Question:easy

A trapezoidal channel carries \(5\ \text{m}^3\text{s}^{-1}\) of water under uniform flow condition. The channel has a bottom width of 2 m, side slope of 2:1 (horizontal: vertical), and a bed slope of 1%. If the Manning roughness coefficient is 0.03, the conveyance of the channel, in \(\text{m}^3\text{s}^{-1}\), is

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Recall that conveyance links discharge and bed slope directly through Manning's equation.
Updated On: Aug 6, 2026
  • 2
  • 5
  • 15
  • 50
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Note what conveyance actually means.
Conveyance $K$ is the part of Manning's formula that depends only on the channel section and roughness, defined so that $Q = K\sqrt{S}$.

Step 2: See that $K$ can be pulled straight out of the given $Q$ and $S$.
Since $Q$ and $S$ are both already given (5 m3/s and 1%), there is no need to compute area or hydraulic radius separately.
$K = Q / S^{0.5}$

Step 3: Plug in the numbers.
$S = 0.01$, so $S^{0.5} = 0.1$.
$K = 5 / 0.1 = 50\ \text{m}^3\text{s}^{-1}$

Step 4: Sanity check with units.
$K$ carries the same units as $Q$ because $S$ is dimensionless, which matches the 50 m3/s result.

Final Answer:
The bottom width, side slope, and n values are extra information here; the conveyance is 50 m3/s. \[ \boxed{K = 50\ \text{m}^3\text{s}^{-1}} \]
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