Explanation for moving fluids having lower pressure

denjay

I've known this fact for a long time and have thought about an explanation for it for just as long. I've observed its effects such as in the shower: as the water flows down it moves the air with it causing the curtain to move inward into the shower. It just seems that with a moving fluid that, if anything, it would create a higher pressure and push things outward.

I cannot come up with an explanation with my intuition so I'm asking for one.

What is the physical explanation for moving fluids having lower pressures?

Drakkith

Are you sure of this? I was under the impression that it was because your shower is normally hot, thus the hot air rises and cool air comes in to the shower to replace it, putting pressure on the curtain.

I can't say for sure, but the wiki article on the Venturi effects states that as the velocity increases the static pressure must decrease in order to obey the conservation of mechanical energy.

Studiot

Hello denjay,

Not sure at what level to pitch this since your physics education is uncertain in your profile (no criticism intended).

Imagine a parcel of fluid at rest, in say a tank.

That fluid has gravitational potential energy, due to its elevation above the centre of the earth. However the top surface of the fluid is further from the centre of the earth than the bottom surface so has more potential energy.

The difference in the potential energies of the top and bottom is held within the fluid as pressure.
We calculate this as the weight of the fluid immediately above a unit square at the bottom. This weight is given by volume of the fluid times its density.
In the case of water in a tank this is proportional to the elevation difference.

Pressure at bottom (or any point ) = density times g times distance down from the surface = ρgh


Now imagine that a tap in the bottom is opened and the water flows out.
since the water is now moving it now possesses kinetic energy.
This kinetic energy has to come form somewhere and it comes from a result in the static potential energy (pressure) of the fluid.

This is known as Bernoulli's theorem.

That the total energy of the parcel is constant.

denjay

Thanks, Studiot.

Makes sense to me.

I should probably state somehow where I am in my education (just starting upper level classes for the record).

Studiot

We can go a little further if you like, without much maths.

The total energy in our parcel of fluid has three components

1)The 'absolute' potential energy due to its height above the centre of the earth (or other reference level)

2) The static pressure due to the weight of fluid above it

3) The kinetic energy of motion due to its velocity.

The sum of these is constant (at constant temperature we can add more energy by heating)

We measure these in the same units to be able to put them together in an equation and it is usual to do this as a distance - what is known as pressure head.

So


[tex]H = z\; + \;\frac{p}{w}\; + \;\frac{{{v^2}}}{{2g}}\; = \;{\rm{constant}}[/tex]


H is known as the total head,
z is the height above datum
p/w is the pressure head and is the static pressure per unit weight
v²/2g is the kinetic energy expressed as the velocity head

Notice that all the terms have the dimensions (units) of length.

This is Bernoulli's equation.

cjl

Studiot's explanation is a good one, and conservation of energy is (in my opinion) the easiest way to visualize this. One important piece that is often missed is that because this is a conservation relation, it only applies to a given parcel of fluid in the absence of any energy loss or gain mechanisms. So, if the fluid passes through a fan, it accelerates, but the pressure doesn't necessarily drop (since it was given energy by the fan). Similarly, the pressure inside your car isn't higher than the pressure outside, even though (from the frame of reference of the car) the air outside is moving. This is because the parcels of air inside the car are different from the parcels of air outside the car, so conservation of energy doesn't say anything about their energy relative to each other.

On the other hand, in a hose with a narrower region and a wider region, the same parcel of fluid passes through both regions, and no energy is gained or lost (assuming inviscid flow), so in this case, you can apply the bernoulli relation and (correctly) surmise that the pressure is lower in the narrower part of the tube, where the flow speed is higher.

H2Bro

Quick joiner question: is this the same mechanism that explains lift on airplane wings?

Studiot

I hesitate to answer this but yes and no - it's complicated.

A simple view is that the air flows faster over the top surface than the bottom so has greater kinetic energy than the underside air so more of its constant head is taken up with KE. So the 'static' pressure head is less on top than underneath. So there is a net upthrust we call lift.

However a word of caution - friction, in the guise of viscosity, and non laminar flow also play a part so - it's complicated.

H2Bro

I recall having a very false theory of lift taught to me back in high school, that a parcel of air when seperated by a wing for some reason must re-form afterwards, entailing the upper portion to travel along the curved wing faster owing to the larger distance.

Which is totally wrong, because the air need not rejoin after separation.

The curvature of a wing plays an important role, but I also know that for some jet fighters the wings don't have significant curvature, instead relying on a high angle-of-attack to generate lifting by basically deflecting air downwards.

Studiot

jet fighters move faster than the air or pressure waves can.

H2Bro

Not when they're taking off.

Studiot

The airflow above the lift surface is undoubtedly faster than the airflow beneath which, as I said, leads to a measurable pressure difference that leads to lift by Bernoulli.

The story of separation and recombination is just a fairy story.

If you want to understand what causes the speed difference you need to understand the mathematics of circulation.

Further discussion of that would really be Hijacking this thread so you would need to start a new one or do a forum search as this question has arisen here before and there has been at least one quite long discussion.

denjay

This is getting slightly more complex than I thought it would.

What explains the fact that paper will fly upwards when you hold it up against your mouth and blow?

If what you said is true (I'm not saying it isn't, I'm sure it is), then, as applied to this situation, the paper would not move as there is no drop in pressure since there there is energy coming from your lungs.

H2Bro

Thanks Studiot, I had a feeling the separation/recomb. was a bit nonsensical. Apologies for getting off-topic, but it seemed related by the Bernoulli mechanism / formula.

Aero51

Believe it or not there is not set theory on how lift is generated. We have a very good mathematical expression, circulation, which is essentially a measure of the rotationality of the air around the wing. If you were to subtract the freestream velocity (the speed of the wing) from the velocity vector field you would find that the vectors form a circular pattern: pointing upwards at the leading edge, backwards at the top (with the freestream flow), downward at the trailing edge, and forwards (against the freestream flow).

Lift is therefore generated through a combination of the conservation of momentum and pressure gradients along the wing. This is not a very specific explanation, but I have yet to find a better one.

Note that changes in pressure due to changes fluid velocity above the wing are insufficient to account for the total lift of a wing generated. Bernoulli's equation is thus not an accurate model of air moving over a wing. On the other hand, potential flow, which uses potential equations to describe flow patterns, is a model that uses Bernoulli's theorem for ideal (no viscosity, no heat transfer, all molecular kinetic energy is translational) fluid behavior.

Aero51

This is because at supersonic speeds a curved airfoil will generate negative lift. Usually hexagonal airfoils at a slight angle of attack is all that is needed to generate lift. Aircraft like the Concord or the Mirage employ vortex lift generated from low aspect ratio wings. It is also possible to use "compression lift", as the XB-70 used, to generate lift from the shockwaves produced under the wing without a significant drag rise.

cjl

I'm not entirely sure, but if I had to guess, I would say that the reason the paper flies upwards is because the air you are blowing along the curved surface will tend to follow the curvature. This causes the air to accelerate, transferring some static pressure to dynamic pressure, and thus causing a low pressure region above the paper. This is just an off-the-cuff guess though, so I could very well be wrong.