About Compressive Forces on Control Volumes

[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?

 

[Chestermiller]

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?

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