$($c$)$ Assuming that the Gaussian profiles are valid for both two$-$dimensional $(2$D$)$ and three$-$dimensional $(3$D$)$ jets.

$($c$-1)$ A slot turbulent jet discharges liquid at a velocity $4\frac{m}{s}$ into a liquid of the same density. Find the maximum time$-$averaged velocity, tracer concentration, and the mean dilution at a distance of $30m$ from the jet slot. Slot width $=15cm,$ and the initial concentration of the tracer $=1025ppm.$

$($c$-2)$ For a round port discharge $($diameter $20cm)$ at a depth $40m$ and an initial velocity $2\frac{m}{s}$ with sediment concentration $300\frac{g}{m^3},$ estimate the centerline velocity, the average dilution and the maximum sediment concentration near the surface.