A rectangular channel width = 3 m, slope S = 0.001 S=0.001, and Manning’s roughness n = 0.015 n=0.015. Find the discharge (Q) when water depth is 1.2 m.

 A rectangular channel width = 3 m, slope 

$S = 0.001$, and Manning’s roughness $n = 0.015$. Find the discharge (Q) when water depth is 1.2 m.

Solution:

Step 1: Manning’s equation

$$Q = \frac{1}{n} A R^{2/3} S^{1/2}$$

Where:

• $A = b \cdot h = 3 \cdot 1.2 = 3.6 m²$

• Wetted perimeter $P = b + 2h = 3 + 2(1.2) = 5.4 m$

• Hydraulic radius $R = A / P = 3.6 / 5.4 \approx 0.667 m$

Step 2: Substitute into Manning

$$Q = \frac{1}{0.015} \cdot 3.6 \cdot (0.667)^{2/3} \cdot (0.001)^{1/2}$$

Step 3: Compute

• $R^{2/3} = 0.667^{2/3} \approx 0.763$

• $S^{1/2} = \sqrt{0.001} \approx 0.03162$

$$Q = 66.67 \cdot 3.6 \cdot 0.763 \cdot 0.03162$$ $$Q \approx 5.8 \text{ m³/s}$$

✅ Answer: Discharge = 5.8 m³/s