{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS4 - MATH 505 Mathematical Fluid Dynamics Problem Set 4...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 505: Mathematical Fluid Dynamics Problem Set 4 due Friday, November 16, 2007 1. Consider a U-shaped tube filled with two different fluids, of equal volumes and densities ρ 1 and ρ 2 > ρ 1 . At t = 0 the two fluids are arranged so that each one occupies half of the “U”, thus they each rise to the same height. Find the equilibrium arrangement of the fluids. 2. Consider steady Poiseuille flow through a pipe of radius R 1 , using cylindrical coordi- nates. Assume that the pressure is given by p ( z ) = Cz , that u z = u z ( r ), and that u r = u θ = 0. Additionally, assume a solid inner cylinder concentric to the first, with radius R 2 < R 1 , such that the fluid flows axially between the two cylinders. Find u z ( r ). Using a Mathematica .nb file (old example still available on the webpage), plot the solution for several values of R 1 with fixed R 2 = 1 (and fixed values of the other constants). Print out your results, and include them with your PS. 3. In class we solved the problem of axisymmetric incompressible Stokes flow past a sphere (radius a ), and by assuming the streamfunction could be written as ψ ( r, θ
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern