# Go with the flow

The study of fluids seems daunting, but a quick cup of tea and mention of air travel should spark interest, says JC Gibbings

Fluids in motion are often found in the final chapter in science textbooks.

This may suggest that this is the most difficult topic in A-level physics.

But at this level of study it need not be.

The teacher can illustrate much of this subject from daily observation: the flow of water down a plughole; the swirl of leaves and rubbish around buildings and fences; the rush of water past bridge piers; the behaviour of the steam in aircraft vapour trails; the piling of snow against walls; the form of streaks on the surface of mud-splattered cars; the intensity of wind at the corners of large buildings and at the constriction between them; the change in the appearance of a water jet from a chemical-bench tap as the flow is increased.

You could also stir tea with tea leaves and no milk in a cup, and observe the motion of the leaves as the motion subsides. To understand this phenomenon is to understand, in simple terms, one of the most complex forms of fluid motion.

When a motorway is partially blocked, the speed in the restricted lane is much greater than when queuing up to enter the restriction. The same happens in an airflow, as illustrated in the diagram (right) of the flow over an aerofoil. Approaching the nose the air is travelling at a comparatively modest speed. Above the upper surface, where the streamlines illustrate a constriction, the air is fairly whizzing along, while below, where the streamlines open out, the air comparatively crawls along.

When in an airflow the pressure is dropping along the flow then a piece of air has a net force on it in the flow direction. Newton's law of motion then says that the flow must be accelerated - and so the air speeds up.

This relation between velocity and pressure is expressed in the well-known Bernoulli equation: static pressure plus dynamic pressure is constant (equation b, right). This can be seen as a special case of the first law of thermodynamics (also known as the law of conservation of energy). This is often expressed as: potential energy plus kinetic energy equals constant (equation a).

The student should also see the connection between the Bernoulli equation and Newton's momentum equation.

You can show the Bernoulli effect quite simply. Fold a piece of paper into a tunnel, place it on a table at the edge and blow into it. The tunnel will flatten, not lift off. Now you can understand why roofs lift off in gales and are not blown in. Over the aerofoil the pressure on top is reduced and that below is increased and this gives the lift.

Let us not be shy in describing to pupils the enormous contribution of engineering and science to the growth of our civilisation. Just think of the enormous influence in the 19th century of the development of the railway locomotive and the laying of city sewage and water systems.

The former opened out social life and emancipated almost the whole population by the freedom of travel and the latter transformed the health of the nation. Both were examples of the application of the science of fluid motion: steam (which drove the engines) is a fluid, as is water, with or without sewage.

Again in the 20th century the achievement of aerial flight made a worldwide change to business and social life. Yet last December 17 was just the first centenary of that remarkable day when the Wright brothers first flew in a controlled and readily repeatable manner. Their success was a superb example of the application of scientific knowledge.

The Wright brothers' aerodynamic knowledge was far in advance of their time and this they gained in two ways. First, they experimented rigorously for four years with gliders and, second, they built two wind tunnels in which they performed a very large programme of experiments on forms of aerofoils.

Dr JC Gibbings is retired from the engineering department of the University of Liverpool

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