Answer to Question #200424 in Math for Raghav

Question

Consider the blood flow in an artery following Poiseuille’s law. If the length of the

artery is 3 cm, radius is 7×10^-3 cm and driving force is 5×10³ dynes/cm² then using blood viscosity, μ = 0 × 027 poise, find the

(i) velocity u( y) and the maximum peak velocity of blood, and

(ii) shear stress at the wall of the artery.

Answer 1

(i) Here, viscosity of blood is given as

 $\mu=0.027\ poise=0.0027\dfrac{N\cdot s}{m^2}$ ,

length of artery $l=3cm=3\times10^{-2}m,$

radius $r=7\times10^{-3} cm=7\times10^{-5}m,$ and $P_1-P_2= 5\times10^{3} \dfrac{dyne}{cm^2}=5\times 10^2\dfrac{N}{m^2}$

We know that maximum velocity in case of fluid flow

$$V_{max}=\frac{\Delta P r^2}{4 \mu l}= \frac{5\times10^{2}\times49\times10^{-10}}{4\times0.0027\times3\times10^{-2}}=0.756\ cm/s$$ $$u=\dfrac{V_{max}}{2}=\dfrac{0.756cm/s}{2}=0.378cm/s$$

(ii) For shear stress we know that,

$$\tau=\frac{\Delta P r}{2l}= \frac{5\times10^{2}\times7\times10^{-5}}{2\times3\times10^{-2}m}=0.583\dfrac{N}{m^2}=5.83 \dfrac{dyne}{cm^2}$$