Intravenous (IV) feeding A patient in the hospital needs fluid from a glucose nutrie...

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.

Assume that there is no resistive friction pressure drop across the needle (as could be determined using Poiseuille’s law). Use the Bernoulli equation and the results from Problems 58 and 59 to determine which answer below is closest to the change in pressure between positions 1 and 2 (P₁ - P₂) in Figure 11.13b.