This question was previously asked in

NWDA JE CE 2019 Official Paper

Option 1 : 0.66 m/sec

**Concept:**

Kutter's formula for mean velocity is used by **Kennedy **for the purpose of the design of alluvial channels in India. It is given as,

V = \(\frac {[\frac{1}{N}+(23+\frac{0.00155}{S})]}{[1+(23+\frac{0.00155}{S})×\frac{N}{\sqrt{m}}]}\)× \(\sqrt{mS}\)

Where,

N = Kutter's constant, m = Hydrualic radius and S = bed slope

**Calculation:**

Given,

N = 0.0225, m = 1 and S = 0.2 m/km

\(\because\) We know that, Velocity, V = \(\frac {[\frac{1}{N}+(23+\frac{0.00155}{S})]}{[1+(23+\frac{0.00155}{S})×\frac{N}{\sqrt{m}}]}\) × \(\sqrt{mS}\)

⇒V = \(\frac {[\frac{1}{0.0225}+(23+\frac{0.00155}{0.0002})]}{[1+(23+\frac{0.00155}{0.0002})×\frac{0.0225}{\sqrt{1}}]}\)× \(\sqrt{1\times0.0002}\)

⇒ **V = 0.62 m/sec**

**None of the options are correct, but the most appropriate answer = 0.66 m/s**