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Frigus

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In summary, Bernoulli's theorem states that the pressure in a fluid decreases as its velocity increases, in order to conserve energy. This can be practically explained by understanding that pressure relates to the microscopic kinetic energy of the fluid molecules. The equation ##\frac{1}{2}\rho v^2## represents the addition of microscopic and macroscopic kinetic energy, as well as potential energy, which is all conserved in the fluid. This explanation is more simplified and practical, compared to more complex conservation arguments. Additionally, this can be seen by multiplying the equation by volume and recognizing that pressure relates to energy. Therefore, pressure is conserved in order to maintain a balance of energy in the fluid.

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Frigus

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- #2

Dale

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I am not sure what would count as a practical explanation if conservation of energy does not.Hemant said:I understood that if if velocity is more so as to conserve energy pressure should be more but how can be this explained practically

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Frigus

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Sir but I can't understand how pressure can be energy.Dale said:I am not sure what would count as a practical explanation if conservation of energy does not.

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russ_watters

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PressureHemant said:Sir but I can't understand how pressure can be energy.

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Frigus

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Sir units of pressure are N/m^2 and units of energy are Nm,so why we are conserving pressureruss_watters said:Pressureisn'tenergy. Please post the units of pressure and the units of energy and compare them.

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Delta2

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well pressure has same units as Energy/volume that is same units as energy density...

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Frigus

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Sir I want to know why we need to conserve pressureDelta2 said:well pressure has same units as Energy/volume that is same units as energy density...

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Delta2

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because pressure relates to the microscopic kinetic energy of the molecules of the fluid. Also it has same units as energy per unit volumeHemant said:Sir I want to know why we need to conserve pressure

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Frigus

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And why we write 1/2 rho v^2 if we are adding microscopic kinetic energyDelta2 said:because pressure relates to the microscopic kinetic energy of the molecules of the fluid. Also it has same units as energy per unit volume

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Delta2

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- #11

Frigus

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Thanks sirDelta2 said:

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sophiecentaur

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Here's a good arm waving explanation. If the fluid is flowing faster in one place than another, there must have been a force (differential) to accelerate it. That implies the higher pressure is in the region where the fluid came from . So its speed increases and its pressure decreases.Hemant said:how can be this explained practically.

Of course there are conservation arguments which are more erudite and complete but the above is certainly very "practical".

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Vanadium 50

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Frigus

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Thanks sir,it is what I was founding.sophiecentaur said:Here's a good arm waving explanation. If the fluid is flowing faster in one place than another, there must have been a force (differential) to accelerate it. That implies the higher pressure is in the region where the fluid came from . So its speed increases and its pressure decreases.

Of course there are conservation arguments which are more erudite and complete but the above is certainly very "practical".

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Frigus

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Thanks sir,physics forum is a place where I don't get answers to only questions but people like you help me to develop myself.Vanadium 50 said:

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russ_watters

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Hemant said:Sir units of pressure are N/m^2 and units of energy are Nm,so why we are conserving pressure

This may be water under the bridge by now, but what I was after was a deconstruction of Bernoulli's equation (but I was on my way to bed...). It isn't readily apparent how pressure relates to energy, but it becomes obvious if you back out of the derivation.Delta2 said:well pressure has same units as Energy/volume that is same units as energy density...

If you multiply the standard form of Bernoulli's equation through by volume, then P becomes PV, which should be recognizable as energy, like when you push down on a piston-pump. 1/2ρV

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Dale

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Which is also why it only works for incompressible flow.russ_watters said:So that's how you see they are part of a conservation of energy statement, and dividing through by volume gives you the standard form, with the funny sounding units of "energy per unit volume".

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sophiecentaur

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You have to admit my noddy explanation works every time.

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russ_watters

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Sure, though it can be modified to work for compressible flow. Depending on the specifics of the flow and the assumptions, you can have varying density and temperature, and it starts to look a lot more like thermodynamics than fluids.Dale said:Which is also why it only works for incompressible flow.

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rcgldr

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The speed of liquid flow directly affects the pressure. As the speed of flow increases, the pressure decreases. This is because faster-moving particles in the liquid collide with each other and the container walls less frequently, resulting in lower pressure.

Yes, the pressure in liquid flow can be increased without changing the speed by increasing the density of the liquid. This can be achieved by increasing the temperature or by adding solutes to the liquid, such as salt in water.

The shape of the container can affect the pressure in liquid flow. A narrower container will result in higher pressure, as the same amount of liquid is forced into a smaller space, increasing the collisions between particles and the container walls.

Viscosity, or the resistance of a liquid to flow, has an inverse relationship with pressure in liquid flow. As the viscosity of a liquid increases, the pressure decreases, as the particles in the liquid are more likely to collide with each other and the container walls, resulting in higher pressure.

The pressure in liquid flow can be measured using a pressure gauge, such as a manometer or a pressure transducer. These devices measure the force exerted by the liquid on a given area, which is then converted into pressure units, such as pounds per square inch (psi) or pascals (Pa).

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