Physics of Intravenous Drips

After analyzing the blood pressure difference between aorta and arterial capillaries, we learned that physics significantly influences the functions and health of living creatures, especially our human beings. Thus, it is not surprising that physics is also widely applied in medical field. Here, I wish to explore the physics behind a very common clinical medication route——intravenous injection.

One of the most important things that we consider during IV is that——how come the medication goes into the vein instead of blood squirting out?

We may first look at the structure of the IV equipment. From the figure, we can see that the intravenous drip equipment is mainly composed of an IV bag that has a medication valve and fluid inside, drip chamber that prevents air embolism, IV tube, and IV catheter connecting with the vein of the patient.

To make the medication get into the vein, the pressure of the fluid containing the medication has to be 109 kPa at the injection point. The IV bag is connected to atmospheric pressure, and the density of the saline fluid injected is about 1020 kg/m³. Assume that the velocity of the dripping is 200ml/hr. The diameter of the IV catheter is 26mm and the cross sectional area of the IV bag is 50 cm².

According to Bernoulli’s Equation:

The velocity of the fluid in IV bag and the velocity of the fluid in the needle:

Plug in to the Bernoulli’s Equation:

From the calculation above, we know that the IV bag should be at least 0.77m higher than the injection site of the patient in order to successfully inject the medication into the vein of the patient. Otherwise, the would be some risks for the blood to squirt out from the catheter.