Problem $3$: Profiling velocity distribution in a converging channel

As shown in Figure $1,$ a two$-$dimensional streamwise velocity

field, u$($x$,$y$),$ for a flow in converging channel is given by

u$($x$,$y$)=$u$\_(0)(1+($x$)/($l$))[1-($y$^(2))/($Y$^(2)($x$))]$

where Y$($x$)$ is the channel half$-$height that varies in x direction

as

Y$($x$)=($Y$\_(0))/(1+($x$)/($l$))$

Here, u$\_(0)=1\mathrm{.}0($m$)/($s$)$ and Y$\_(0)=1\mathrm{.}0$m$.$

Determine if this flow is steady. $(1$ pts $)$

Plot the sectional velocity distribution, u$($y$),$ at $($x$)/($l$)=0,$

$0\mathrm{.}5,$ and $1\mathrm{.}0$ across the entire channel, yin$[-$Y$($x$),$Y$($x$)],$

Figure $1$: Flow in a converging channel.

using a formal plotting tool. Note that the channel height,

Y$($x$),$ is varying in the x$-$direction. $(2$ pts$)$