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Putting the pressure on the IV

Page history last edited by Joe Redish 8 years, 4 months ago

A simplified version arrangement that is used to provide IV (intravenous, literally “inside the vein”) fluids to patients is shown in the figure below shows a simplified version of such a setup with some hypothetical numbers. 


Source of photo: Wikipedia commons


An IV bag is filled initially with saline solution (with density 1020 kg/m3 and the same viscosity as water) and is connected to a vertical IV tube with a total length 2.00 m, and inner diameter 3.0 mm.  The bottom of the IV tubing is inserted into the patient’s vein, where the gauge pressure is 7500 Pa.  The IV bag is collapsible and very flexible, so you may assume that the bag never has any air in it, and also that the pressure everywhere outside the bag is just atmospheric pressure.   (In this scenario, there is no need for a pump.  Actual IV “drips” may also employ a pump.) 


(a)  What value must the height, h, have in order for the pressure at the bottom of the IV tubing to be equal to the pressure in the vein, so the IV fluid can just start to flow?


 (b)  What is the resulting volume flow rate of the fluid out the bottom of the IV tubing in the scenario described above?  Here, use the fact that 103 liters = 1 m3 to express your answer in ml/sec.  (Your answer will illustrate why real IV’s have a flow-limiting devices we haven’t considered here!)


 (c)  When a nurse goes to change the IV bag, she accidentally disconnects the IV tubing from the bag in this configuration.  What is the flow speed of the IV fluid as it squirts out of the hole where the IV tube inserts?  (Assume the fluid is approximately at rest everywhere inside the bag.)


Suzanne Amador-Kane, Haverford College, 1/20/12

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