What is the difference in blood pressure (mm-Hg) between the bottom of the feet and the top of the head of a 1.57-m-tall person standing vertically? 1 mm-Hg = 133 N/m2. The density of blood is 1050 kg/m3.
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To calculate the difference in blood pressure (in mm-Hg) between the bottom of the feet and the top of the head of a person standing vertically, we need to consider the change in hydrostatic pressure due to the change in height.
Here's how you can calculate it:
1. Determine the height difference between the bottom of the feet and the top of the head:
Since the person is standing vertically, the height difference would simply be the person's height. So, the height difference is 1.57 m.
2. Convert the height difference to centimeters:
Multiply the height difference by 100 to convert it to centimeters:
Height difference = 1.57 m * 100 cm/m = 157 cm.
3. Calculate the hydrostatic pressure difference:
The hydrostatic pressure difference between two points at different heights can be calculated using the formula:
Pressure difference (P) = (Density of the fluid) * (Gravitational acceleration) * (Height difference).
Given:
Density of blood = 1050 kg/m3,
Gravitational acceleration = 9.8 m/s2 (approximate value).
Convert the density of blood to kg/cm3:
Density of blood = 1050 kg/m3 * (1 cm/100 m)3 = 0.00105 kg/cm3.
Convert the height difference to meters:
Height difference = 157 cm * (1 m/100 cm) = 1.57 m.
Now, calculate the pressure difference using the formula:
Pressure difference (P) = (0.00105 kg/cm3) * (9.8 m/s2) * (1.57 m) = 0.01653 kg/(cm·s2).
4. Convert the pressure difference to mm-Hg:
Since 1 mm-Hg (millimeter of mercury) is equal to 133 newton/m2 (N/m2), we can convert the pressure difference to mm-Hg:
Pressure difference (P, mm-Hg) = (0.01653 kg/(cm·s2)) * (133 N/m2)/(1 mm-Hg) = 2.19 mm-Hg (approximately).
Therefore, the difference in blood pressure between the bottom of the feet and the top of the head of a 1.57 m tall person standing vertically is approximately 2.19 mm-Hg.