The pressure drop per unit length $p_l($at any instant$)$ along a pipe flow depends on fluid density $()$ and viscosity $(),$ flow velocity $($V$),$ and pipe diameter $($D$).$ Perform a dimensional analysis to find out the non$-$dimensional parameters important in this pipe flow problem.

$p_l=f(,,V,D)$

A $\frac{1}{3}$ scale model uses the same fluid as in the prototype. What will be the pressure drop in the prototype if the pressure drop in the model is $5900$ pascal$/$m