In a hospital, a flexible \"TV\" (intravenous) solution bag contains a drug solu

Question

In a hospital, a flexible "TV" (intravenous) solution bag contains a drug solution (1250. kg/m^2). If the upper part of the bag is flaccid, we can assume that it is in pressure-equilibrium with the surrounding air, so the top surface of the solution inside the bag is at a pressure of 760.0 mm Hg (the hospital is located at sea level) The IV hag is connected by a flexible tube to a needle inserted into a patient's vein located at a height h below the top surface of the solution. If the pressure inside the patient's vein is 790.0 mm Hg. find the minimum height h so that the fluid just barely flows into the patient (and so that the patient's blood does not flow back up the IV tube). (Assume that the top surface of the solution falls with negligible speed. Assume nearly zero flow speed of the blood in the vein.) Show your work. A nurse removes the needle from the patient's vein, and instead just holds the IV needle in the air at the same height h below the IV bag as calculated in part (a). What is the speed of the solution as it flows out of the needle into the air? Show your work.

Explanation / Answer

gauge pressure dP = rho*g*h

(790-760)*10^-3*13600*9.8 = 1250*9.8*h

minimum height h = 0.3264 m

+++++++++++++++++++++

speed = sqrt(2*g*h) = sqrt(2*9.8*0.3264) = 2.53 m/s

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