Question

The flow of blood in a blood vessel is \intaster toward the center of the vessel and slower toward the outside. The speed of the blood $v$, in millimeters per second $(\mathrm{mm} / \mathrm{sec})$ is given by $$V=\frac{p}{4 L v}\left(R^{2}-r^{2}\right)$$ where $R$ is the radius of the blood vessel, $r$ is the distance of the blood from the center of the vessel, and $p, L,$ and v are physical constants related to pressure, length, and viscosity of the blood vessels, respectively. Assume that dV/dt is measured in millimeters per second squared ( $\mathrm{mm} / \mathrm{sec}^{2}$ ). (IMAGE CANNOT COPY) Assume that $r$ is a constant as well as $p, L,$ and $v$ a) Find the rate of change $d V / d t$ in terms of $R$ and $d R / d t$ when $L=70 \mathrm{mm}, p=400,$ and $v=0.003$ b) When shoveling snow in cold air, a person with a history of heart trouble can develop angina (chest pains) due to contracting blood vessels. To counteract this, he or she may take a nitroglycerin tablet, which dilates the blood vessels. Suppose that after a nitroglycerin tablet is taken, a blood vessel dilates at a rate of $$\frac{d R}{d t}=0.00015 \mathrm{mm} / \mathrm{sec}$$ at a place in the blood vessel where the radius $R=0.1 \mathrm{mm} .$ Find the rate of change, $d V / d \iota$

          The flow of blood in a blood vessel is \intaster toward the center of the vessel and slower toward the outside. The speed of the blood $v$, in millimeters per second $(\mathrm{mm} / \mathrm{sec})$ is given by
$$V=\frac{p}{4 L v}\left(R^{2}-r^{2}\right)$$
where $R$ is the radius of the blood vessel, $r$ is the distance of the blood from the center of the vessel, and $p, L,$ and v are physical constants related to pressure, length, and viscosity of
the blood vessels, respectively. Assume that dV/dt is measured in millimeters per second squared ( $\mathrm{mm} / \mathrm{sec}^{2}$ ).
(IMAGE CANNOT COPY)
Assume that $r$ is a constant as well as $p, L,$ and $v$
a) Find the rate of change $d V / d t$ in terms of $R$ and $d R / d t$ when $L=70 \mathrm{mm}, p=400,$ and $v=0.003$
b) When shoveling snow in cold air, a person with a history of heart trouble can develop angina (chest pains) due to contracting blood vessels. To counteract this, he or she may take a nitroglycerin tablet, which dilates the blood vessels. Suppose that after a nitroglycerin tablet is taken, a blood vessel dilates at a rate of
$$\frac{d R}{d t}=0.00015 \mathrm{mm} / \mathrm{sec}$$
at a place in the blood vessel where the radius $R=0.1 \mathrm{mm} .$ Find the rate of change, $d V / d \iota$

Added by Antonia B.

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