In post 17.15, we saw how fluid flow could be explained by two equations – Bernoulli’s equation (conservation of mechanical energy) and a continuity equation (conservation of mass). But, conservation of mechanical energy assumes that the viscosity of the fluid is negligible because viscosity dissipates mechanical energy (post 17.17) and so is similar to friction… Continue reading 20.35 Incompressible and compressible fluid flow

Before you read this post, you should understand the dot product of vectors (appendix 2 post 17.13), the cross product of vectors (post 17.37) and partial differentiation (post 19.11). I have been asked to write a post on the Navier-Stokes equation that was briefly introduced in post 17.15. Before I write it, I need to… Continue reading 20.34 The operator ∇

I have written this post to help students who are studying mechanics. My blog is recommended as a source of information to first-year undergraduate students studying mechanics at a UK university. Unfortunately, they have found it difficult to relate the structure of the blog to the list of topics in a conventional mechanics course. So… Continue reading 20.33 Using this blog to study mechanics

Before you read this, I suggest you read post 16.30. In post 20.27 we met optical isomers – molecules that have thee same atoms joined to each other but are not identical to their mirror images. Isomerism is the existence of different molecules with the same chemical formula; the different molecules are called isomers. Isomerism… Continue reading 20.32 Isomerism

The picture shows a line of length a and another line of length b that are joined to make a line of length a + b. Note that a is longer than b. Now if a/b = (a + b)/a the result is called the golden ratio, φ. It has other names: for example, the… Continue reading 20.31 The golden ratio

Before you read this, I suggest you read post 20.27. The picture above shows a molecule of tartaric acid. This molecule is chiral – it is not identical to its mirror image (post 20.27). The form of tartaric acid shown in the picture is called D tartaric acid; its mirror image is called L tartaric… Continue reading 20.30 Diastereoisomers

Introductions Before you read this, I suggest you read posts 20.27 and 20.28. In post 20.27, we saw that optical isomerism occurs when a molecule is not identical to its mirror image. The two forms of the molecule are called optical isomers. They exist as the D or the L form that are mirror images… Continue reading 20.29 Properties of optical isomers

Before you read this, I suggest you read post 19.9. In post 19.9, we saw that light can be considered as an electromagnetic wave. This wave consists of an electric field and a magnetic field that oscillate perpendicular to the direction of propagation of the wave, as shown in the picture above. The electric field… Continue reading 20.28 Polarised light

Have you ever tried to put your right shoe on your left foot? Or your left shoe on your right foot? If you can do either, the result will be very uncomfortable! But the width, length and height of both shoes are identical. And the outer, inner and upper curvatures are all the same. So… Continue reading 20.27 Chirality

Before you read this, I suggest you read post 20.25 Normally, we think that objects spontaneously minimise their potential energy so that, for example, an object falls to the ground when it is released (post 16.21) and a stretched spring recoils when released (post 16.49). But this can’t be true for the molecules in a… Continue reading 20.26 Boltzmann and other distribution laws