Question

A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Figure 1). The inside diameter of the 34 mm long needle is 0.90 mm , and the required flow rate is 3.2 cm3 of blood per minute.

How high h should the bottle be placed above the needle? Use ρblood = 1.05×103kg/m3, ηblood = 4.0×10−3Pa⋅s. Assume the blood pressure is 66 torr above atmospheric pressure.

Answer 1

briren : - Length of the 0.45X loom li As d=0.90 Length of the needle (L) = 34 x 103 m Inner radius of the needle (6)= 0.45X lo m Requried flow rate (O) = 3.2 cm² O- 3.2 x 106 60 mm) o= 5.33 x 103 m3/s Density of blood P = 1.05 810 kg / m² viscosity of blood h = 4 x 10² pas Blood pressure (P) = 66 torr P. - 66 X L33 133.322 P = 8799.252 pa Acceleration due to gravity (g) = 9.8 m/s2 We have the egn giving the flow rate of the liquid through a tobe - Altis SetaL So, the reguned Pressure difference between the ends of the tobe for the given flow rate AP = ax 8n L TIRA AP= 5.33 x 108 x 8 x 4 x 16 x 34 x16 TX 10.45x103) 4 5799.04 x 10th DP = 0.1287 x 102 TAP = 450.58 pa

let P2 be the pressure at the other and of the needle inserted to the patient Then we hare, ap = P₂ - P. So, the reqused Pressure at the other and of the needle P2 = Pit op P2 = 8799.252 + 450.58 to be P2 = 9249.832 Pal let h be the height to which the bottle of blood raised to get the desired Pressure. Then, the requried height h =P 59 h = 9249.832 1.054 103 9.8 Th= 0.898 m