Holooly Plus Logo

Question 11.9: The streamlines for the 2D, inviscid, constant density flow o...

The streamlines for the 2D, inviscid, constant density flow over a cylinder are shown in Figure 11.8. The streamfunction for this flow is given in cylindrical coordinates by ψ(r, θ) = Ur(1− R²/r²) sin θ, where U is the freestream velocity and R is the cylinder radius. If the body force is neglected, the pressure distribution is given by p(r, θ) = p+ 1 2ρU^2 _∞ [1−(1− R2/r2)2 −4(R2/r2) sin2 θ]. Show that the velocity field in this case is described by

v_r=U _∞\left(1-\frac{R^2}{r^2}\right)\cos \theta ,         v_θ=U _∞\left(1-\frac{R^2}{r^2}\right)\sin \theta ,         and            v = 0

and that the continuity and Euler equations are satisfied. Comment on the boundary conditions.

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.
Already have an account?

Related Answered Questions