Question

An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.07 cm³/s through a needle of radius 0.2 mm and length 4.64 cm.

What gauge pressure (in Pa) is needed at the entrance of the needle to cause this flow?
Assume that the viscosity of the saline solution to be the same as that of water, η = 1.0*10^-3 Pa-s, and that the gauge pressure of the blood in the vein is 1500 Pa.

Enter an integer.

Answer 1

Using Poiseuelle's law:

Q = dP*pi*r^4/(8*n*L)

r = radius of needle = 0.2 mm = 0.2*10^-3 m

n = Viscosity of water = 1.0*10^-3 Pa.sec

L = length of needle = 4.64 cm = 0.0464 m

dP = Pressure difference = P2 - P1

P2 = Pressure at the entrance of needle = ?

P1 = Gauge Pressure of the blood in the vein = 1500 Pa

Q = flow rate of saline solution = 0.07 cm^3/s = 0.07*10^-6 m^3/sec

So,

dP = 8*Q*n*L/(pi*r^4) = P2 - P1

P2 = P1 + 8*Q*n*L/(pi*r^4)

P2 = 1500 + 8*0.07*10^-6*1.0*10^-3*0.0464/(pi*(0.2*10^-3)^4)

P2 = 6669.35 Pa

In integer form

P2 = 6670 Pa

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