# The Stokes equations for chyme flowing down the gut

Equip the gut with a coordinate system with coordinates and let be the direction pointing along the length of the gut. Write for the velocity of the chyme. Here is the component of the velocity in the direction of the -axis and and are the velocity components in the other two directions. Write for the viscosity of the chyme (a measure of its stickiness) and for the pressure forcing the chyme to flow down the intestine. The Stokes equations relate velocity, pressure and viscosity as follows:

Here is the vector , where (similarly for and ).

The expression stands for the vector

and is defined as