Question

The human heart delivers a blood flow of about 5000ml/min. The diameter of the blood vessel leaving the heart is 1.8cm. a. Determine the Re of the flow in this vessel. b. Is the flow laminar or turbulent? Explain. c. The smallest blood vessels have a diameter of 10m and a total area about 1000 times greater than the area of the vessel leaving the heart. Determine the Re in a typical capillary. d. By what factor does the diameter of a capillary have to increase in order to double the flow rate for a given pressure drop?

Answer 1

Page No 5000 m1 Gosec Soln. (a) Given, Volumetric flow rate of blood soron x 10-32 u min 5L 5x15 3 m3 Goseca 2260 sec noool Q25 6 n x 10-4 sec Also, diameter of blood vessel, d = 1.8cm = 018m . . Area nd? प nx (1.82x104m2 4 flow rate, & Area : Velocity of flow 5 6 x 10-4 mi Тх see (1.8)²x104 VE 20 .3276m 6a xl1.8) ? sec Nom, the density of blood approximately . m3 Pa 106x103 kg Viscosity of blood , 4 = (3-4)x10'' Pars

Date Page No. .. kinematic viscosity of blood Р 3-4) x 103 1.068103 m²ls 3.8x10-6 maximum ano onlt i USA valve, 1. Reynolds no. of flow, Re = PVD Home otor wolz M R VDI MIP us Re AND - Re 3276 m/s x 1018m 3.8 x 10-6 m2lsea Re= 2 1552 6) Since & the flow of blood occurs in blood vessel which is generally considered as circulay pipe. Therefore, the flow in the blood vessel will be Laminar if the Reynolds number is less than v 2100. r. Since Re =1552 X 2100. Hence, the flow of blood is Laminar.

Page No The pressure drop for Laminar (d) flow is given by Hagen - Poiseulliegn. Soix dog tre. AP2 32 MFL kin x 8.02 Assuming the Length of capillary and blood vessel to be same in het the flow rate be Q, and Oz through blood vessel & Capillary. Di and be there diameters, N & Given AP is same. cox 32 ML & V 32 M L X V₂ 0,3 221 DzZ V2 Q zou o Gold Dhol D2 23 noi 27 Nino 16220v, boold 44 Qulia DI 4 saboros 4 XD24 4 boca 02 Given Q₂ 320, 14 14 2.2) Q,272 Lorino 20 gold ( 2 ) D2 2 D 14. 84 2 D₂ 1:19 Therefore, Diameter of Capillary must be long times of blood vessel Di +84

Part c of the question was unclear to me as there was some square box along with value10 forwhich I didn't get its actual meaning.