4 ട്ട. Differentiate between Lagrangian and Eulerian descriptions of fluid
motion. (4 marks)

c. The lagrangian coordinates of a material particle is(x(t), y(t),z(t)) .
Obtain mathematical expression for the component of acceleration
along the direction of motion of the material particie. (5 marks)

5 2. Explain infinitesimal deformation theory. Obtain an expression for
Linearized strain (3 marks)

0. Whatis localization theorem. Write down its relevance in the derivation
of differential equations (3 marks)
c. Derive the differential form of conservation of energy. (3 marks)
6 9. Write down the six compatibility equations. (3 marks)
b. Discuss the physical interpretations of components of Linearized
strain tensor. (6 marks)
PART C
7 a. What is orthotropic material? Write down the number of independent
elastic constants for orthotropic material . Write down the structure of
the elasticity matrix relating the stress vector and strain vector.
(1+1+2=4 marks)

b. Write down the general stress strain relation through the 4 7 order
elasticity tensor. Discuss the changes in the number of independent
constants due to symmetry conditions applicable for all linear elastic
materials. (1+4=5 marks)

c. Write down the stress strain relations of a linear isotropic
material.(3 marks)

8. a. Derive the stress compatibility equation for a plain stress problem with
body force. State the condition under which it becomes the biharmonic
equation. (6 marks)

b. Derive Navier-Stokes equation for incompressible flow. (6 marks)

9. a. Write down the radial and tangential components of stress in
terms of Air's stress function. (2 marks)

b. Derive the governing equation of Prandtl stress function for the

torsion of a prismatic bar. (10 marks)