Suppose you measure a standing person's blood pressure by placing the cuff on his leg 0.580 m below the heart. Calculate the pressures you would observe if the pressures at the heart are 121 over 80 mm Hg. Assume there is no loss of pressure due to resistance in the circulatory system (a reasonable assumption, since major arteries are large).

The answer is supposed to be in mmHg over mmHg. I don't even know where to begin.

To solve this problem, we need to consider the effect of hydrostatic pressure on blood pressure. Blood pressure is typically measured at the level of the heart, which is the reference point for measuring blood pressure. However, if we measure blood pressure at a different location, such as the leg in this case, we need to take into account the difference in height.

The hydrostatic pressure due to the column of blood is directly proportional to the height difference. The formula to calculate the hydrostatic pressure is:

P = ρgh

Where:
P is the pressure
ρ (rho) is the density of the fluid (in this case, blood)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height difference relative to the reference point (in this case, the heart)

To solve this problem, we'll need to convert the given height difference from meters to millimeters, as the desired answer is in mmHg over mmHg.

Given:
Height difference (h) = 0.580 m
Pressure at the heart = 121/80 mmHg

First, we need to convert the height difference from meters to millimeters:
0.580 m * 1000 mm/m = 580 mm

Next, we need to calculate the hydrostatic pressure difference:
ΔP = ρgh

Using the density of blood, which is approximately 1050 kg/m^3, and the acceleration due to gravity (g = 9.8 m/s^2), we can calculate the pressure difference:

ΔP = 1050 kg/m^3 * 9.8 m/s^2 * 0.580 m
= 6,006.6 N/m^2

To convert the pressure difference in pascals to mmHg, we can use the following conversion factor:
1 mmHg = 1,333.22 N/m^2 (approximately)

ΔP in mmHg = (6,006.6 N/m^2) / (1,333.22 N/m^2/mmHg)
≈ 4.51 mmHg

Now, we need to calculate the observed blood pressure at the leg by subtracting the pressure difference from the pressure at the heart:

Observed blood pressure = Pressure at the heart - Pressure difference
= 121/80 mmHg - 4.51 mmHg
= 116.49/75.49 mmHg

Therefore, the pressures you would observe when measuring blood pressure at the leg, 0.580 m below the heart, would be approximately 116.49/75.49 mmHg.