Problem 1: Consider a person who is 1.7 m tall. The height difference between the heart and the brain is 0.5 m and the height difference between the heart and the feet is 1.2 m. Assume that gravity is the primary contributor to pressure differences (which is not completely true since there is a flow involved). The maximum pressure at the heart is 120 mm of mercury column. The density of mercury is given as 13550 kg/m³ and the density of blood is 1000 kg/m³ (a) Compute the blood pressure in the heart in units of Pa by converting the column of mercury to a pressure using the hydrostatic equation. (b) Compute the blood pressure in the brain (c) Compute the blood pressure in the feet (d) What is the difference in pressure between brain and feet relative to the pressure in the heart and expressed as a percentage?
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Blood pressure in humans is normally expressed as a ratio $x / y,$ where $x$ is the maximum arterial pressure in $\mathrm{mm} \mathrm{Hg},$ called the systolic pressure, and $y$ is the minimum arterial pressure in $\mathrm{mm} \mathrm{Hg},$ called the diastolic pressure. A typical blood pressure is $120 / 70$. Blood pressure readings are normally taken as the same level as the heart, and blood at $37^{\circ} \mathrm{C}$ has a density of around $1060 \mathrm{~kg} / \mathrm{m}^{3}$. (a) Consider a (tall) person whose head is $0.48 \mathrm{~m}$ above her heart and whose toes are $1.46 \mathrm{~m}$ below her heart. Assuming static conditions, compare the blood pressure in her head to the blood pressure in her toes. (b) If a tube were connected to the artery in which the blood pressure was being measured, what would be the maximum height that blood would rise in the tube?
When a person sits erect, increasing the vertical position of their brain by 36.0 $\mathrm{cm}$ , the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 $\mathrm{mL}$ of blood raised 36.0 $\mathrm{cm} ?$ (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.
Calculate the pressure of the blood in the brain and in the feet of a person when standing. The average pressure of the blood in the heart is 1.3×10^4 N/m^2 above atmospheric pressure. The brain is located 0.50 m above the heart and the feet are located 1.2 m below the heart. The density of blood is 1050 kg/m^3. a. Calculate the pressure of the blood in the brain above atmospheric pressure. b. Calculate the pressure of the blood in the feet above atmospheric pressure.
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