Question

How its solved

5 A Small blood vessel near the skin has a radius of 10-5 m and length of 1 mm. The pressure drop along the blood vessel is 2.5 Pa. The viscosity of the blood is 2.5 x 10-3 Pa.s. The volume flow rate of blood through this blood vessel is A) 4.17 x 10-4m3/s B) 1.83 x 10-15m3/s C) 3.93 x 10-15m3/s D) 6.25 x 10-"m3/s

Answer 1

DATA

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$r=10^{-5} \, m$

$\Delta x=1\times 10^{-3} \, m$

$\Delta P=2.5 \, Pa$

$\eta =2.5\times 10^{-3} \, Pa\cdot s$

$Q=?$

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SOLUTION

$\:$

Using Poiseuille's equation, we obtain

$\:$

$\Delta P=\frac{8 \eta Q \Delta x}{\pi r^{4}}$

$\Rightarrow \: \: \: Q=\frac{ \pi \Delta P r^{4}}{8 \eta \Delta x}$

$\Rightarrow \: \: \: Q=\frac{ \pi (2.5 \, Pa) (10^{-5} \, m)^{4}}{8 (2.5\times 10^{-3}\, Pa\cdot s) (1\times 10^{-3} \, m)}$

$\Rightarrow \: \: \: Q=0.393\times 10^{-20}\times 10^{6} \, m^{3}/s$

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or

$\:$

${\color{Blue} Q=3.93\times 10^{-15} \, m^{3}/s}$