$1-$ A pharmaceutical company needs to pump a delicate liquid drug through a pipe over a distance of

$25$ meters. The flow rate must be $0\mathrm{.}1$ cubic meters per minute. To protect the quality of the drug, the

flow must be laminar with no turbulence or high shear rates. Specifically, shear rates cannot exceed

$100$ per second.

The liquid drug has a density of $0\mathrm{.}830\frac{g}{c}{m}^3$ and a viscosity of $0\mathrm{.}0052Pa*s.$ It demonstrates Newtonian

flow behavior. What is the minimum diameter of pipe that can transport the liquid drug within the

stated constraints?

Also, calculate the pressure drop that would occur when pumping $0\mathrm{.}1\frac{m^3}{m}in$ of the drug through $25$

meters of pipe with that minimum diameter.