Question

Suppose a viscous oil, whose flow is in the laminar regime is to be pumped through a 10 cm diameter horizontal pipe over a distance of 15km at a rate of 10^{-3} m^3/s. Viscosity of the oil is 0.03 poise. What is the required pressure drop to maintain such a flow?

Answer 1

The number of units of fluid flowing per unit time through the cross section of the pipe:

$Q= \frac{\pi R^4} {8 \eta l} \Delta P$ , where:

$R$ - radius of pipe, $R = 0.05m$ ;

$\eta$ -  viscosity of the oil, $\eta=0.03 poise$ ;

$l$ -pipe length, $l=15000m;$

$\Delta P$ - the required pressure.

$\Delta P= \frac{Q}{\pi R^4}8\eta l = \frac{10^{-3}}{3.14\cdot 0.05^4}8\cdot0.03\cdot15000 = 183439.5 Pa$