Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m . The bed slope of the channel is 0.0001 . The Manning roughness coefficient value is 0.02 . Acceleration due to gravity, g can be taken as $9.81 \mathrm{~m} / \mathrm{s}^2$.

The critical depth (in m ) corresponding to the flow rate resulting from the above conditions is ________ (round off to one decimal place).

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 $9.81 \mathrm{~m} / \mathrm{s}^2$.