oriol
Well-Known Member
Hi!
I am reading Fundamentals of Aero to be able to understand airfoil theory. It takes a bit of reading before being able to do somethig meaningful, but I believe the effort is worth it. I am bit lost about how Anderson, the author, proceeds in example 2.3 of the book below.
In the first image the author deduces graphically, the equation for a stream.
Which is by definition a curve, whose tangent at any point is in the direction of the velocity vector at that point.
The vector diagram dy/dx = v/u, is equal to tangent alpha = sin alpha/cos alpha. It all seems coherent.
However when integrating instead of having y^2/2 = -x^2/2 + K.
The author gets y^2 = -x^2 + K.
You can guess that the missing 2, on both the denominator of y and x, is buried inside K?
But if this was the case, when evaluating at (0,5), the result ought to be 5^2 = 0 + 2*K. That is K = 25/2, not K = 25.
What is going on in here? I can not tell if there is something that I am missing?
Thanks a lot in advance for any comments!
Oriol
I am reading Fundamentals of Aero to be able to understand airfoil theory. It takes a bit of reading before being able to do somethig meaningful, but I believe the effort is worth it. I am bit lost about how Anderson, the author, proceeds in example 2.3 of the book below.
In the first image the author deduces graphically, the equation for a stream.
Which is by definition a curve, whose tangent at any point is in the direction of the velocity vector at that point.
The vector diagram dy/dx = v/u, is equal to tangent alpha = sin alpha/cos alpha. It all seems coherent.
However when integrating instead of having y^2/2 = -x^2/2 + K.
The author gets y^2 = -x^2 + K.
You can guess that the missing 2, on both the denominator of y and x, is buried inside K?
But if this was the case, when evaluating at (0,5), the result ought to be 5^2 = 0 + 2*K. That is K = 25/2, not K = 25.
What is going on in here? I can not tell if there is something that I am missing?
Thanks a lot in advance for any comments!
Oriol
