A patient is receiving medication through an intravenous infusion, as the figure shows. The medication has a viscosity of 2.2 × 10−3 N · s/m2 (do NOT neglect viscosity) and a density of 1050 kg/m3. The needle being used has a length of 0.035 m, has an inner radius of 5.0 × 10−4 m, and has been inserted into a vein that has a gauge pressure of 2.0 × 103 Pa. The IV bag hangs 0.43 m above the location of the needle. What volume of medication enters the vein in 10.0 minutes? Assume the height of the column of medication in the IV bag and connecting tube remains constant during the 10.0 minutes. Give your answer in cm3, and as a point of reference, note that the volume of a standard IV bag is about 1000 cm3.

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Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.