Why pressure decreases with increase in velocity

[Villa]

We know that pressure= force/area...
If the area of the pipe is reduced then the pressure must increase... But according to Bernoulli's, the pressure will decrease ... How is it?

 

[boneh3ad]

We know that pressure= force/area...
If the area of the pipe is reduced then the pressure must increase... But according to Bernoulli's, the pressure will decrease ... How is it?

Force has nothingn to do with it. It really has to do with energy. A given fluid flow has a finite pool of energy, and that pool comes from the energy stored as pressure and the kinetic energy of the moving fluid. If the flow encounters a constriction, the velocity must increase due to mass conservation. That increased velocity means the flow has more kinetic energy. That energy had to come from somewhere, so the pressure has to drop to match that energy change.

 

[Villa]

Pressure is defined as force per unit area..(i.e) the average force exerted by liquid molecules on the surface of the pipe per unit area... If i reduce the area then there should be more collisions and hence pressure should increase...

 

[boneh3ad]

Pressure is defined as force per unit area..(i.e) the average force exerted by liquid molecules on the surface of the pipe per unit area... If i reduce the area then there should be more collisions and hence pressure should increase...

Pressure can also be defined as energy per unit volume.

 

[russ_watters]

Pressure is defined as force per unit area..(i.e) the average force exerted by liquid molecules on the surface of the pipe per unit area... If i reduce the area then there should be more collisions and hence pressure should increase...

"If I reduce the area" means you are altering the piping configuration between the two cases. Bernoulli's Principle applies to one one piping configuration at a time: you are misusing it.

 

[Chestermiller]

The fluid does not just exert pressure force on the walls of the pipe. It also exerts pressure on the fluid ahead of it and behind it. If fluid is flowing in a pipe, and the pipe diameter is decreasing in the direction of flow, the fluid is accelerating in the direction of flow. In order to bring about this acceleration, the upstream force must be higher than the downstream force. This means that the upstream pressure times cross sectional area must be higher than the downstream pressure times cross sectional area. But the area decrease is not enough to provide all the force necessary. So the pressure must also be decreasing along the pipe.

Chet

 

[Villa]

I saw someone saying that " if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases " ... Is this correct... It seems to be logical...

 

[Chestermiller]

I saw someone saying that " if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases " ... Is this correct... It seems to be logical...

It doesn't seem logical to me in any sense.

Chet

 

[jtdrexel]

It doesn't seem logical to me in any sense.

Chet

@Chestermiller: Villa asked if it made sense that "if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases ". And you said It doesn't seem logical in any sense. Why not? I would think that in static a condition like a sealed box with air in it, pressure is contributed by molecules bouncing off walls, ie: at any given instant on average, equal parts of molecules are hitting each wall in the box. In a flow condition, the trajectory of most molecules are in the direction of flow and not much bouncing off the wall. Ie: if two opposing sides of the box was removed and air is allowed to flow through, then now the #-of-molecules per unit area per unit time hitting the walls of the box would be reduced than in the static condition. Please explain how this simple argument does not make any sense.

 

[jbriggs444]

@Chestermiller: Villa asked if it made sense that "if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases ". And you said It doesn't seem logical in any sense. Why not? I would think that in static a condition like a sealed box with air in it, pressure is contributed by molecules bouncing off walls, ie: at any given instant on average, equal parts of molecules are hitting each wall in the box. In a flow condition, the trajectory of most molecules are in the direction of flow and not much bouncing off the wall. Ie: if two opposing sides of the box was removed and air is allowed to flow through, then now the #-of-molecules per unit area per unit time hitting the walls of the box would be reduced than in the static condition. Please explain how this simple argument does not make any sense.

Given a fixed temperature, the molecules have the same average kinetic energy and hence velocity relative to the flow. This means that their velocity perpendicular to the flow is unchanged. Given a fixed density, the molecules have the same spacing along the flow. How then could pressure change?

Edit: Whoops, responded to a necro-post.

 

[jtdrexel]

Given a fixed temperature, the molecules have the same average kinetic energy and hence velocity relative to the flow. This means that their velocity perpendicular to the flow is unchanged. Given a fixed density, the molecules have the same spacing along the flow. How then could pressure change?

Edit: Whoops, responded to a necro-post.

Why would velocity perpendicular to flow be unchanged? My simple thought would be that there would be a preference in trajectory for molecules in a flow situation to be aligned more along the direction of flow. The only rigid surfaces in flow are perpendicular to the direction of flow.

 

[jbriggs444]

Why would velocity perpendicular to flow be unchanged? My simple thought would be that there would be a preference in trajectory for molecules in a flow situation to be aligned more along the direction of flow. The only rigid surfaces in flow are perpendicular to the direction of flow.

Change your reference frame to one in which the flow is at rest. If temperature is fixed then, in this frame, perpendicular velocity is the same as ever.

 

[Khashishi]

To increase the velocity, you pretty much have to press the fluid through a constriction. Since $\rho A v$ is constant, shrinking $A$ increases $v$. The fluid kinetic energy is $\frac{1}{2} \rho A v^2$. Clearly, this quantity increases with $v$. This increased energy must come from the internal energy of the fluid. It is this internal energy that produces the pressure.

 

[Chestermiller]

To increase the velocity, you pretty much have to press the fluid through a constriction. Since $\rho A v$ is constant, shrinking $A$ increases $v$. The fluid kinetic energy is $\frac{1}{2} \rho A v^2$. Clearly, this quantity increases with $v$. This increased energy must come from the internal energy of the fluid. It is this internal energy that produces the pressure.

You are aware that it is possible to change the pressure of a substance without changing its internal energy, correct?

 

[Khashishi]

No, I wasn't aware. Where does the energy come from then?

 

[Chestermiller]

No, I wasn't aware. Where does the energy come from then?

For an ideal gas, you can cause the gas to do work by adding heat without changing its internal energy (isothermal expansion and compression).

 

[Chestermiller]

@Chestermiller: Villa asked if it made sense that "if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases ". And you said It doesn't seem logical in any sense. Why not? I would think that in static a condition like a sealed box with air in it, pressure is contributed by molecules bouncing off walls, ie: at any given instant on average, equal parts of molecules are hitting each wall in the box. In a flow condition, the trajectory of most molecules are in the direction of flow and not much bouncing off the wall. Ie: if two opposing sides of the box was removed and air is allowed to flow through, then now the #-of-molecules per unit area per unit time hitting the walls of the box would be reduced than in the static condition. Please explain how this simple argument does not make any sense.

Are you saying that the pressure at a given location in a fluid is different in directions? How would you reconcile this with Pascal's principle? See the following link: https://www.princeton.edu/~asmits/Bicycle_web/pressure.html

 

[sophiecentaur]

Villa asked if it made sense that "if velocity of liquid molecules increases then they will have less time to collide with the walls and so pressure decreases ". And you said It doesn't seem logical in any sense. Why not?

Even though the molecules are moving along the tube, there are just as many molecules entering at the start as leaving the end. So you would expect just as many collisions per second. The wall doesn't 'know' what's causing the collisions.