Question

in a plate, a sucrose solution of coefficient of visocity `1.5 xx10^(-3) Nsm^(-2)` is driven at a velocity of `10^(-3) ms ^(-1)` throught x ylem vessel of radius `2mu` m and length`5mu`m. Find the hydrostatic pressure difference across the length of xylem vessel.

Answer 1

Correct Answer - `15 Nm^(-2)`
Here, `eta = 1.5 xx10^(-3) N.s m^(-2) , upsilon = 10^(-3) ms^(-1),`
`r = 2xx 10^(-6)m, l = 5xx 10^(-6)m`
`V = pi r^2 upsilon = (pi p r^4)/(8 eta l)`
`or p = (8 eta l upsilon)/(r^2) = 8xx1.5 xx10^(-3)xx(5xx10^(-6)xx10^(-3))/((2xx10^(-6))2)`
`= 15 N m^(-2)`