3. Upon inserting a catheter into the aorta, the blood (incompressible fluid of density p and viscosity μ) flow must pass around the catheter. Assume that the catheter is placed directly in the center line and is not moving with time. Use appropriate equation of continuity and Navier-Stokes equation to derive an expression for velocity profile assuming that the flow is only driven by др az' the pressure gradient in axial direction The outer radius of aorta is R and the outer radius of catheter is kR. (Note: you do not need to solve for the pressure gradient, use the pressure gradient in differential form i.e. ӘР

Fig: 1