5. Glycerine is flowing in a small capillary of diameter...

5. Glycerine is flowing in a small capillary of diameter 0.25 cm and length 30 cm. For a pressure difference of 3 bars applied across the tube a flow rate of 0.001 m³/s was obtained. Find the viscosity of the liquid using the Hagen Poiseuille equation (10 P). ANSWER: ? = 9.577 × 10?? Pa. s

The laminar-pipe-flow example of Prob. 1.12 can be used to design a capillary viscometer [27]. If $Q$ is the volume flow rate, $L$ is the pipe length, and $\Delta p$ is the pressure drop from entrance to exit, the theory of Chap. 6 yields a formula for viscosity: $$\mu=\frac{\pi r_{0}^{4} \Delta p}{8 L Q}$$ Pipe end effects are neglected [27]. Suppose our capillary has $r_{0}=2 \mathrm{mm}$ and $L=25 \mathrm{cm} .$ The following flow rate and pressure drop data are obtained for a certain fluid: $$\begin{array}{l|l|l|l|l|l} Q, \mathrm{m}^{3} / \mathrm{h} & 0.36 & 0.72 & 1.08 & 1.44 & 1.80 \\ \hline \Delta p, \mathrm{kPa} & 159 & 318 & 477 & 1274 & 1851\end{array}$$ What is the viscosity of the fluid? Note: Only the first three points give the proper viscosity. What is peculiar about the last two points, which were measured accurately?

Question

5. Glycerine is flowing in a small capillary of diameter 0.25 cm and length 30 cm. For a pressure difference of 3 bars applied across the tube a flow rate of 0.001 m³/s was obtained. Find the viscosity of the liquid using the Hagen Poiseuille equation (10 P). ANSWER: ? = 9.577 × 10?? Pa. s

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