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jdgotts
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- TL;DR Summary
- Professor asked to explain why Bernoulli works in a boundary layer, and I don't believe it can. Any explanations that agree with his reasoning out there?
Hey all,
I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied. Because a boundary layer is formed through skin friction and friction in the flow, a boundary layer can therefore not exist in an inviscid flow, i.e. the premise of the question is flawed.
Where Bernoulli works, no boundary layer, where there is a boundary layer, no Bernoulli (as far as I understand it).
My professor has since responded to the widespread criticism of this question with the following explanation:
"Bernoulli's principle can always be applied along a streamline, the latter of which can exist in rotational flow. Bernoulli therefore can be applied in rotational flow, hence in the boundary layer. Bernoulli exists for compressible, time variant, and friction flow. Recall how we used Bernoulli's principle to equate the loss of pressure to drag force in the airfoil inside wind tunnel problem? We were able to do this with the Bernoulli equation despite the existence of viscous flow (if it were inviscid, there would be no drag)."
If anyone could explain either why his explanation makes sense, or explain why or where his explanation is flawed, I'd greatly appreciate it. I feel like the solution that Bernoulli works along a streamline, and streamlines exist in rotational flow, therefore Bernoulli can be applied in viscous flows and boundary layers, is oversimplified. A staggering amount of the internet seems to agree with me based on some Googling, but I can't really disprove what he wrote as his solution with what I know.
Thanks for any help you're able to give!
I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied. Because a boundary layer is formed through skin friction and friction in the flow, a boundary layer can therefore not exist in an inviscid flow, i.e. the premise of the question is flawed.
Where Bernoulli works, no boundary layer, where there is a boundary layer, no Bernoulli (as far as I understand it).
My professor has since responded to the widespread criticism of this question with the following explanation:
"Bernoulli's principle can always be applied along a streamline, the latter of which can exist in rotational flow. Bernoulli therefore can be applied in rotational flow, hence in the boundary layer. Bernoulli exists for compressible, time variant, and friction flow. Recall how we used Bernoulli's principle to equate the loss of pressure to drag force in the airfoil inside wind tunnel problem? We were able to do this with the Bernoulli equation despite the existence of viscous flow (if it were inviscid, there would be no drag)."
If anyone could explain either why his explanation makes sense, or explain why or where his explanation is flawed, I'd greatly appreciate it. I feel like the solution that Bernoulli works along a streamline, and streamlines exist in rotational flow, therefore Bernoulli can be applied in viscous flows and boundary layers, is oversimplified. A staggering amount of the internet seems to agree with me based on some Googling, but I can't really disprove what he wrote as his solution with what I know.
Thanks for any help you're able to give!