B$3.$ Uniform flow in a $6m$ wide rectangular channel carries a discharge of $60m^{\frac{3}{s}}.$ The steady velocity is measured to be $1\mathrm{.}5\frac{m}{s}.$ For certain engineering purposes, a backward$-$facing step of size $0\mathrm{.}1m$ has to be built in the channel, as shown in Figure B$3.$ The upstream flow is assumed to remain unchanged in the new channel configuration. Assume the entire channel bed is horizontal and the energy loss is negligible, then

a$)$ Calculate the water depth $y_2$ and velocity $V_2$ downstream of the step;

$[10$ marks$]$

b$)$ Calculate the force on the vertical face of the step and indicate its direction.

$[15$ marks$]$

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