please solve problem 4 part (ii). clear detail! A viscous liquid (density of 118

Question

please solve problem 4 part (ii). clear detail!

A viscous liquid (density of 1180 kg/m3 and dynamic viscosity of 0.0045 N s/m2) flows at a volumetric rate of 12.6 mL/s through a horizontal 4mm diameter tube. Determine the pressure drop in kPa along a 2m length of the tube, which is far from the tube entrance so that the only component velocity is parallel to the tube axis. Clear state and justify assumptions. A viscous liquid (density of 1180 kg/m3 and dynamic viscosity of 0.0045 N s/m2) flows at a volumetric rate of 12.6 mL/s through a horizontal 4-mm-diameter tube. After developing the velocity profile of this Poiseuille flow across the 2m long tube, what is the estimated velocity in m/s at a radius of 1.2 mm in the tube?

Explanation / Answer

Velocity profile, v(r) = P(R^2 - r^2) / 8nL

But Volumetric flow rate, V = P (3.14 * R^4) / 8nL

So v(r) = 2V (R^2 - r^2) / (3.14 * R^4)

= 2 * 12.6 ( 4^2 - 1.2^2 ) / 3.14*(4^4)

= 0.45 m/s

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