Page 183 - Introduction to Continuum Mechanics
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168 Problems
for an incompressible fluid, determine k such that the equation of mass conservation is
satisfied.
3.49. Given the velocity field in cylindrical coordinates
For an incompressible material, from the conservation of mass principle, obtain the most
general form of the function/(r, 0).
3.50, An incompressible fluid undergoes a two-dimensional motion with
3.51. Are the fluid motions described in (a) Prob.3.15 and (b) Prob.3.16 incompressible?
3.52. In a spatial description, the density of an incompressible fluid is given by p = k%i. Find
the permissible form for the velocity field with v 3 = 0, so that the conservation of mass
equation is satisfied.
3.53. Consider the velocity field
(a) Find the density if it is independent of spatial position, i.e., p = p(t).
(b) Find the density if it is a function xi alone.
3.54. Given the velocity field
determine how the fluid density varies with time, if in a spatial description it is a function of
time only.
3.55. Check whether or not the following distribution of the state of strain satisfies the
compatibility conditions:
where k = 10 .
3.56. Check whether or not the following distribution of the state of strain satisfies the
compatibility conditions:
