Gauge pressure:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{h}}{\mathbf{\rho}}{\mathbf{g}}}$

Poiseuille’s law:

$\overline{){\mathbf{Q}}{\mathbf{=}}\frac{\mathbf{\pi}\mathbf{\u2206}\mathbf{P}{\mathbf{r}}^{\mathbf{4}}}{\mathbf{8}\mathbf{\eta}\mathbf{l}}}$, where Q is the flow rate, P is pressure, r is the radius, η is fluid viscosity, and l is the length of tubing.

Q = (P_{2} - P_{1})πr^{4}/8ηl

P_{2} = 8ηlQ/πr^{4} + P_{1} = 8Qηl/πr^{4} + hρg

P_{1} is the pressure in the patients vein

An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.120 cm^{3}/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 20 C)

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