QUESTION $2$

$[20$ Marks$]$

The pressure drop between the entrance and exit of a $150-$mm$-$diameter $90$ elbow, through which ethyl alcohol at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is flowing, is to be determined with a geometrically similar model. The velocity of the alcohol is $\backslash (5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The model fluid is to be water at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and the model velocity is limited to $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)$ What is the required diameter of the model elbow to maintain dynamic similarity?

$($b$)$ A measured pressure drop of $20$ kPa in the model will correspond to what prototype value?