Question

In designing hydraulic structure in alluvial river, the equation that is used to calculate the normal depth of scour R for a discharge intensity of $q{m}^3/s/m$ is :

• A.
  $R=1.35{\left(\frac{q}{f}\right)}^{2/3}$
• B. $R=1.2{\left(\frac{q^2}{g}\right)}^{1/3}$
• C. $R=1.35{\left(\frac{q^2}{f}\right)}^{1/3}$
• D. $R=4.75(q{)}^{1/2}$

Answer 1

The correct option is C $R=1.35{\left(\frac{q^2}{f}\right)}^{1/3}$

$R=1.35{\left(\frac{q^2}{f}\right)}^{1/3}q=\frac{Q}{B}=\frac{discharge}{width}f=\text{Silt factor}R=\text{Normal scour depth.}\text{Note:}\text{Lacey's 3 basic equation :}\left(i\right)V=\sqrt{\frac{2}{5}fR}\left(ii\right)A{f}^2=140V^5\left(iii\right)V=10.8R^{2/3}{S}^{1/3}$

where A = Area of channel section
V = Velocity of flow in the channel.
f =Silt factor
R=Hydraulic mean depth of the channel.
The above 3 basic equations are further used to derive certain relations for being used in the design of lacey's channel as given below :
$1.V={\left(\frac{Q{f}^2}{140}\right)}^{1/6}2.R=\frac{5}{2}\frac{V^2}{f}3.P=4.75\sqrt{Q}4.S=\frac{f^{5/3}}{3340Q^{1/6}}$
where, f = Silt factor, Q in cumecs

$f=1.76\sqrt{d_{mm}}$

where,
$d_{mm}$ = Average particle size of alluvial in (mm)
p = Perimeter in (m).