# About Compressive Forces on Control Volumes

1. Jan 12, 2014

### masshakar

Why is it that forces (for changes in pressure across a fluid) on the control volume are generally considered compressive? Even in the derivation of the Navier-Stokes equation, it is assumed that forces from fluid pressure will be compressive? Why?

2. Jan 13, 2014

### Staff: Mentor

Hi Masshakar. Welcome to Physics Forums!!!

Pressure represents the isotropic part of the overall stress tensor. In the overall stress tensor $\vec{σ}$ for an incompressible fluid, the stress tensor is represented by:
$$\vec{σ}=-p\vec{I}+\vec{σ_v}$$
where $\vec{σ_v}$ represents the viscous part of the stress tensor and $\vec{I}$ is the identity tensor. If we use the Cauchy stress relationship to determine the stress on a surface of arbitrary orientation (by dotting the stress tensor with a unit normal), the contribution of the pressure term to the overall traction vector is compressive.

Chet