Hydrodynamic torque
= Hydrodynamic torque
{title2=$\mathbf T$}
The hydrodynamic torque on a body about a reference point is $T=\int_S r\times(\sigma\cdot n)dS$, with $r$ measured from that point and $n$ pointing from the body into the fluid. The <stress> includes pressure and viscous contributions, and $\sigma\cdot n$ is the fluid <traction> on the body. Changing the reference point by $d$ changes the <torque> by $-d\times F$, where $F=\int_S\sigma\cdot n dS$ is the fluid force. A <torque-free> body has zero resultant torque, including any external torque.