Question

The Darcy-Weisbach 'f' is related to Mannings 'n' as

• A. $f=\frac{8g{n}^2}{R^{1/3}}$
• B. $f=\frac{n^2}{R^{1/3}}$
• C. $f=\frac{R^{1/3}}{8g{n}^2}$
• D. $f=\frac{64ng}{R^{1/3}}$

Answer 1

The correct option is A $f=\frac{8g{n}^2}{R^{1/3}}$

We know
$v=C\sqrt{RS}andC=\sqrt{\frac{8g}{f}}$

$\Rightarrow V=\sqrt{\frac{8gRS}{f}}$

$f=\frac{8gRS}{v^2}$

$f=\frac{8gRS}{{\left(\frac{1}{n}{R}^{2/3}{S}^{1/2}\right)}^2}$

$\Rightarrow f=\frac{8gRS}{\frac{1}{n^2}{R}^{4/3}S}=\frac{8g{n}^2}{R^{1/3}}$