Introduction

This title covers several things that are of interest to the mechanical engineer. Our interest is in liquids that are at rest in a container under the effect of the gravitational field of the Earth. These liquids can exert very large forces even when they are stationary. Installations like flood barriers, river control devices and ships are subjected to large forces exerted by liquid in contact with them and we need some way of estimating these forces. Even when the liquid exerting the force is moving it might still be good enough for the purposes of engineering to regard the liquid as being at rest for calculations involving pressure. For example, even a cursory look at a ship under way shows that there are surface waves along the hull. I think that it is inescapable that the pressure under the hull must vary in some way along the length and that that pressure variation is closely connected with the profile of the surface as seen on the side of the ship. It is better to quantify this variation by calculating it from the wave profile than to do nothing.

 

So we need to make a start. We need to form a mental picture of a liquid at rest. The trouble is that any substantial body of liquid is usually on the move as a result of the wind or tide or perhaps an outflow and inflow. Whilst the flow within the liquid in this state can be both interesting and complicated my interest here comes from regarding it as a liquid at rest. However I think that I have only once seen a substantial body of liquid that was at rest in the sense meant in this chapter. It was a pool of water in a limestone cave. It was lit artistically for visitors to the cave and the surface was like a mirror and the reflection of the roof of the cave appeared to be identical to the cave. Of course someone could not just look at such perfection and dabbled fingers in it. I wondered just how long it would take to get back to its former state. Engineers do not deal with liquids that are at rest but with liquids that they think are near enough at rest for the purpose of analysis. It is a major step forward to understand a liquid at rest.

 

I think that it is helpful to have some idea of what goes on in a liquid at molecular level. Substances that are in a liquid state are well known to all of us. However the internal structure of a liquid is only recently being understood. The most common liquid is obviously water and water is also the liquid with the most extraordinary properties. The most important matter for us is its molecular behaviour. The molecule of water has a shape that stems from its structure. The two hydrogen atoms are bonded together and the oxygen atom is bonded to both of them to produce a T shaped arrangement. These T shaped molecules pack together closely and, under the action of intermolecular forces, the molecules form clusters. These clusters are very short lived and a single molecule may change the molecules with which it forms clusters as many as 10¹² times every second[1]. The size of the clusters varies but the dominant size is five molecules.

 

These facts do not concern us directly but they do tell us that the size of molecules is unimaginably small and the distance between them, when they form part of a liquid, is also very small. Even if we start to talk about large molecules like the long chain molecules of some plastics they are still very small. What does concern us is that if water, and any other liquid with a similar structure, is continually in a such a state of internal agitation it cannot retain a shape like a solid does. It follows that it can change shape in response to any force that might be applied to it. In fact I can see no way that it can offer any resistance except during a change in shape.