Suppose you measure a standing person's blood pressure by placing the cuff on his leg 0.470 m below the heart. Calculate the pressures you would observe if the pressures at the heart are 119 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).
760mmHG is equvalent to 13.6*.760 m =10.34mH2O
so add .470/10.34 *760mmHg to each of the readings. I get about 34.6mmHg added.
To calculate the pressures you would observe at the leg cuff, we can use the hydrostatic pressure formula:
P = P₀ + ρgh
Where:
P is the pressure at the leg cuff
P₀ is the initial pressure at the heart
ρ is the density of the blood
g is the acceleration due to gravity
h is the vertical distance between the heart and the cuff
Given:
P₀ = 119 mm Hg (systolic pressure)
P₁ = 80 mm Hg (diastolic pressure)
h = 0.470 m
First, we need to convert the pressures from mm Hg to Pa (Pascal) since we'll be using SI units for the formula.
1 mm Hg = 133.32 Pa
Now we can calculate the pressures:
Systolic Pressure:
P_systolic = P₀ + ρgh
= 119 mm Hg * (133.32 Pa/mm Hg) + (density of blood) * 9.8 m/s^2 * 0.470 m
Diastolic Pressure:
P_diastolic = P₁ + ρgh
= 80 mm Hg * (133.32 Pa/mm Hg) + (density of blood) * 9.8 m/s^2 * 0.470 m
Keep in mind that we still need to determine the density of blood and convert the pressures from Pascal to mm Hg at the end of the calculations.
To calculate the pressures observed when measuring blood pressure at a specific location in the body, we need to take into account the hydrostatic pressure and the pressure due to the heart.
The hydrostatic pressure is the pressure due to the weight of a fluid. In this case, it is the pressure resulting from the weight of the blood column above the measurement location. The height difference between the heart and the measurement location is 0.470 m.
We can calculate the hydrostatic pressure using the formula:
P = ρgh
where P is the hydrostatic pressure, ρ is the density of blood, g is the acceleration due to gravity, and h is the height difference.
Given:
Height difference (h) = 0.470 m
Pressure at heart = 119 mm Hg (systolic) / 80 mm Hg (diastolic)
First, we need to convert the pressures at the heart from mm Hg to Pascal (Pa) since the hydrostatic pressure will be in Pa. We can use the conversion factor: 1 mm Hg = 133.322 Pa.
Pressure (systolic) at heart = 119 mm Hg * 133.322 Pa / 1 mm Hg = 15,898.82 Pa
Pressure (diastolic) at heart = 80 mm Hg * 133.322 Pa / 1 mm Hg = 10,665.76 Pa
Next, we can calculate the hydrostatic pressure at the measurement location:
P = ρgh
where ρ is the density of blood (approximately 1,060 kg/m³) and g is the acceleration due to gravity (approximately 9.8 m/s²).
P = 1060 kg/m³ * 9.8 m/s² * 0.470 m = 4,904.52 Pa
Finally, we can add the hydrostatic pressure to the pressures at the heart to calculate the observed pressures at the measurement location.
Observed Systolic Pressure = Pressure (systolic) at heart + Hydrostatic Pressure
Observed Diastolic Pressure = Pressure (diastolic) at heart + Hydrostatic Pressure
Observed Systolic Pressure = 15,898.82 Pa + 4,904.52 Pa = 20,803.34 Pa
Observed Diastolic Pressure = 10,665.76 Pa + 4,904.52 Pa = 15,570.28 Pa
Converting the observed pressures back to mm Hg, we get:
Observed Systolic Pressure = 20,803.34 Pa / 133.322 Pa/mm Hg ≈ 156 mm Hg
Observed Diastolic Pressure = 15,570.28 Pa / 133.322 Pa/mm Hg ≈ 117 mm Hg
Therefore, if you measure a standing person's blood pressure by placing the cuff on their leg 0.470 m below the heart, you would observe a blood pressure of approximately 156 mm Hg (systolic) over 117 mm Hg (diastolic).