First slide

Fluid dynamics

Question

In a plant a sucrose solution of coefficient of viscosity 0.0015 N-sm^-2 is driven at a velocity of 10^-3ms^-1 through xylem vessels of radius 2 µm and length 5 µm. The hydrostatic pressure difference across the length of xylem vessels in Nm^-2 is

Moderate

A

15
B

5
C

8
D

10

Solution

η = 0.0015 N-s/m²; V = 10^-3m³/sec; r = 2µm = 2 x 10^-6m; l = 5µm = 5 x 10^-6m
$\large \frac Vt=\frac {\pi Pr^4}{8\eta l}$
$\large P=\left ( \frac Vt \right )\frac {8\eta l}{\pi r^4}=(Av)\frac {8\eta l}{\pi r^4}=\frac {\pi r^2v\times 8\eta l}{\pi r^4}$
$\large P=\frac {8\eta l v}{r^2}=\frac {8\times15\times10^{-4}\times5\times10^{-6}\times10^{-3}} {(2\times10^{-6})^2}=15Pa$

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