# PS3 - MATH 505 Mathematical Fluid Dynamics Problem Set 3...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 505: Mathematical Fluid Dynamics Problem Set 3 due Friday, October 19, 2007 1. Consider the incompressible irrotational flow of a fluid which fills an open tank to an initial height h . The fluid is steadily escaping through a small hole at the bottom with speed U . By considering a streamline which runs from the upper surface to the surface at the hole, use Bernoulli’s equation to obtain a relation between U and the change in height of the fluid dh/dt . Under the assumption that the cross-sectional area of the hole is much smaller than any cross-section of the tank, obtain a simple approximate relation between U ( t ) and h ( t ) (Torricell’s Law). Does the fluid speed up or slow down as the tank drains? 2. Download the Mathematica .nb file from the webpage, and try out several values of the circulation G . Print out your results, and include them with your PS. Try including a pt vortex somewhere outside the cylinder - be careful about using Milne-Thompson!...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online