A 3.0 m wide rectangular channel flowing at its normal depth of 0.8 m carries a discharge of 9.5 cumec. The bed slope of the channel is

Concept:

To determine the type of bed slope of a rectangular channel, we need to compare the normal depth (\( y_n \)) with the critical depth (\( y_c \)). The type of slope is categorized based on whether the normal depth is greater than, less than, or equal to the critical depth.

Calculation:

Given:

• Width of the rectangular channel (\( b \)) = 3.0 m
• Normal depth (\( y_n \)) = 0.8 m
• Discharge (\( Q \)) = 9.5 cumec (cubic meters per second)

1. Calculate the Cross-Sectional Area (\( A \)) of Flow:

2. Calculate the Hydraulic Radius (\( R \)):

The hydraulic radius \( R \) is given by:

, where \( P \) is the wetted perimeter.

3. Calculate the Critical Depth (\( y_c \)):

The critical depth for a rectangular channel is calculated using the formula:

4. Determine the Slope Type:

• **Mild Slope**: \( y_n > y_c \)
• **Steep Slope**: \( y_n < y_c \)
• **Critical Slope**: \( y_n = y_c \)

Given:

Since \( y_n < y_c \), the slope of the channel is considered steep.