Example 11.7 from College Physics, 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement

Calculating Height of IV Bag: Blood Pressure and Intravenous Infusions

Intravenous infusions are usually made with the help of the gravitational force. Assuming that the density of the fluid being administered is 1.00 g/ml, at what height should the IV bag be placed above the entry point so that the fluid just enters the vein if the blood pressure in the vein is 18 mm Hg above atmospheric pressure? Assume that the IV bag is collapsible.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy for (a)
For the fluid to just enter the vein, its pressure at entry must exceed the blood pressure in the vein (18 mm Hg above atmospheric pressure). We therefore need to find the height of fluid that corresponds to this gauge pressure.
Solution
We first need to convert the pressure into SI units. Since $1.0 mm Hg = 133 Pa$ ,
$P = 18 mm Hg \times \frac{133 Pa}{1.0 mm Hg} = 2400 Pa .$
11.28

Rearranging $P_{g} = hρg$ for $h$ gives $h = \frac{P_{g}}{ρg}$ . Substituting known values into this equation gives
$\begin{array}{l} h & = & \frac{2400 N {/m}^{2}}{(1 . 0 \times 10^{3} {kg/m}^{3}) (9.80 {m/s}^{2})} \\ = & 0.24 m. \end{array}$
11.29
Discussion
The IV bag must be placed at 0.24 m above the entry point into the arm for the fluid to just enter the arm. Generally, IV bags are placed higher than this. You may have noticed that the bags used for blood collection are placed below the donor to allow blood to flow easily from the arm to the bag, which is the opposite direction of flow than required in the example presented here.

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How did it go?

Strategy for (a)

Solution

Discussion

Strategy for (a)

Solution

Discussion