Question

(a) What is the \(difference\) between the pressure of the blood in your brain when you stand on your head and the pressure when you stand on your feet? Assume that you are 1.85 m tall. The density of blood is 1060 kg/m\(^3\). (b) What effect does the increased pressure have on the blood vessels in your brain?

Short answer

The pressure difference is 19235.97 Pa. The increased pressure might dilate or burst brain blood vessels.

Step-by-step solution

Define the Variables

First, we will define the variables needed to solve the problem. We have the height, \( h = 1.85 \) m, and the density of blood, \( \rho = 1060 \) kg/m\(^3\). We also need the acceleration due to gravity, \( g = 9.81 \) m/s\(^2\), which is a constant.

Understand Pressure Change

Pressure due to a fluid column is given by the formula \( P = \rho g h \). When standing on feet, the brain is at an elevation of \(1.85\) m from the feet, and when standing on the head, the elevation difference would be the same but in the opposite direction, so \(h = 0\) for the brain.

Calculate Pressure While Standing on Feet

While standing on feet, \(h = 1.85\) m. So, the pressure in the brain is \( P_{feet} = \rho g h = 1060 \times 9.81 \times 1.85 \). Calculate this value.

Calculate Pressure While Standing on Head

While standing on the head, the brain's elevation compared to the feet is \( h = 0 \). Therefore, \( P_{head} = \rho g \cdot 0 = 0 \). The pressure contribution from the column height is zero.

Determine the Difference in Pressure

The difference in pressure \( \Delta P \) is given by \( P_{feet} - P_{head} = 1060 \times 9.81 \times 1.85 \). Calculate this to find the pressure difference.

Analyze the Effects on Blood Vessels

The increased pressure from standing on your head results in a significant increase in blood vessel pressure in the brain. This can lead to dilation or potential bursting of blood vessels because they are not accustomed to handling such increased pressure.

Key concepts

Hydrostatic Pressure

Hydrostatic pressure is a fundamental concept in fluid dynamics. It is the pressure exerted by a fluid due to the force of gravity. This pressure depends on the density of the fluid, gravity, and the height of the fluid column above the point in question.
For any fluid at rest, hydrostatic pressure can be calculated using the formula: \[ P = \rho g h \] where

• \( \rho \) is the fluid density
• \( g \) is the acceleration due to gravity
• \( h \) is the height of the fluid column

In the context of our exercise, when a person stands on their feet, their brain experiences hydrostatic pressure due to the column of blood from the heart to the brain. However, when upside down, the pressure changes because the height of the blood column relative to the brain is negligible.

Blood Pressure

Blood pressure is the force exerted by circulating blood on the walls of blood vessels. It is an essential part of how the cardiovascular system functions. Blood pressure varies within the body depending on the height and orientation of different body parts.
A key point in understanding this exercise is recognizing that blood pressure in the brain changes based on whether you're upright or inverted. This happens because the blood column height from the heart to the brain changes drastically.
When standing upright, the height-related component increases the pressure in the brain. Whereas in an inverted position, the height is minimized, thereby reducing or altering the distribution of that pressure.

Impact on Blood Vessels

The pressure changes in blood flow directly impact blood vessels. Blood vessels are designed to withstand normal pressure; however, they can respond adversely to significant pressure changes.
When standing on your head, the blood vessels in the brain can experience increased pressure due to the gravitational pull on the entire column of blood. This can lead to serious consequences, such as the dilation or even rupture of vessels if the vessel walls cannot accommodate the increased load.
This phenomenon is a prime example of how bodily orientation and gravity affect physiological functions, particularly affecting sensitive structures like the blood vessels in the brain.

Effect of Gravity on Fluids

Gravity plays a crucial role in fluid dynamics. It affects how fluid pressures are developed and maintained within the body. In terms of human physiology, gravity's effect means that fluids like blood will tend to exert more pressure in parts of the body that are lower in a gravitational field.
In an upright position, blood is under more pressure in the lower body, meaning the heart has to work hard to push it upwards against gravity. In contrast, when inverted, gravity assists in the movement of blood to the head, leading to potential overpressure in cerebral vessels.
As a result, our bodies have mechanisms, like valves in veins, to manage these pressure differences. These allow the maintenance of appropriate blood flow and pressure, although sudden changes in position can sometimes temporarily overwhelm these mechanisms.