is essential in civil and hydraulic engineering applications, particularly in the design of canals, sewers, drainage systems, and river modeling. It enables engineers to estimate flow rates accurately, optimize cross-sectional designs, and ensure efficient water conveyance in various hydraulic structures.
