Blood flows up a vein with a uniform radial velocity and radius of 5 cm. Doppler ultrasound tells you that the velocity between 3 points spaced 40 cm apart are 0.64, 0.6, and 0.52 mm/s moving up the vein, respectively. Assuming blood's density of 1025 kg/m3 at the middle point, determine the blood's density gradient at the middle measurement location calculating the velocity gradient across the 80 cm height of the vessel. (hint: solve the problem using cylindrical coordinates but you do not need to use the full Navier-Stokes equation)