Answer to Question #197490 in Mechanics | Relativity for saron

Question

An intravenous (IV) system is supplying saline solution to a patient at the rate of

0.120 cm3 /s through a needle of radius 0.150 mm and length

2.50 cm. What pressure is needed at the entrance of the needle to cause this flow,

assuming the viscosity of the saline solution to be the same

as that of water? The gauge pressure of the blood in the patient’s vein is 8.00 mm

Hg. (Assume that the temperature is 20ºC .)Strategy Assuming laminar flow,

Poiseuille’s law applies.

Answer 1

Gives

Q=0.120 $cm^3/sec$

$$=12\times10^{-8}m^3/sec$$

$l=2.50cm =2.50\times10^{-2}m$

$$r=0.150mm=0.150\times10^{-3}=15\times 10^{-5} meter$$

Viscosity$(\eta)=8.00mmHg =1066.58pa$

1mmHg =133.322 Pa

We know that

$Q=\frac{\pi ∆p r^4}{8\eta l}$

$∆p=\frac{8Q\eta l}{\pi r^4}\rightarrow(1)$

equation (1) Put value

$$12\times10^{-8}=\frac{3.14\times∆p\times (15\times10^{-5})^4}{8\times10^{-3}\times2.50\times10^{-2}}$$

$∆p=\frac{8\times12\times10^{-8}\times10^3\times2.50\times10^{-2}}{3.14\times(15\times10^{-5})^4}$

∆p=15097.90 Pa

∆p=p-1066.58

P=15097.90+1066.58=16164.48 Pa