Follow-up Question to: The Concept of Pressure in Bernoulli’

In summary, the relationship between pressure and velocity in Bernoulli's equation can be explained through the concept of dynamic pressure, which is equal to the increase in pressure that could potentially be achieved if the fluid motion were stopped. This is different from static pressure, which pushes in all directions, as dynamic pressure only pushes in the direction of its velocity. However, it is not considered a real pressure as it is a measure of kinetic energy and does not have direction. This is why it does not contribute to making the column of water above it go up.
  • #1
rdgn
9
0
I have been looking all over the net for answers for the unintuitive relationship between pressure and velocity in Bernoulli's equation and this thread (https://www.physicsforums.com/threads/the-concept-of-pressure-in-bernoullis-principle.585231/) answered most of my questions.

I have one last question lingering in my mind though. What exactly is the difference between static and dynamic pressure?

bernoullis-principle-3-638.jpg
The examples here: http://www.engineeringtoolbox.com/dynamic-pressure-d_1037.html
Hint that there is nothing magical about dynamic pressure. Same units, same effect.

Except that (from what I think) in contrast to static pressure that pushes in all directions, dynamic pressure only pushes in the direction of its velocity.
It's as if the pressure that was supposed to be pushing in all directions, some of that pressure is being converted into pressure that acts in only one direction by virtue of the shape of the tube?
Is this correct? Or am I wrong?

Thanks
 
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  • #2
rdgn said:
dynamic pressure only pushes in the direction of its velocity.
Why would you say that? Have you read that explicit statement anywhere? Think Newton's Third Law.
 
  • #3
No, it's just something I've thought of since if dynamic pressure also behaves the same way as static pressure, then in the diagram of my first post, all three water levels should be equal right?

I'm not really sure about this to be honest, and you're hinting that it's probably wrong.
The way I came up with this explanation is, by Bernoulli's equation, the total pressure in any cross-section is equal throughout a pipe.
If the total pressure throughout the pipe is the same, then it doesn't make sense that the water levels due to pressure would be unequal.

For example:
PS1, PV1 = Static, velocity pressure for wider part
PS2, PV2 = Static, velocity pressure for wider part
PS1 + PV1 = PS2 + PV2

PS1 > PS2
PV2 > PV1

Their total pressures are the same but the amount of water pushed upwards is different.
The amount of water pushed in '1' is greater than '2'. The only quantity that's greater in 1 is PS1, so I assume it's the quantity responsible for pushing the column of water upwards.

What would be a better way of thinking about static vs velocity pressure?
 
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  • #4
Dynamic pressure is the same as the "kinetic energy per unit volume" of a fluid. It is not real pressure...yet. It is equal to the increase in pressure that could potentially be achieved if the fluid motion were stopped. Since it is a measure of kinetic energy, it does not have direction.
 
  • #5
I see. That makes more sense, thanks!

I guess that's the reason it doesn't contribute to making the column of water above it go up right?
 

Related to Follow-up Question to: The Concept of Pressure in Bernoulli’

1. What is Bernoulli's principle and how does it relate to pressure?

Bernoulli's principle states that as the velocity of a fluid increases, the pressure decreases. This is based on the conservation of energy in a fluid flow. In other words, as a fluid speeds up, the kinetic energy of the fluid increases while the potential energy (pressure) decreases.

2. How does Bernoulli's principle explain the lift of an airplane?

Bernoulli's principle plays a crucial role in explaining the lift of an airplane. The shape of an airplane's wing is designed to create a faster flow of air on the top surface compared to the bottom surface. This creates a difference in pressure, with lower pressure on top and higher pressure on the bottom, causing the wing to lift up.

3. Can Bernoulli's principle be applied to non-ideal fluids?

While Bernoulli's principle is often demonstrated using ideal fluids, it can also be applied to non-ideal fluids. However, in non-ideal fluids, other factors such as viscosity and turbulence may also play a role in the flow and pressure distribution.

4. How is pressure related to the velocity of a fluid in Bernoulli's principle?

Pressure and velocity are inversely related in Bernoulli's principle. As the velocity of a fluid increases, the pressure decreases. This is because the faster-moving fluid particles exert less pressure on their surroundings compared to slower-moving particles.

5. How is Bernoulli's principle used in real-world applications?

Bernoulli's principle has various applications in real-world situations, such as in airplane and car design, the functioning of carburetors and atomizers, and the measurement of airspeed in pitot tubes. It is also used in the design of ventilation systems and air conditioning units.

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