Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

(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

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

Step by step solution

01

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.
02

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.
03

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.
04

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.
05

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.
06

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) As you can tell by watching them in an aquarium, fish are able to remain at any depth in water with no effort. What does this ability tell you about their density? (b) Fish are able to inflate themselves using a sac (called the \(swim\) \(bladder\)) located under their spinal column. These sacs can be filled with an oxygen\(-\)nitrogen mixture that comes from the blood. If a 2.75-kg fish in freshwater inflates itself and increases its volume by 10%, find the \(net\) force that the \(water\) exerts on it. (c) What is the net \(external\) force on it? Does the fish go up or down when it inflates itself?

A piece of wood is 0.600 m long, 0.250 m wide, and 0.080 m thick. Its density is 700 kg/m\(^3\). What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just even with the water level? What is the mass of this volume of lead?

A solid aluminum ingot weighs 89 N in air. (a) What is its volume? (b) The ingot is suspended from a rope and totally immersed in water. What is the tension in the rope (the \(apparent\) weight of the ingot in water)?

A closed and elevated vertical cylindrical tank with diameter 2.00 m contains water to a depth of 0.800 m. A worker accidently pokes a circular hole with diameter 0.0200 m in the bottom of the tank. As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure of 5.00 \(\times\) 10\(^3\) Pa at the surface of the water. Ignore any effects of viscosity. (a) Just after the hole is made, what is the speed of the water as it emerges from the hole? What is the ratio of this speed to the efflux speed if the top of the tank is open to the air? (b) How much time does it take for all the water to drain from the tank? What is the ratio of this time to the time it takes for the tank to drain if the top of the tank is open to the air?

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m\(^2\), and the magnitude of the fluid velocity is 3.50 m/s. (a) What is the fluid speed at points in the pipe where the cross- sectional area is (a) 0.105 m\(^2\) and (b) 0.047 m\(^2\)? (c) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free