Fluid flow,acceleration and bernoulli's theorem

[meghana1704]

Even though the velocity of each particle is constatnt in staedy flow,all the fluid particles are accelerating.If velocity of every particle in the steady state fluid flow is constant how does the fluid accelerate?In that case,why is there a bernoulli theorem for unsteady flow?

 

[rcgldr]

I assume you mean the average velocity of the molecules of a fluid. What can happen is as the fluid accelerates, the movement of the molecules becomes less random, and the net component of velocity in the direction of flow increases.

 

[Ryoko]

Not understanding the question. The velocity in a steady flow is not necessarily constant. It may be constant at a particular point, but may vary at different locations in the stream. For example, bernoulli's principle is usually applied to a venturi. The pressure drops and the velocity increases in the narrow part of the venturi. This is a result of the conservation of mass and the conservation of energy.

 

[Chestermiller]

Even though the velocity of each particle is constatnt in staedy flow,all the fluid particles are accelerating.If velocity of every particle in the steady state fluid flow is constant how does the fluid accelerate?In that case,why is there a bernoulli theorem for unsteady flow?

In a steady flow, the velocity of the particles passing through each specific spatial location does not change with time. But if you follow the motion of an individual particle along its streamline, its velocity will change with time. At a given spatial location, each new particle replaces the one that previously occupied that spatial location before it, and when the new particle arrives at that spatial location, its velocity will be the same as that of the particle that had just departed.

 

[rcgldr]

If velocity of every particle in the steady state fluid flow is constant ...

It's not clear if you're referring to the average velocity of the molecules of a fluid, including random direction components, or if you mean the net velocity of the molecules. The net velocity is not constant.

 

[Chestermiller]

It's not clear if you're referring to the average velocity of the molecules of a fluid, including random direction components, or if you mean the net velocity of the molecules. The net velocity is not constant.

The OP is talking about the situation when you treat the fluid as a continuum. The OP is not referring to the molecules. Bernoulli's equation does not refer to the velocities of the individual molecules. When the fluid is treated as a continuum, and the flow is at steady state, the velocity at each fixed location in the flow field does not change with time.