Trapezoidal Channel Conveyance Calculation

This problem requires finding the conveyance factor ($K$) for a trapezoidal channel. Given the specific discharge ($Q$) and the bed slope ($S$), we can directly calculate the conveyance factor associated with this flow condition. The bottom width, side slope, and Manning's roughness coefficient are implicitly accounted for in the given discharge value for the specified slope.

Conveyance Formula for Uniform Flow

The relationship between discharge ($Q$), conveyance factor ($K$), and uniform flow bed slope ($S$) is given by:

$Q = K \sqrt{S}$

To find the conveyance ($K$), we rearrange the formula:

$K = \frac{Q}{\sqrt{S}}$

Given Parameters

• Discharge, $Q = 5\text{ m}^3\text{.s}^{-1}$
• Bed Slope, $S = 1\% = 0.01$

Calculation Steps

1. Calculate the square root of the bed slope:

   $\sqrt{S} = \sqrt{0.01} = 0.1$

2. Substitute the values of $Q$ and $\sqrt{S}$ into the conveyance formula:

   $K = \frac{5\text{ m}^3\text{.s}^{-1}}{0.1}$

3. Compute the final value for conveyance ($K$):

   $K = 50\text{ m}^3\text{.s}^{-1}$

Result

The calculated conveyance of the channel is $50\text{ m}^3\text{.s}^{-1}$. This matches Option D.