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ME 6601 Introduction to Fluid Mechanics

Fall 2015 Prof. Devesh Ranjan

Home-Work 1

Due Date: Friday Sep 4th, 2015 by 5:00 PM (EST)

Problem 1: Prove the vector identity:

Problem 2: Verify Stokes’ theorem for where A is the upper half

surface of the sphere and C is its boundary.

Problem 3: Consider a steady, two-dimensional, incompressible flow whose velocity components are

given by where U and H  are characteristic velocity and length scales, respectively.

Determine the acceleration vector, a.

Problem 4: For flow near the stagnation point of a cylinder, the velocity is u = (4U/D)(x  –  y ), where D

is the cylinder’s diameter and U  is the speed of the incident flow. Determine the Lagrangian descriptionof the fluid-particle position vector, r = x + y , terms of U, D, t and the initial values of the coordinates

 xo and yo.

Problem 5:Verify that the circulation,