Velocity Profile u(x,y) x y

... Now use the equations of motion to find the pressure, p(r, t), at any position, r, in the water. Neglect all body forces. One integration step has to be performed which introduces an integration constant; this can be evaluated by assuming the pressure far from the bubble (r → ∞) is known (denoted by ...

... Now use the equations of motion to find the pressure, p(r, t), at any position, r, in the water. Neglect all body forces. One integration step has to be performed which introduces an integration constant; this can be evaluated by assuming the pressure far from the bubble (r → ∞) is known (denoted by ...

ME 750A: Spring 2005 HW Due on Wednesday, March 9

... 1. It has been suggested that the velocity field near the core of a tornado may be approximated by V = – er (q/r) + e (K/r). Does this represent incompressible flow? Is this an irrotational flow? [FM 5.16, 5.78] 2. An incompressible fluid of negligible viscosity is being pumped through two tiny hol ...

... 1. It has been suggested that the velocity field near the core of a tornado may be approximated by V = – er (q/r) + e (K/r). Does this represent incompressible flow? Is this an irrotational flow? [FM 5.16, 5.78] 2. An incompressible fluid of negligible viscosity is being pumped through two tiny hol ...

Abstract

... The Hitchin theorem says that pr,s (τ ) is a solution of a Painlevé VI equation. Remarkably, the denominator ζ(r + sτ |τ ) − rη1 (τ ) − sη2 (τ ) is the Eisenstein series of weight one if (r, s) is an N -torsion point. Set Zr,s (τ ) = ζ(r + sτ |τ ) − rη1 (τ ) − sη2 (τ ). Then Zr,s (τ ) has another l ...

... The Hitchin theorem says that pr,s (τ ) is a solution of a Painlevé VI equation. Remarkably, the denominator ζ(r + sτ |τ ) − rη1 (τ ) − sη2 (τ ) is the Eisenstein series of weight one if (r, s) is an N -torsion point. Set Zr,s (τ ) = ζ(r + sτ |τ ) − rη1 (τ ) − sη2 (τ ). Then Zr,s (τ ) has another l ...