# Fluid mechanics, balance of angular momentum, ignoring body/surface couples

In fluid mechanics, we derive the fact that the Cauchy stress tensor is symmetric by using a balance of angular momentum argument. We start the derivation by assuming that no body/surface couples act on fluid elements.

My question is, why is that a necessary assumption? To be exact, I don't think I get why body/surface couples are considered separately - why aren't they included in the integrals

$$\int_V \mathbb{x}\times \rho b \,dV + \int_S\mathbb{x}\times \mathbb{t}\,dS$$

where $b$ is body force per mass, $\mathbb{t}$ is surface force per area, and $x$ is the position vector.

My background is in math, not physics, so even a seemingly trivial physics description explanation would help.

• I think the sentence "no body/surface couples act on fluid elements." may be not too clear. – jaromrax Feb 20 '17 at 16:05