Chapter 14, Problem 65RPP

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 there is a Poiseuille resistive friction pressure decrease form the top of the glucose solution (position A in Figure 14.12 a) through the tube and down to position C near the entrance to the needle. How will this affect the placement of the bag relative to the arm?

a. The bag will need to be higher.

b. The bag can remain the same height above the arm.

c. The bag can be placed lower relative to the arm.

d. Tool little information is provided to answer the question.