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The flow through an artificial kidney is described by three dimensionless groups: Re (pvd/u). Eu (Ap/v2p), and the reduced length (1/d). Use these groups to design a model for flow through an artificial kidney. In this hypothetical artificial kidney, blood (density=1,000 kg/m and viscosity = 1.0 x102 Pa-s) is pumped through 10 m of tubing of diameter 0.0010 m. The average velocity of the blood is 0.010 m/s. For a model using glycerin (density = 1,260 kg/m and viscosity = 1.49 Pa-s) flowing through a tube of diameter 0.0050 m; a. What length of tube do we need for the model system? b. What should be the average velocity of the glycerin in our model system? c. Determine the model to prototype pressure drop ratio (Apmodel/ Apprototype). (15 points) parameter density (p) viscosity () model 1,260 kg/m prototype 1,000 kg/m 1.49 Pa-s velocity (v) 1.0 x10-2 Pa-s 0.010 m/s length (1) 10 m diameter (d) 0.0050 m 0.0010 m