In a planet a sucrose solution of coefficient of viscosity 0.0015 Nsm^-2 is driven at a velocity of 10^-3 ms^-1 through xylem vessels of radius 2 $μ$ m and length 5 $μ$ m. The hydrostatic pressure difference across the length of xylem vessels in Nm^-2 is

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answer is D.

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Detailed Solution

$\begin{array}{l} η = 0 .015 Ns / m^{2}; V = 10^{- 3} m^{3} / \sec \\ r = 2 μm = 2 \times 10^{- 6} m; ℓ = 5 μm = 5 \times 10^{- 6} m \\ \frac{V}{t} = \frac{{πPr}^{4}}{8 ηℓ} \\ P = (\frac{V}{t}) \frac{8 ηℓ}{{πr}^{4}} = (Av) \frac{8 ηℓ}{{πr}^{4}} = \frac{{πr}^{2} v \times 8 ηℓ}{{πr}^{4}} \\ P = \frac{8 ηℓv}{r^{2}} = \frac{8 \times 15 \times 10^{- 4} \times 5 \times 10^{- 6} \times 10^{- 3}}{{(2 \times 10^{- 6})}^{2}} \\ P = 15 Pa \end{array}$