At what acceleration would you expect the blood pressure in the brain to drop to zero for an erect person? Why?
(Assume there are no body mechanisms operating to compensate for such conditions)
To determine the acceleration at which blood pressure in the brain would drop to zero for an erect person, we would need to analyze the factors involved in blood pressure regulation.
In an erect position, blood pressure is primarily regulated by the difference in the height of the heart and the brain. When standing, the height difference between the heart and brain results in a hydrostatic pressure gradient that helps maintain blood supply to the brain.
The key concept here is that for blood pressure in the brain to drop to zero, the hydrostatic pressure gradient between the heart and brain would need to be eliminated. Therefore, we need to consider the height difference between the heart and brain, as well as the gravitational acceleration.
The average height of the heart above the head is approximately 1.5 feet or 0.45 meters. Now, to calculate the acceleration required for the blood pressure in the brain to drop to zero, we can utilize the equation:
ΔP = ρgh
Where:
ΔP is the pressure difference,
ρ is the density of blood (roughly 1,060 kg/m³),
g is the acceleration due to gravity,
and h is the height difference between the heart and brain.
Rearranging the equation to solve for g, we get:
g = ΔP / (ρh)
Considering a typical blood pressure of 120 mmHg (millimeters of mercury), the pressure difference (ΔP) would be 120 mmHg. Converting this to the SI unit (pascal), the pressure difference becomes approximately 16,000 Pa.
Plugging in the values, we have:
g = 16,000 Pa / (1,060 kg/m³ * 0.45 m)
Simplifying the equation, we find that the acceleration required for the blood pressure in the brain to drop to zero for an erect person is approximately 32.85 m/s².
So, if an erect person were subjected to an acceleration of approximately 32.85 m/s² or higher, their blood pressure in the brain would be expected to drop to zero.