Vascular resistance recent results showing the sheath flow surrounding the plug flow in a vessel, the sheath flow size is not neglectible in the real blood flow velocity profile in a vessel. The velocity profile is directly linked to flow resistance in a vessel. The viscosity variations, according to Thurston, are also balanced by the sheath flow size around the plug flow. The secondary regulators of vascular resistance, after vessel radius, is the sheath flow size and its viscosity. Thurston, as well, shows that the resistance R is constant, where, for a defined vessel radius, the value η(δ)/δ is constant in the
Incompressible flow to ensure incompressible "flow". When we speak of the partial derivative of the density with respect to time, we refer to this rate of change within a control volume of "fixed position". By letting the partial time derivative of the density be non-zero, we are not restricting ourselves to incompressible "fluids", because the density can change as observed from a fixed position as fluid flows through the control volume. This approach maintains generality, and not requiring that the partial time derivative of the density vanish illustrates that compressible fluids can still undergo incompressible flow. What interests us is the change