0 mN/m radius is 3cm? Pa 4) a) Consider blood plasma with protein volume fraction 8%. What is the viscosity of the plasma. Use viscosity of water = 0.69 mPa·s. b) Consider critical hematocrit = 0.04, and actual hematocrit = 72%. What is Yield stress and Newtonian viscosity? c) Consider a blood vessel of diameter 2cm. Q = 5L/min. What is the pressure gradient? Use casson's equation model for parts b and c. d) What is the <u> and Re? ?_blood = 1050 kg/m³ e) Find entrance length.
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a) Use the Einstein relation for viscosity of suspensions: \[ \eta = \eta_0 (1 + 2.5\phi) \] where \(\eta_0\) is the viscosity of the solvent (water) and \(\phi\) is the volume fraction of the solute (protein). Given: \(\eta_0 = 0.69 \, Show more…
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Consider blood flow in an artery. Blood is nonNewtonian; the shear stress versus shear rate is described by the Casson relationship: $$\left\{\begin{array}{ll} \sqrt{\tau}=\sqrt{\tau_{c}}+\sqrt{\mu \frac{d u}{d r}} & \text { for } \tau \geq \tau_{c} \\ \tau=0 & \text { for } \tau<\tau_{c} \end{array}\right.$$ where $\tau_{e}$ is the critical shear stress, and $\mu$ is a constant having the same dimensions as dynamic viscosity. The Casson relationship shows a linear relationship between $\sqrt{\tau}$ and $\sqrt{d u / d r},$ with intercept $\sqrt{\tau_{c}}$ and slope $\sqrt{\mu} .$ The Casson relationship approaches Newtonian behavior at high values of deformation rate. Derive the velocity profile of steady fully developed blood flow in an artery of radius $R$. Determine the flow rate in the blood vessel. Calculate the flow rate due to a pressure gradient $d p / d x=-100 \mathrm{Pa} / \mathrm{m},$ in an artery of radius $R=1 \mathrm{mm},$ using the following blood data: $\mu=3.5 \mathrm{cP}$ $\tau_{c}=0.05$ dynes $/ \mathrm{cm}^{2}$
What is the largest average velocity of blood flow in an artery of radius 2*10^-3 m. If the flow must remain laminar. Given viscosity of blood = 2.084*10^-3 Pa , density of blood =1.06*10^3 kg/m^3 and Reynolds number for laminar flow= 2000
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