Question

Topic: Fluid mechanics

One patient receives saline solution injected into a vein through a needle 4 cm long and 0,2 mm radius. The saline solution has a density and viscosity approximately equal to the water at ambient temperature and exits from a tank located 1m above the needle

a)Find the saline solution pressure at the needle inlet

b)Knowing that the blood pressure in the vein is about 2000 Pa above atmospheric pressure, calculate the time it takes to exhaust the saline solution contained in cylindric deposit of 20cm in height and 5cm radius

Answer 1

The saline solution is at atmospheric pressure. This can be ascertained from the fact that it does not explode or implode in the room conditions.

The pressure at the needle inlet due to the saline solution hanging 1 m above it (effectively acting as a reservoir) is:

The total pressure is

The blood pressure is given as:

The pressure difference is 7810 Pa

Torricelli's equation is:

The rate of flow is given by:

The volume of fluid in the packet is

Thus the time to completely unload all the fluid is: