$(5)$ Flow through granular$-$based porous media $($such as a mixture of water and crude oil through a layer of porous

rock in fracking or hydraulic fracturing$)$ can be described by Ergun equation, which correlate the pressure drop

per thickness of porous media $(\frac{p}{L})$ to the superficial velocity $(U),$ sand diameter $(d),$ porosity $()$ and viscosity

$()$ as

$\frac{p}{L}=150\frac{(1-{)}^2}{{}^3}\frac{U}{d^2}+1\mathrm{.}75\frac{(1-)}{{}^3}\frac{U^2}{d}$

Derive an expression of uncertainty in pressure drop in terms of the measurements and uncertainties of the

thickness of porous media, flow velocity, granular diameter, porosity, and viscosity.