$($a$)$ Figure A$3$a shows a sketch of a race car that is travelling $($to the left$)$ at $\backslash (144\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ).$ The underbody of the car $($length $2$ m and width $1\mathrm{.}5$ m $)$ is designed to produce a downward force on the car. It can be assumed that the forward motion of the car forces air $($density $\backslash (1\mathrm{.}2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ))$ to enter the $30$ cm gap at the front and pass through the $15$ cm gap between the underbody and the road.

$($i$)$ Assuming air to be incompressible and inviscid $($and ignoring the effects of gravity$)$ use the Bernoulli equation to estimate the downward force on the car generated by the flow between the underbody and the road.

$(6$ marks$)$

$($ii$)$ The forward motion of the car means that road travels backwards relative to the car body. Considering viscous effects, would this help or worsen the underbody$-$flow strategy to create a downward force. Briefly explain your answer.

$(3$ marks$)$