Lacey's regime equations, followed in India for making scour calculations while designing hydraulic structures across alluvial channels, are given below. Regarding these equations, which of the following statements is/are true:
$$ \begin{aligned} & D=0.470 \times\left[\frac{Q}{f_s}\right]^{1 / 3} \\ & P=4.75 \times \sqrt{Q} \\ & f_s=1.76 \times \sqrt{d} \end{aligned} $$
where, $Q$ is discharge and $f_s$ is silt factor
A hydraulic jump is formed in a 5 m wide rectangular channel, which has a horizontal bed and is carrying a discharge of $15 \mathrm{~m}^3 / \mathrm{s}$. The depth of water upstream of the jump is 0.5 m . The power dissipated by the jump (in kW ) is ________ (rounded off to the nearest integer).
Note:
Acceleration due to gravity $=9.81 \mathrm{~m} / \mathrm{s}^2$
Density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$
Kinetic energy correction factor $=1.0$
A 5.0 m wide rectangular channel carries a discharge of $10 \mathrm{~m}^3 / \mathrm{s}$ at a depth of 1.5 m under uniform flow. To produce critical flow conditions without affecting the upstream conditions, the channel bottom elevation should be raised (in m ) by _________ (rounded off to 2 decimal places).
Assume that there is no loss of head at the raise, kinetic energy correction factor is 1.0 , and acceleration due to gravity is $9.81 \mathrm{~m} / \mathrm{s}^2$.