Topic VI: Dimensional Analysis & Similitude $(10$ points$)$

An experimental setup is being built to study the flow in a large water main $($i$.$e$.,$ a large pipe$).$ The water main is

expected to convey a discharge $(Q_p).$ The experimental tube will be built at a length scale of $\frac{1}{20}$ of the actual

water main. After building the experimental setup, the pressure drop per unit length in the model tube $(\frac{P_m}{L_m})$

is measured.

Problem $(19)$: Given the value of $Q_p[\frac{m^3}{s}],$ and assuming Reynolds number similitude between the water main

and experimental tube, calculate the flow rate in the model tube $(Q_m)$ in $[$lit$/$s$].$ Givens: answers:

Problem $(20)$: Given the value of $\frac{P_m}{L_m}[kP\frac{a}{m}],$ and assuming pressure coefficient similitude, calculate the

drop in the pressure per unit length of the water main $(\frac{P_p}{L_p})$ in $P\frac{a}{m}.$

Givens: answers:

$\frac{D_m}{l_m}=378\mathrm{.}524kP\frac{a}{m}1$

answers:

$28\mathrm{.}673P\frac{a}{m}$

$38629P\frac{m}{m}$

$33\mathrm{.}837P\frac{g}{m}$

$47316P\frac{a}{m}$