Tag Archives: mechanics

Reynolds’ World

What’s it like for little things like bacteria to move around? How do they swim from place to place?

We know that swimming feels different from walking. Part of it is the feeling of being suspended, where instead of the firm solidity of the earth and the  insubstantial give of air, we have the water on all sides, supporting not just our feet but our legs, arms, and body. But also, it’s a lot harder to move through water! The same quality that makes us feel supported also impedes movement, so that even a very efficient swimmer will be easily outpaced by someone strolling along on dry land.

Scientists have a way to quantify that  difference, using a measure called the Reynolds number. The Reynolds number compares how strong inertial forces are in a fluid, which come from the particle size and the weight of the particles, with the viscosity of the fluid. If a fluid has low inertial forces compared to its viscosity, it has a low Reynolds number, and if it has high viscosity compared to its inertial forces, then its Reynolds number is low. So fluids with a high Reynolds number are easier to move through, and fluids with a low Reynolds number are harder to move through. The pitch of the Trinity pitch drop would have a very low Reynolds number! And fluid flow in high Reynolds number environments tends to have more chaos, vortices and eddies that can arise because of how easy it is to move light things that don’t stick together, like molecules of air.

So it turns out that what strategy you use to move in a low Reynolds number environment is different from what you’d use in a high Reynolds number environment. Of course, we already know that, because if we try to walk or run in water, it doesn’t work very well! Running is a great way to get around when you are moving through thin air with the solid ground beneath you, but humans have developed various modes of swimming for water, that take advantage of our anatomy and account for the different nature of water.

But remember, we are largely made up of water! So what about our moving cells and bacteria, which have to get around in a low Reynolds number environment all the time? And keep in mind that our cells are very small, subject to molecular forces and a lot closer to the size of water molecules than we are. Not surprisingly, there are different forms of swimming that take place in our cells. One of the most common is using a rotating propeller, a little like the blade on a helicopter, to move forward. These structures are called flagella and are common on the surface of various types of cells, to use rotary motion as a way of easily moving through the high Reynolds number environment.

So the next time you are walking around with ease, take a moment to imagine how different it is for everything moving from place to place in and around your cells. It is a whole different world, right inside our own!

Video

How Differential Gear Works

An explanation of how differential gear works in a straightfoward and clear video. Skip to the end – does what they’re talking about make sense? Now watch from the beginning (start from 1:50 if you want to skip the intro) and see them build up from basic principles until they’ve reached the same point. Does it make sense now?

Contrast this with a written explanation:

A differential is a device, usually, but not necessarily, employing gears, which is connected to the outside world by three shafts, through which it transmits torque and rotation. The gears or other components make the three shafts rotate in such a way that a=pb+qc, where  ab, and  c are the angular velocities of the three shafts, and  p and  q are constants. Often, but not always,  p and  q are equal, so  a is proportional to the sum (or average) of  b and c. Except in some special-purpose differentials, there are no other limitations on the rotational speeds of the shafts. Any of the shafts can be used to input rotation, and the other(s) to output it.

In automobiles and other wheeled vehicles, a differential allows the driving roadwheels to rotate at different speeds. This is necessary when the vehicle turns, making the wheel that is travelling around the outside of the turning curve roll farther and faster than the other. The engine is connected to the shaft rotating at angular velocity  a. The driving wheels are connected to the other two shafts, and  p and  q are equal. If the engine is running at a constant speed, the rotational speed of each driving wheel can vary, but the sum (or average) of the two wheels’ speeds can not change. An increase in the speed of one wheel must be balanced by an equal decrease in the speed of the other.

(taken from Wikipedia)

While this is almost certainly an accurate description of the forces behind the device, it’s nowhere near as easily understood as a visual representation. It’s important to understand when visuals can help your explanation and if you do use them it’s extremely important to make sure it’s clear and accessible.

And lest you think these are newfangled concepts – this video is from the 1930’s!