Question

In a plant, sucrose solution of coefficient of viscosity $0.0015N.m^{-2}$ is driven at a velocity of ${10}^{-3}m{s}^{-1}$ through xylem vessels of radius $2\mu m$ and length $5\mu m$ . The hydrostatic pressure difference across the length of xylem vessels in $N{m}^{-2}$ is :

• A. $5$
• B. $8$
• C. $10$
• D. $15$

Answer 1

Answer: (D)

$15$

Fow rate $q=v\times \pi r^2$

also $q=\frac{\pi P{r}^4}{8\mu l}=v\pi r^2$

now $v={10}^{-3}m/s,\mu =0.0015N/m^2,r=2\times {10}^{-6}m$

on solving above equation and putting value in SI unit we get

$P=15N/m^2$