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 the blood pressure in the brain would drop to zero for an erect person, we need to consider the hydrostatic pressure in the blood vessels.
The hydrostatic pressure is the pressure exerted by a fluid column due to its weight. In the case of blood pressure, it is caused by the weight of the blood in the vessels. In an erect position, the heart needs to work against gravity to pump blood to the brain, so the blood pressure in the brain is generally higher compared to when lying down.
However, if we consider a situation where there are no body mechanisms operating to compensate for such conditions, we would have to account for the maximum hydrostatic pressure that can be sustained by the blood vessels before blood flow to the brain stops.
The blood vessels in the brain have different levels of resistance, and the resistance becomes increasingly critical as the height of the blood column increases. When the hydrostatic pressure reaches a certain threshold, it can overcome the resistance in the blood vessels, causing blood flow to stop.
To calculate the acceleration at which the blood pressure in the brain would drop to zero, we can equate the hydrostatic pressure to the resistance in the blood vessels. This can be done using the following equation:
Pressure = Density × Gravity × Height
Here, Density represents the density of blood, Gravity is the acceleration due to gravity (approximately 9.8 m/s²), and Height represents the vertical distance or height of the blood column from the heart to the brain.
Assuming the average height of an erect person to be around 1.7 meters, we can substitute the values into the equation and solve for the acceleration:
Pressure = Density × Gravity × Height
0 = Density × 9.8 × 1.7
To find the acceleration (a), we can rearrange the equation:
a = 0 / (density × height)
a = 0 m/s²
From this calculation, it appears that the acceleration required to cause the blood pressure in the brain of an erect person to drop to zero, assuming no compensatory mechanisms, is 0 m/s². This means that any sustained acceleration in the upward direction greater than 0 m/s² would cause the blood pressure to drop to zero.