$($a$)$ Consider a point in an inviscid flow, where the local density is $\backslash (1\mathrm{.}1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$3\}\backslash ).$ As a fluid element sweeps through this point, it is experiencing a spatial change in velocity of $2$ percent per millimeter. Calculate the corresponding spatial change in pressure per millimeter at this point if the velocity at the point is $\backslash (100\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($b$)$ Repeat the calculation for the case in which the velocity at the point is $\backslash (1000\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ What can you conclude by comparing your results for the low$-$speed flow in part $($a$)$ with the results for the highspeed flow in part $($b$)?$