Chapter 14, Problem 64RPP

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 $0.20\times {10}^{-6}{\text{m}}^{\text{3}}\text{/s}\text{(0}\text{.2}{\text{cm}}^{\text{3}}\text{/s)}$.

Suppose that there is no Poiseulle resistive friction pressure decrease from the top of the glucose solution in the open bag (position A in Figure 14.12 a) through the tube and down to position C near the entrance to the needle. Which answer below is closest to the minimum height of the top of the bag in order for the glucose to flow down from the tube and through the needle into the blood? Remember that the pressure at position A is atmospheric pressure, which is zero gauge pressure.

a. 0.04 m

b. 0.08 m

c. 0.14 m

d. 0.27 m

e. 0.60 m