When fluid flows through a tube...

Let’s assume a perfect scenario, where fluid of the same consistency (gas or liquid) flows through a perfectly straight pipe. As Isaac Newton reminds us, “For every action, there is an equal and opposite reaction.” In other words, whenever something is pushed, it is also pulled. When you sit in a chair, gravity is pulling your butt into the seat, and the seat is pushing up onto your butt. In our pipe and fluid example, one force is pushing the fluid through the pipe, and the other force is preventing the fluid from moving. When considering fluids, the difference in pressure between the beginning of the tube and the end of the tube is what drives the flow forward. The flow is slowed, however, by resistance from the walls of the tube.

In perfect circumstances, when a fluid flows in a laminar (“straight”) manner through a tube, the rate of flow is dependent upon the amount of resistance it encounters. Close to the sides of the tube, there is a lot of resistance from the fluid ‘rubbing’ onto the walls. This makes the flow very low. As you examine the fluid farther and farther from the wall, the flow will increase because the contribution of wall resistance is smaller.

This flow relationship in the pipe ends up looking like a parabola. To demonstrate this principle in action, I have drawn you a picture of laminar flow through a tube.

With a smaller diameter tube, the contribution of resistance will be higher than a really large tube, where the center of flow is very far from the wall.

The second thing to consider is the length of the tube. The longer a tube, the more time that fluid will be in contact with its walls, which contributes to resistance. This is the same reason why you don’t see any 50 ft USB cables. The flow through the wire (electricity) is also impacted by resistance. Since USB uses a relatively low voltage, there isn’t enough driving force to get a quality signal more than about 16 feet without significant signal degradation (according to USB specifications).

The final two things to consider are viscosity and turbulence.

Turbulence is unavoidable in real life. In the human body, we don’t see perfectly straight pipes like the ones shown above. Our vessels are dynamic, and differ in size and shape along their course. When turbulence does occur, the flow through the pipe is no longer nice and straight. Rather, it becomes chaotic, and disrupts the normal layering of flow. This creates additional resistance. Thus, factors that increase turbulence also increase resistance to flow.

The conversion of laminar flow to turbulent flow can be predicted using Reynold’s number, and takes into account viscosity (‘stickiness’) of fluid, and the speed (velocity) of the fluid. Viscosity can be easily understood by comparing water to maple syrup. Water flows easily and is very ‘thin’ as compared to maple syrup, which has a thick and sticky quality, which holds its flow together.

When the speed of the fluid is high, this promotes increased turbulence. Likewise, when the viscosity of the fluid is low, turbulence is promoted.

Turbulence may also be affected by the diameter of the tube. If you try to push 100cc of fluid through a coffee straw, and then try to push 100cc of fluid through a garden hose, you will find that you must push the fluid through the coffee straw at a much faster speed in order to finish at the same time as the garden hose. As we said earlier, when the speed of the fluid is high, turbulence is promoted. Thus, a larger pipe is inherently less prone to turbulent flow when the same volume of fluid must be infused over the same period of time.