Problem $1(10$ points$)$: Learning Outcome $\backslash$#$1,\backslash$#$4$

The thickness $\backslash (\backslash$delta $\backslash )$ of the boundary layer for a fluid flowing over a flat plate depends on the distance x from the plate's leading edge, the free$-$stream velocity $\backslash ($ U $\backslash ),$ the density of fluid, $\backslash (\backslash$rho $\backslash ),$ and the viscosity of the fluid $\backslash (\backslash$mu $\backslash ).$ Use the Buckingham Pi Theorem to determine the Pi Group or Groups. Let $\backslash (\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$U$\}\backslash )$ and $\backslash (\backslash$rho $\backslash )$ be your repeating variables.