Problem 62P

For the velocity field of Prob. 4‒63, calculate the shear strain rate in the xy-plane.

PROBLEM: A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is

Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.

Solution to 61P

Step 1

We need to find the linear strain rates for the given velocity field:

Velocity field is given as :

Where, u and v are material velocity components, a and b are arbitrary constants, x and y are coordinates.

The linear strain rates are given by,

U and v are velocity components.