Forces and Stresses

In previous chapters, we have discussed the kinematic structure of a flow but made no reference to the external action that is necessary to establish a flow and to the physical mechanism that is necessary to sustain the motion of the fluid. To address these issues, we now turn our attention to the hydrodynamic forces developing in a fluid as a result of the motion, and introduce constitutive equations relating the stresses developing at the surface of infinitesimal fluid parcels to the parcel motion and deformation. The constitutive equations will then be incorporated into an integrated theoretical framework that allows us to compute the structure of a steady flow and the evolution of an unsteady flow from a specified initial state.