Conveyance Calculation Using Discharge and Slope

This problem requires calculating the channel conveyance based on the given discharge and bed slope. The units requested ($m^3 s^{-1}$) suggest using the relationship $Q = K \sqrt{S}$, where $K$ represents conveyance.

Given Parameters

• Discharge, $Q = 60 \text{ m}^3 \text{ s}^{-1}$
• Bed slope, $S = 0.01\% = 0.0001$
• Bottom width, $b = 5 \text{ m}$ (Note: Not directly used in this calculation method)
• Manning's roughness coefficient, $n = 0.025$ (Note: Not directly used in this calculation method)

Formula and Calculation

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

$ Q = K \sqrt{S} $

To find the conveyance ($K$) in the specified units ($m^3 s^{-1}$), we rearrange the formula:

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

Substitute the given values:

$ K = \frac{60 \text{ m}^3 \text{ s}^{-1}}{\sqrt{0.0001}} $

Calculate the square root of the slope:

$ \sqrt{0.0001} = 0.01 $

Perform the division:

$ K = \frac{60}{0.01} \text{ m}^3 \text{ s}^{-1} $

$ K = 6000 \text{ m}^3 \text{ s}^{-1} $

Result

The conveyance of the channel, calculated using the provided discharge and slope, is $6000 \text{ m}^3 \text{ s}^{-1}$.