First slide

Viscosity

Question

Glycerine flows steadily through a horizontal tube of length 1.5m and radius 1.0cm. If the amount of glycerine collected per second at one end is 4.0 x $10^{- 3} K g S^{- 1}$ , what is the pressure difference between the two ends of the tube? Density of glycerine = 1.3 x $10^{3} K g m^{- 1}$ and viscosity of glycerine = 0.83 Ns $m^{- 2}$ (You may also like to check if the assumption of laminar flow in the tube is correct.)

Moderate

A

9.8 x $10^{2}$ Pa
B

9.8 x $10^{8}$ Pa
C

6.6 x $10^{4}$ Pa
D

7.2 x $10^{3}$ Pa

Solution

From Poiseuille's equation
$\large \frac Vt=\frac {\pi Pr^4}{8nl}\Rightarrow P=\frac Vt\times \frac {8nl}{\pi r^4}$
$\large \Rightarrow P=\frac {m/d}{t}.\frac {8nl}{\pi r^4}$
$\large \Rightarrow P=\frac {4\times 10^{-3}}{1.3\times 10^3\times 1}\times \frac {8\times 0.83\times 15}{3.14\times (10^{-2})^4}Pa$
$\large =9.8\times 10^2\;Pa$

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