Using scale analysis and the equation for shear stress in a Newtonian fluid (tau

Question

Using scale analysis and the equation for shear stress in a Newtonian fluid (tau = mu * (du/dr) calculate the shear stress on the wall of typical small artery when the flow is fully developed. Given that real blood flow is pulsatile, we know that the boundary layer near the wall of the artery will grow in size as the fluid starts to move. Develop an expression for the shear stress at the wall of the artery as a function of time starting at the inception of motion that results from the a beat of the heart. Assume that the blood instantaneously goes from u = 0 to its average velocity as soon as the heart beats. Determine the shear stress on the wall of the artery at a time 0.5 seconds after the start of the beat.

Explanation / Answer

shear stress is Force per unit area. Diameter of small arteries is > 160 micromt. Radius >= 80 micromt.

So, shear stress (tau) = F/3.14 * 80; it comes out in the range 10 -19 dyn/cm2

Shear stress decreases with increase in radius. When flow increases radius of the artery also increases and can reach a maximum value of 80 micromt...

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