Question

Suppose you measure a standing person’s blood pressure by placing the cuff on his leg 0.485 m below the heart. For this problem, assume that there is no loss of pressure due to resistance in the circulatory system (a reasonable assumption, since major arteries are large). The density of blood is 1.05×10³kg/m³.

Calculate the systolic pressure you would observe, in units of mm Hg, if the pressure at the heart was 120 over 80 mm Hg. Note that the top (and greater) number is the systolic pressure.

Answer 1

To calculate the pressure observed when measuring a person's blood pressure on their leg, we use the equation Pressure = ρgh, where ρ is the density of blood, g is the acceleration due to gravity, and h is the height difference between the heart and the leg.

Step-by-step explanation:

To calculate the pressure observed when measuring a standing person's blood pressure on their leg, 0.500 m below the heart, we use the equation:

Pressure = ρgh

Where:

• ρ is the density of blood (1.05 x 10^3 kg/m^3)
• g is the acceleration due to gravity (9.8 m/s^2)
• h is the height difference between the heart and the leg (0.500 m)

Using the given values, we can substitute them into the equation to find the pressure observed.

Answer 2

If the blood pressure at the heart is 120/80 mm Hg, measuring it at the leg, 0.485 m below the heart, would result in a systolic pressure of approximately 129 mm Hg and a diastolic pressure of around 89 mm Hg.

Step-by-step explanation:

The blood pressure in a column of fluid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the column. In this case, the column of blood extends from the heart to the leg, with the cuff placed 0.485 m below the heart. The systolic pressure at the heart is 120 mm Hg, so we can use this information to find the pressure at the leg.

For the systolic pressure, we add the pressure due to the height of the column to the initial pressure at the heart. Using the formula P = ρgh, we calculate the pressure at the leg for both systolic and diastolic values. The density of blood, ρ, is given as 1.05 × 10³ kg/m³, and the acceleration due to gravity, g, is approximately 9.8 m/s². By substituting these values into the equation, we find that the systolic pressure at the leg is approximately 129 mm Hg, and the diastolic pressure is around 89 mm Hg.

This calculation assumes ideal conditions, without accounting for factors such as the elasticity of arteries or the resistance in the circulatory system. Nevertheless, it provides a reasonable estimate of the pressure difference due to the height of the blood column between the heart and the measurement site.