Chapter 14, Problem 63RPP

EST Intravenous (IV) feeding A patient in the hospital needs fluid from a glucose nutrient bag. The 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 14.12a). 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 solution (density 1000 kg/m³ and viscosity $1.0\times {10}^{-3}\text{N}\cdot {\text{s/m}}^2$) drains from the open bag down the 0.6-m-long, $2.0\times {10}^{-3}-\text{m}$ radius tube and then through the 0.020-m-long, $4.0\times {10}^{-4}-\text{m}$ radius needle and into the vein? The gauge pressure in the vein in the arm is $+930{\text{N/m}}^2$

(or 7 mm Hg). The nurse says the flow rate should be $0.20\times {10}^{-6}{\text{m}}^{\text{3}}\text{/s}\text{(0}\text{.2}{\text{cm}}^{\text{3}}\text{/s)}$.

The blood pressure in the vein at position C in Figure 14.12 b at the exit of the needle into the blood is 930 N/m². Use this value and the results of Problems 14.61 and 14.62 to determine which answer below is closest to the gauge pressure at position B in the tube carrying the glucose to the needle.

a. 1010 N/m²

b. 1410 N/m²

c. 1980 N/m²

d. 2800 N/m²

e. 4620 N/m²