A patient is to be given a blood transfusion. The blood is to flow through a tub

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 cm^3 of blood per minute. How high h should the bottle be placed above the needle? Use rho_blood = 1.05 times 10^3 kg/m^3, eta_blood = 4.0 times 10^-3 Pa middot s. Assume the blood pressure is 72 torr above atmospheric pressure. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

blood pressure is 72 torr above atmospheric pressure

so blood pressure=9599.21 Pa+101325 Pa=110924.21 Pa

density of blood=pho=1.05*10^3 kg/m^3

viscocisty coefficient=n=4*10^(-3) Pa.s

radius=r=diameter/2=0.9 mm/2=0.9*0.001/2=4.5*10^(-4) m

length=l=34 mm=0.034 m

flow rate=3.2 cm^3/min

=3.2*10^(-6) m^3/(60 seconds)

=5.3333*10^(-8) m^3/s

as flow rate=pi*r^4*pressure difference/(8*n*l)

==>pressure difference=5.3333*10^(-8)*8*4*10^(-3)*0.034/(pi*(4.5*10^(-4))^4)=450.43 Pa

then pressure at the entry point of the needle=blood pressure + 450.43

=110924.21+450.43

=111374.64 Pa

then 1 atm+pho*g*h=111374.64

==>1.05*10^3*9.8*h=111374.64-101325

==>h=0.9766 m

so the height of the bottle should be 0.9766 m

in 2 significant figures, answer=0.98 m

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