Question

Given that a fluid at rest is incapable of sustaining any shear stress, set up the relation between the surface traction on an arbitrarily oriented surface element and the pressure. From this, find the relation between the stress tensor and the pressure.

Answer 1

Relation between the stress tensor and the pressure is attached below

Step-by-step explanation:

Expressing the Relation between the surface traction on an arbitrarily oriented surface element

For an arbitrary element

net force can be represented as : P + dp/dx ( dx/2 ) - P + dp/dx ( dx/2 )

= dp/dx * dx

∴ The surface traction can be expressed as

= dp/dx * dxdydz + dp/dx * dxdydz

attached below is the remaining part of the solution