# Air flow over a circular cylinder

• mrajkumar

#### mrajkumar

Hi,
Could you explain the reason why the velocity varies in the wake region behind the cylinder in "flow over a circular cylinder"? the velocity variation is, minimum at a point parallel to the centre point of the cylinder and increases to free stream velocity as the vertical distance increases from the centre point. rough image file is added.
And is there a possibility that stagnation pressure varies in the wake region? Because my understanding is stagnation pressure should remain constant everywhere in the flow field. only static pressure varies in relation to dynamic pressure to maintain constant stagnation pressure.
Thank you

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mrajkumar said:
Could you explain the reason why the velocity varies in the wake region behind the cylinder in "flow over a circular cylinder"? the velocity variation is, minimum at a point parallel to the centre point of the cylinder and increases to free stream velocity as the vertical distance increases from the centre point. rough image file is added.

Perhaps the easiest way to visualize this is to think in terms of a frame of reference where your move along with the free stream (i.e. the velocity of the free stream is zero in your frame and the cylinder moves through it). The cylinder will, as a result of viscosity, tend to drag some of the fluid along with it, so while the free stream looks stationary to you before the cylinder passes, a small region behind the cylinder will be moving slightly following its passing. If you then transform that back into the frame with the stationary cylinder, that simply looks like a region of slowed flow in the wake region.

mrajkumar said:
And is there a possibility that stagnation pressure varies in the wake region? Because my understanding is stagnation pressure should remain constant everywhere in the flow field. only static pressure varies in relation to dynamic pressure to maintain constant stagnation pressure.

This is sometimes a true statement, as it is essentially a verbal statement of Bernoulli's equation. So then the question is, do you know under what conditions this statement holds?

Perhaps the easiest way to visualize this is to think in terms of a frame of reference where your move along with the free stream (i.e. the velocity of the free stream is zero in your frame and the cylinder moves through it). The cylinder will, as a result of viscosity, tend to drag some of the fluid along with it, so while the free stream looks stationary to you before the cylinder passes, a small region behind the cylinder will be moving slightly following its passing. If you then transform that back into the frame with the stationary cylinder, that simply looks like a region of slowed flow in the wake region.

This is sometimes a true statement, as it is essentially a verbal statement of Bernoulli's equation. So then the question is, do you know under what conditions this statement holds?

Thank you sir for the response. That Bernoulli's equation is valid for steady flow, inviscid, incompressible fluid and irrotational flow. And in the above situation can the stagnation pressure increase? Or if it decreases, is it converting to heat? Kindly clarify sir. thank you.

So out of those reasons why Bernoulli's equation is not valid, assuming incompressible, steady flow, that leaves only phenomena that imply dissipation. In other words, some of the flow energy is being dissipated by the viscous effects of the cylinder. This results in a decrease in stagnation pressure.