Case study: Polymer flow $($Example $3\mathrm{.}1)$

A polymer flows steadily in the horizontal pipe of Fig. E$3\mathrm{.}1($a$)$ under the

following conditions: $=900k\frac{g}{m^3},=0\mathrm{.}01$Pas$(k\frac{g}{m}s),D=0\mathrm{.}02m,$ and

$u_m=0\mathrm{.}5\frac{m}{s}.$ Evaluate the following, clearly indicating the units:

$($a$)$ The Reynolds number.

$($b$)$ The frictional dissipation per meter per $kg$ flowing.

$($c$)$ The pressure drop per meter.

$($d$)$ The elevation decrease for every meter of length if the polymer were to flow

steadily at the same rate without any pumping needed. In this case, gravity

provides the necessary energy for flow $($i$.$e$.,p=0),$ as in Fig. E$3\mathrm{.}1($b$).$

$($a$)$

Fig. E$3\mathrm{.}1$ Polymer flow in pipeline: $($a$)$ horizontal, $($b$)$ inclined.