During a blood transfusion, gravity is used to provide the pressure to overcome the blood pressure and force the flow through a small needle into a vein. Consider a case where the needle is 3.0 cm long and has an internal diameter of 0.75 mm. If the required rate of flow is 0.03 cm3/s and the blood pressure in the vein is 11.00 kPa higher than atmospheric pressure (Pa), how high should the bottle be placed above the needle

Density of blood = 1.06x10³

Viscosity = 4 mpas

It should be 1.10 higher

Explanation:

L = 0.93

D = 0.75

R = 0.75/2 = 0.375

Q = 0.03x10^-3

Blood pressure = 11x10³

Pn = 4x10^-3

n = 4 x 10^-3

Density of blood = 1.06x10³

Pn - Pv = 8*Q*n*L/pi*r⁴

Pn - pv = 463.57pa

Pn - pv = 463.57pa

Make pn subject

Pn = Pv + 463.57pa ----1

Vn = Q/An

= 0.0679m/s

To get height above needle

Pn + 1/2pv²n = Pa + pgh ----2

We equate 1 and 2 together

We get

Pgh = 11466

To get h we divide through by pg

h = 11466/pg

h = 11466/(1.06x10³)x9.81

h = 1.1026

Approximately

Height = 1.1 meters

So it should be 1.10 meters higher

the full calculations are in the attachment.

thank you!

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