The discussion centers on the relationship between pressure and velocity in fluid dynamics, specifically referencing Bernoulli's Principle. When fluid flows through a constricted pipe, its velocity increases due to mass conservation, resulting in a decrease in pressure. This phenomenon occurs because the total energy of the fluid remains constant; as kinetic energy rises, pressure energy must decrease to maintain equilibrium. The argument that increased velocity leads to fewer wall collisions, and thus lower pressure, is refuted by the understanding that the number of collisions remains consistent in a flowing fluid.
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Villa said: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?
Villa said: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.Villa said: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...
It doesn't seem logical to me in any sense.Villa said: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: 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.Chestermiller said:It doesn't seem logical to me in any sense.
Chet
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?jtdrexel said:@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 said: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.
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.jtdrexel said: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.
You are aware that it is possible to change the pressure of a substance without changing its internal energy, correct?Khashishi said: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.
For an ideal gas, you can cause the gas to do work by adding heat without changing its internal energy (isothermal expansion and compression).Khashishi said:No, I wasn't aware. Where does the energy come from then?
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.htmljtdrexel said:@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.
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.jtdrexel said: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?