Question

The branching of a blood vessel is shown in Fig. B.8. Blood at a pressure of 18.5 kPa flows in the main vessel at 4.5 L/min. Determine the blood pressure in each branch, assuming that blood vessels behave as rigid tubes, the flow is frictionless, and that the vessel lies in a horizontal plane. You may approximate blood to have a SG of 1.06.

02 dz=3mm (2) di=1cm Qi-4.5L/min P=18.5 kPa (1) d=5mm Q:=2L/min (3) Q3 Fig. B.8

Answer 1

dq=3 mm -5 Is = 7.5015xlo X105n2 Solution :- jog dizlem Q=4.54m2 Pi=10.5 kpa 03=2L/min dz=5mm 01 = Og taz Qq = 4.5-2=2,5 L/min 01 = 4.5 L/min 4.5 * 1.667x10 m/ ms di= lcm = 0.0lm 74, = I x 0.012= 7,854 V = 0 = 7.5015*10-5 AL = 0.955 m/s 7.854x105 Og = 2.54m = 215x1.6674105 = 401675x105 da = 3 mm = 0.003m → Ag = I x00032 = 7,069 x 10 mit Ag 5.896 m/s 7.069xlor O₂ = 24/m 2x1.667x105 = 3.334x10 m/s d3= 50mm = 0.005 m A3=Ix010052 1.9635x105 m2 V3 = 63 = 3.334x10-5 Az 1.9635X8-5 m/ Vg = 4. 1675x10-5 4 = 1.698 m/s

NOW Using Bernoulles theorm V2 Pa tz, + + Zg Yw ag Yw zg 2 Pi V2 + Z1=22 ag qx9,81 7 P2 = P, + v, - Ve Yw = 18.5+ 0.955²5.896² x9.81 kN/m² = 18.5+ (-16.925) = 1.575 kpl simellesly P2 = Pit 0.9552-1-6987 P₂ = Pit V1²_V3 ? xYw -8 1815 t x9,01 2 x 9.81 - 18.5 + 1-0.986) 17:514 kpa