Question

Coronary heart disease is caused by a buildup of plaque in the arteries that supply blood to the heart. When the flow of blood to the heart is restricted or blocked, the heart can be damaged due to a lack of oxygen. Further, if a large piece of plaque buildup gets dislodged from an artery wall, it can get stuck in other arteries throughout the body, including arteries in the brain. For simplicity, let's assume that the artery is cylindrical with a radius of R. The flow rate of a viscous fluid is given by Poiseuille's Law Q=(π/8)(ΔP/ηl)r4.

1.) If plaque buildup reduces the radius of the artery by a factor of 2, by what factor does the flow rate change?

a.)	The rate is 4 times the original.
b.)	The flow rate is 1/4th of the original.
c.)	The flow rate is 16 times the original.
	d.)The flow rate is now 1/16th of the original. 2.) If the plaque buildup (modeled as a cylinder as well) completely blocks the artery, a pressure difference of Pbetween each side of the clot builds up. What is the force on the clot?   a.) 2Pπr   b.) 2Pπr2   c.) Pπr2   d.) P 3.) If the clot breaks free and only experiences a force due to the blood pressure, what is the relationship between the pressure on each side of the clot as it moves with a constant velocity toward the heart? a.) The pressure on the side closest to the heart is higher because the clot is moving toward the heart. b.) The pressure on each side is the same. c.) There is a pressure differential in order to keep the clot moving. d.) The pressure on the side furthest from the heart is higher because the clot is moving toward the heart.

Answer 1

The rate of flow of liquid from poiselle's equation,

$$ \frac{V}{t}=\frac{\pi p r^{4}}{8 \eta l} $$

Here, \(P\) is the pressure differcne, \(r\) is the radius of the pipe, \(\eta\) is the coefficient of viscosity and \(l\) is the length of the pipe. Then,

$$ \begin{array}{c} \frac{V}{t} \propto r^{4} \\ \frac{\left(\frac{V}{t}\right)_{f}}{\left(\frac{V}{t}\right)_{i}}=\frac{r_{f}^{4}}{r_{i}^{4}}=\frac{\left(r_{i} / 2\right)^{4}}{r_{i}^{4}} \\ \left(\frac{V}{t}\right)_{f}=\frac{1}{16}\left(\frac{V}{t}\right)_{i} \end{array} $$

Correct option is (D)

(2) Pressure difference is the ratio of force on clot per unit area.

$$ \begin{array}{c} P=\frac{F}{A}=\frac{F}{\pi r^{2}} \\ F=P\left(\pi r^{2}\right) \end{array} $$

Correct option is \((C)\)

(3) The pressure on each si de is same.

Correct option is \((b)\)