A patient is given sucrose intravenously. Her venous pressure is 18 mm Hg, and the elevation difference between the intravenous needle and sucrose bottle is 0.80 m. If the rate of sucrose flow is to be 2.0 mL/min, what should the diameter of the 4.0- cm-long needle be? Assume the sucrose has the same viscosity and density as blood.
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Explanation:
Intravenous (IV) feeding A patient in the hospital needs fluid from a glucose nutrient bag. The glucose solution travels from the bag down a tube and then through a needle inserted into a vein in the patient’s arm (Figure 11.13a). Your study of fluid dynamics makes you think that the bag seems a little low above the arm and the narrow needle seems long. You wonder if the glucose is actually making it into the patient’s arm. What height should the bag (open at the top) be above the arm so that the glucose
drains from the open bag down the 0.6-m-long, 2.0 X 10-3-m radius tube and then through the 0.020-m-long, 4.0 X 10-4-m radius needle and into the vein? The gauge pressure in the vein in the arm is +930 N/m2 (or 7 mm Hg). The nurse says the flow rate should be 0.20 X 10-6 m3/s 10.2 cm3/s2.
The blood pressure in the vein at position 2 in Figure 11.13b at the exit of the needle into the blood is 930 N/m2. Use this value and the results of Problems 60 and 61 to determine which answer below is closest to the gauge pressure at position 1 in the tube carrying the glucose to the needle.
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