QUESTION $1$

$($a$)$ The vector velocity of a water flow is given in Equation $1.$

vec$(V)=(u,v,w)=(0\mathrm{.}32+2\mathrm{.}1x)vec()+(3\mathrm{.}6-1\mathrm{.}1y)vec()$

$+(3+0\mathrm{.}6z)vec(k)$

Equation $1$

i$)$ Describe the flow behaviour based on given velocity vector.

$(2$ marks$)$

ii$)$ Determine the velocity component, $(u,v)$ and resultant velocity, vec$(V)$ at point $P,$ with its position vector, vec$(r)=3$vec$()+$vec$()+$vec$(2k).$

$(7$ marks$)$

iii$)$ Determine the acceleration component and its resultant at the same point $P.$

$(6$ marks$)$

iv$)$ Is there a stagnation point in this flow field? If so$,$ determine the location of stagnation point.

$(4$ marks$)$