The Physics Philes, lesson 92: Slow as Molasses
So far in our discussion of fluid mechanics, we’ve assumed that the fluid we’re talking about has no internal friction and has a laminar flow. However, there are important fluids that don’t follow this pattern. What about those? In that case we need know about viscosity and turbulence.
First, let’s take a look at viscosity. As we learned a couple of weeks ago, viscosity is the internal friction of the fluid. Viscous forces oppose the motion of one area of fluid relative to another. Very viscous fluids tend to be kind of thick, like honey or molasses. Viscosity varies with the temperature, but the temperature effects gases and liquids differently. An increase in temperature decreases the viscosity of liquids, but increases the viscosity of gases.
Fluids will tend to stick to solid surfaces. There is something called a boundary layer where the fluid is almost at rest relative to the surface. It’s why dust can stick to the top of a ceiling fan, even when that fan is whirling around.
Last week we learned about Bernoulli’s equation. That equations says that when the two cross sections of a flow tube are at the same height, the flow speed is the same at both ends, as well as the pressure. But that isn’t true when we have a fluid with non-negligible viscosity. Because of that boundary layer, the speed of a fluid is almost zero at the pip walls. The greatest speed will be at the center of the pipe. Viscous forces between the tubes oppose sliding, so we must apply a greater pressure at the back of the flow than at the front to keep the fluid going.
There is a nice, neat relationship to describe the pressure difference required to sustain a given volume flow rate through a cylindrical pipe. If L is the length of the pipe and R is the radius, the relationship
Decreasing R causes in increase in pressure. It might not be obvious, but there are important implications for biology. This relationship explains the connection between high cholesterol (which tends to make blood vessels narrower) and high blood pressure.
Turbulence is also important to biology. Turbulence is an irregular or chaotic flow. It happens when a fluid flows too fast; it will become irregular and continuously change. Bernoulli’s equation doesn’t apply to turbulent flows. That equation requires the flow to be steady state.
Turbulence depends greatly on viscosity. The greater the viscosity, the more likely that the flow flows in thin, smooth layers. That is, that the flow is laminar. Interestingly, in previous weeks we’ve been working off the assumption that fluids have no viscosity and have a laminar flow. In fact, some viscosity is needed to ensure a laminar flow.
Speed is also a determining factor. Fluids are stable at low speeds but can become turbulent if they start flowing too fast. This can be caused by a variety of things, including roughness in pipe walls or variations in fluid density. At low speeds, the disturbances are damped out. However, at high speeds, those disturbances cannot be damped out and the flow becomes turbulent, i.e. the laminar flow is destroyed. Doctors can use this to help diagnose heart problems. Small disturbances in blood flow can be caused by heart problems. The turbulence that results makes a little noise that can be heard through a stethoscope.
Welp, it’s been real, but that’s all we have for fluid mechanics. Next week we’ll start in on mechanical waves.
Featured image credit: Marshall via Flickr