Question

th 1.(40 points total) The interstitial (inside) space of a bone is a porous physical matrix arrow filling the space. The left picture below is a CT scan of the interstitial and a space in a typical vertebra. The porous structure can be modeled of as a regula structure of cylinders where the cvlinders have a diameter of D and a spacing of x total length, X. Nutrients are brought in and out of this region by interested in the pressure drop, AP, in the blood through this space, as it has direc consequences on many biological processes within the bone blood flow, we are pinst-1060 kg m Hslod -1.5x 101 kg) or Ns/m'21. For a vertebral bone D-0.25mm, x=0.75mm. X=2.54 cm. Vblood-1.5 x 10-6 m/s AP (a) (10 points) Find the non-dimensional groups for this problem. Use D, y repeating variables. V, and p as the p as the that is (b) (10 points) To perform experiments an engineer making a largers scale model that is has a scale ration of 10:1 and will use water as the fluid. What are themd parameters D, x, L, V for the experiments? (c) (10 points) The model measures a pressure drop of 11-15 Pa. Wha pressure drop in the real bone? (d) (5 points) What is dynamic similarity? (e) (5 points) How did you achieve dynamic similarity for this

Answer 1