Questions about pressure

[boxerfangg]

I had a couple of lessons about pressure at my high school last week and my teacher taught us some principles but not why they are true.

 

Why is this statement true: Pascal's principle : Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container.

Why is pressure transmitted? Why not force?

 

 

Why is this statement true: Archimedes principle : An object that is partly or completely submerged in a fluid will experience a buoyant force equal to the weight of the fluid the object displaces.

 

 

Why is the buoyant force equal to the weight of the fluid the object displaces? And why is there a buoyant force at all? Why do less dense things float and more dense things sink?

 

Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluids potential energy. Why is this true? And what is a fluids potential energy?

 

 

I was also told that pressure will act in all directions equally at a certain depth. Why is this? Why is the pressure on the wall of the container the same as the pressure on an object at the same depth?

 

I was also wondering why fluids exert pressure on their container (why do fluids take the shape of their container?).

Why is there more pressure in a can when the gas inside is compressed?

 

This pressure stuff confuses and frustrates me. Any help is appreciated.

[Schrödinger's hat]

I had a couple of lessons about pressure at my high school last week and my teacher taught us some principles but not why they are true

...

 

This pressure stuff confuses and frustrates me. Any help is appreciated.

 

 

Okay, I'll use a particle model of a fluid for this explanation. Imagine it as a bunch of slippery balls which are jiggling about a little bit and can slide past each other freely.

I might also re-order your questions a bit to try and answer them coherently.

 

I was also wondering why fluids exert pressure on their container (why do fluids take the shape of their container?).

 

Imagine some sand (or our balls) being placed into a container in a big stack in the middle.

Give it a bit of a shake, anywhere the balls aren't pushing against something (the edges or another ball) they'll tend to move out.

This will keep happening until they are pushing against something, so the end result is they'll spread out and flatten until they are bumping into the container everywhere below the surface, and the top is flat.

 

Why is this statement true: Pascal's principle : Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container.

Why is pressure transmitted? Why not force?

 

Pressure is the force acting inward from all directions on something in the fluid.

Imagine all our balls bumping and pushing against each other. If there is more pushing on one side than another, the ball will move. Eventually things will reach an equilibrium where everything is bumping into everything else equally so there is no net force (although there are many forces acting inwards ie. pressure).

 

Let's ignore gravity for the moment.

 

If I exert a force on some part of the fluid (let's say with my hand), one of two things will happen:

The fluid will get out of the way.

I'll momentarily but an uneven force on some of the balls, they'll move, bump into others and so on until things are in equilibrium again.

 

Or the fluid will have nowhere to go.

In this case my hand will not move into the fluid, I'll meet resistance.

I'll push balls I am touching which will push harder on the balls they are touching and so on until they are all pushing on each other or the walls of the container by the same amount.

If this didn't happen then the balls would move, but they cannot move (well, individually they can, but there'd just be another ball there to take its place if the fluid as a whole has nowhere to go) so the pressure increases.

 

Why is there more pressure in a can when the gas inside is compressed?

 

You can modify our model a bit for a gas. Instead of having the balls mostly touching, they're all whizzing about at roughly the same speed (on average).

When they bang into something and turn around they exert a small impulse (force for a tiny bit of time).

This happens so often that the result is a fairly steady average force.

The faster they move, the stronger each individual force (so high temp = more pressure).

Also if you confine them to a tighter space, they bang into the walls more often, so there are more impulses, increasing the average force.

 

Back to liquids:

 

I was also told that pressure will act in all directions equally at a certain depth. Why is this? Why is the pressure on the wall of the container the same as the pressure on an object at the same depth?

 

Before with my no-gravity example, all the forces from the bumping exactly cancelled.

Once we include gravity, this can't be the case.

 

If we had the same force on a ball from every direction (excluding gravity), it would still accelerate downwards. So the bumping from below must be stronger than the bumping from above (you can see that this must be true for the top layer in a liquid because there is nothing on top).

Then the next layer down has enough pressure on it to hold up the stuff above it and keep itself still, but then it has to hold itself up as well, so there is even more pressure on the layer below.

And so on.

 

A slightly different picture/way of wording is that all the horizontal forces cancel out exactly, but there has to be more force from the layer below than from the layer above to cancel gravity.

 

Why is this statement true: Archimedes principle : An object that is partly or completely submerged in a fluid will experience a buoyant force equal to the weight of the fluid the object displaces.

 

 

Why is the buoyant force equal to the weight of the fluid the object displaces? And why is there a buoyant force at all? Why do less dense things float and more dense things sink?

 

From the explanation above we have that the increase in pressure as you go down matches the weight of the fluid.

So the bumping on the bottom part of an object would be more than the bumping on the top part.

If the object is lighter than the fluid, then this will be more than is required to cancel the gravity, so it will accelerate up.

If the object is heavier, it will be less than is required to cancel gravity, so it will accelerate down.

 

This force comes from the fluid coming into equilibrium (not accelerating on average), so the force (difference in pressures, or difference in force) must be exactly enough to cancel something the same density as the fluid (ie. the buoyant force is equal to the weight of the fluid displaced).

 

Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluids potential energy. Why is this true? And what is a fluids potential energy?

 

Hmm, I can't think of a good way to fit this one into my analogy.

The best explanation comes from conservation of energy.

If you look at all the types of energy in a fluid (pressure, gravitational potential, kinetic energy) then the total must remain constant.

So if one increases (kinetic) then another must decrease.

 

 

If any of this is still unsatisfying, feel free to ask some more. Further questions may help improve my explanation

Edited December 3, 2011 by Schrödinger's hat

[DrRocket]

I had a couple of lessons about pressure at my high school last week and my teacher taught us some principles but not why they are true.

 

Why is this statement true: Pascal's principle : Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container.

Why is pressure transmitted? Why not force?

 

Pressure is part of the stress state of a material. Because liquids and gasses cannot support shear, it describes the stress state in such materials. The dimensions of stress are force per unit area. Force is not reflected directly in stress.

 

 

Why is this statement true: Archimedes principle : An object that is partly or completely submerged in a fluid will experience a buoyant force equal to the weight of the fluid the object displaces.

 

 

Why is the buoyant force equal to the weight of the fluid the object displaces? And why is there a buoyant force at all? Why do less dense things float and more dense things sink?

 

Archiimedes principle is easily derived from Pascal's Principle. I leave to to you as and exercise to do just that.

 

Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluids potential energy. Why is this true? And what is a fluids potential energy?

This results from simple principles of thermodynamics. You may not yet be ready for thermodynamics but if you feel that you are then you can read, for instance, Elements of Thermodynamics and Heat Transfer by Obert and Young.

 

 

equally at a certain depth. Why is this? Why is the pressure on the wall of the container the same as the pressure on an object at the same depth?

See Pascal's Principle

 

I was also wondering why fluids exert pressure on their container (why do fluids take the shape of their container?).

Why is there more pressure in a can when the gas inside is compressed?

 

This pressure stuff confuses and frustrates me. Any help is appreciated.

 

Try reading a good book. You have asked the same question several times, all depending on Pascal's Principle. You can start by studying those questions and recognizing why they are the same.

 

It is important to recognize that the laws of classical physics are all derivable from a very few basic principles. What you should learn in a good physics class is what the basic principles really are and how other useful results, like Pascal's Principle, are derived from them. To do that you have to become able to derive those results for yourself.