Estimate the transition length of the following:

$($a$)$ Estimate the transition length at the entrance to a $15mm$ tube through

which $100$ percent glycerol at $60C$ is flowing at a velocity of $0\mathrm{.}3\frac{m}{s}.$ The

density of glycerol is $1,240k\frac{g}{m^3}$ and its viscosity is $0\mathrm{.}098$ Pa$.$s$.$

$($b$)$ Repeat part $($a$)$ for $100$ percent n$-$propyl alcohol entering a $3$ in$.$ pipe at

$30C$ and a velocity of $7f\frac{t}{s}.$ The density of n$-$propyl alcohol is $50l\frac{b}{f}{t}^3$

and its viscosity is $1\mathrm{.}9cP.$