Answer to Question #111400 in Physics for marie

Question

You are giving an IV to a patient (using the old- fashioned way of using gravity to dictate the flow rate of the fluid into the patient). The bag has a volume of 1 L and empties through a needle of radius 0.42 mm whose length is 6.9 cm. Assume the viscosity of the fluid is that of water (0.001 Pa s), the
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density of water is 1000 kg/m , and the pressure in
the vein can be assumed to be 18 mmHg. If you want to administer the fluid in 1 hour, how high should you raise the bag of fluid above the patient?

Answer 1

$$\frac{\Delta V}{\Delta t}=\frac{\pi r^4\Delta p}{8\eta l}\to \frac{0.001}{3600}=\frac{\pi (0.00042)^4\Delta p}{8(0.001 )(0.069)}$$

$$\Delta p=1568.5\ Pa=\rho g h -P_v$$

$$1568.5=(1000)(9.8) h -18(133)$$

$$h=0.40\ m=40\ cm$$