If an erect person's systolic pressure is measured at 120 mm-Hg at the level of heart, please calculate the arterial systolic blood pressure in the head of this person (in the unit of mm-Hg). Assume that the head is 50 cm above the heart (the density of blood is 1050 kg/m^3), and 1 mm-Hg = 133 N/m2
To calculate the arterial systolic blood pressure in the head of the person, we need to take into account the difference in height between the heart and the head.
1. First, we need to convert the height from centimeters to meters. Since 1 meter = 100 centimeters, the height of the head is 50 cm / 100 = 0.5 meters above the heart.
2. Next, we need to calculate the pressure difference due to the height difference. We can use the formula: ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of blood, g is the acceleration due to gravity, and h is the height difference.
Given that the density of blood is 1050 kg/m^3 and 1 mm-Hg = 133 N/m^2, we can convert the units to calculate the pressure difference.
Density of blood = 1050 kg/m^3
1 mm-Hg = 133 N/m^2
ΔP = (1050 kg/m^3) * (9.81 m/s^2) * (0.5 m)
= 5147.25 N/m^2
3. Finally, we add the pressure difference to the measured systolic pressure at the level of the heart to get the arterial systolic blood pressure in the head.
Arterial systolic blood pressure in the head = 120 mm-Hg + (5147.25 N/m^2 / 133 N/m^2 per mm-Hg)
= 120 mm-Hg + 38.72 mm-Hg
= 158.72 mm-Hg
Therefore, the arterial systolic blood pressure in the head of this person is approximately 158.72 mm-Hg.