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Solutions of the Navier-Stokes equations for flows of incompressible fluids satisfying no-slip boundary conditions are discussed in the frame of the Helmholtz decomposition. The focus is on the steady flow of a body in an unbounded fluid. The decomposition of the velocity into rotational and irrotational parts can be uniquely determined as the velocity generated by the vorticity in the Biot-Savart law plus a harmonic velocity in which the body and boundary conditions are identified. It is shown that contribution of the rotational velocity to the drag is larger than the total which includes a negative contribution from the irrotational velocity, The dissipation due to the potential flow cannot be neglected in any exact theory as it is in the conventional boundary layer theory and elsewhere. [ABSTRACT FROM AUTHOR]