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While ago I was studying drag coefficients (or pressure coefficients, as we call them in the context of wind loads in structural engineering) and I wondered how can they be more than 1, for example a small cylinder can have a drag coefficient of 1.15 according to Wikipedia. This seemed weird to me, since pressure upon a surface is caused by the fact that the presence of the surface brings moving fluid to rest, therefore applying force to the fluid, which in turn causes pressure to the surface according to Newton's third law. Wikipedia explains that for positive pressure, a drag coefficient of 1 would mean that all of the fluid coming into the front of the surface is brought to rest, and so all the momentum of the fluid is transferred to the object. In real surfaces, some fluid "escapes" over the sides of the object, continuing to move forward, keeping their momentum. Therefore not all of the momentum of the fluid is transferred to the object and the drag coefficient is less than 1. So this would mean that for drag coefficient over 1, we would need extra momentum from somewhere!

The explanation (from Wikipedia) lies in the fact that there is suction on the other side of the object, so the total pressure can be more than the momentum which the fluid transfers to the object. I'm curious, how does this mechanism work? How does the moving fluid cause suction on the other side of the object? One thing that comes to mind is that the fluid escaping over the sides of the object starts to flow to the back-side of the object instead of forward, therefore slowing the fluid and to conserve momentum, there has to be more force to the object, but this would only bring the coefficient closer to 1, not over it.

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    $\begingroup$ Interesting question. Have you found other references besides Wikipedia (which has its deficiencies)? The section you mention doesn't even have references. $\endgroup$
    – pglpm
    Commented Oct 11, 2020 at 11:49
  • $\begingroup$ The point about suction sounds circular to me: suction is not a negative pressure, but the effect of a lower pressure on one side with respect to the other (for example, in a room without air it'd be impossible to sip a liquid from a glass with a straw). I also have difficulty with the idea that "the fluid approaching the object is brought to rest": first, being nearly incompressible the fluid can't just accumulate at the object. Second, if it comes to rest then the relative velocity would be zero and the drag coefficient infinite, according to the initial formula. $\endgroup$
    – pglpm
    Commented Oct 11, 2020 at 11:50
  • $\begingroup$ I'd suggest consulting a text like Bird & al's Transport Phenomena. $\endgroup$
    – pglpm
    Commented Oct 11, 2020 at 11:57
  • $\begingroup$ @pglpm I don't think the coefficient would be infinite with zero velocity. The velocity there refers to ambient fluid velocity, the velocity of the fluid before it getting close to the object, not the velocity at the surface. $\endgroup$
    – S. Rotos
    Commented Oct 11, 2020 at 12:06
  • $\begingroup$ I agree. I just wanted to point out that the discussion on Wikipedia is too vague, possibly misleading or incorrect. I was taking a look at drag coefficients in Transport Phenomena, and they show graphs with values of $10^3$. So I think the discussion in that Wikipedia section is too simplistic. $\endgroup$
    – pglpm
    Commented Oct 11, 2020 at 12:32

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In short, this "suction" effect really has to do with the fact that it's possible for the pressure surrounding an object to be smaller in some regions than the "ambient" pressure far away from the object. So how can we show that happens?

We have two avenues:

  1. We can try to ignore viscous losses and assume that the fluid is conserving momentum everywhere. This has a problem—in these sorts of flows, the idea that the fluid comes to a complete stop on the surface of the object is incompatible with ignoring viscous losses. For flow past a sphere, for example, you find that the regions on the sphere which have a smaller pressure than ambient are those on the top and bottom of the sphere, but you also find that the velocity on those sides of the sphere is not just nonzero, but actually larger than the ambient speed. You can intuit this from a conservation of mass argument; imagine the flow under consideration was inside of some massive invisible pipe, and the sphere was an obstacle within it. The flow should have to speed up in order to ensure the mass flow rate is constant, and that speed increase is connected to the pressure drop on the sides that leads to a $>1$ drag coefficient.

  2. We can try to consider flows where viscous forces dominate, and the only momentum exchange in the fluid happens between viscous stresses and the pressure. Here we don't have too many intuitive arguments—we can't use Bernoulli—but in these flows, the pressure unambiguously drops near the "back" faces of a submerged object, causing the "suction" effect your link refers to. This is one reason why $>1$ drag coefficients mostly show up on the low-Re end of drag coefficient graphs; that's when viscous forces dominate, and the negative gauge pressures pop up behind submerged objects.

In reality, it's a mix of both; and which of them applies the most depends on the context of the flow at hand, particularly the Reynolds number.

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