Page 177 - Introduction to Continuum Mechanics

162 Problems

corresponds to the motion

(b) Find the acceleration of this motion in the material description.
3.10. Given the two-dimensional velocity field

(a) Obtain the acceleration field.

(b) Obtain the pathline equations,
3.11. Given the two-dimensional velocity field

(a) Obtain the acceleration field.
(b) Obtain the pathline equations.
3.12. Given the two-dimensional velocity field,

Obtain the acceleration field.
3.13. In a spatial description the equation to evaluate the acceleration

is nonlinear. That is, if we consider two velocity fields v andv ,then

where a and a denote respectively the acceleration fields corresponding to the velocity fields
4
V and v each existing alone, a' 4 denotes the acceleration field corresponding to the
combined velocity field ^r + TT. Verify this inequality for the velocity fields

3.14. Consider the motion