Chapter 11, Problem 080 GO A blood transfusion is being set up in an emergency r

Question

Chapter 11, Problem 080 GO A blood transfusion is being set up in an emergency room for an accident victim. Blood has a density of 1060 kg/m3 and a viscosity of 4.0 × 10-3 Pa-s. The needle being used has a length of 3.0 cm and an inner radius of 0.25 mm. The doctor wishes to use a volume flow rate through the needle of 3.9 x 108 m3/s. What is the distance h above the victim's arm where the level of the blood in the transfusion bottle should be located? As an approximation, assume that the level of the blood in the transfusion bottle and the point where the needle enters the vein in the arm have the same pressure of one atmosphere. (In reality, the pressure in the vein is slightly above atmospheric pressure.) the tolerance is +/-2% LINK TO TEXT Question Attempts: 0 of 6 used SAVE FOR LATER SUBMIT ANSWE SUBMIT ANSWER powered by MapleNet

Explanation / Answer

We use Poiseulle law,

Q= (*P*R4 )/(8L)

Where Q= Flow rate, P= Pressure difference, R= radius of cross section of needle, L= length of the needle, =viscosity of the needle

Rearranging for

P= (8LQ) / (R)----------------(1)

We also have other eqn for pressure difference,

P = gh ---------------(2)

Combining (1) & (2),

(8LQ) / (R) = gh

h = (8LQ) / (gR)

Plugging values,

h =[ (8*4*10^-3*0.03*3.9*10^-8) / (1000*9.8**(0.00025)]

h =0.311 m=31.1cm

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