Although, we are all absolutely familiar with the everyday behaviour of water, with our understanding encapsulated in folksy sayings such as ‘Water always finds its own level’ and ‘It’s like trying to push water uphill!’ these sayings are not sufficient to allow us to accurately predict how water will behave in a given set of circumstances. To do this, we need rather more detail, as encapsulated in hydraulic theory.

The principles of hydraulics really are quite simple and intuitive. First and foremost is the principle of conservation of mass: water is neither created nor destroyed as it moves around, so a simple process of carefully adding up the volumes of water passing fixed points over time should allow us to ‘close the water balance’, and make sure every drop is accounted for. This is often easier said than done, but there are no circumstances in which mass conservation does not apply.

The second key principle is that of conservation of energy, which states that energy cannot be created or destroyed; it can only be transformed from one form to another. In hydraulics it is the interplay between two forms of energy – potential and kinetic – that dominates. Potential energy is simply that energy inherent in a mass of water perched above a drop, and is readily calculated by multiplying the mass of water by the height of the drop and by the acceleration due to the force of gravity. Kinetic energy is the energy inherent in flowing water – the energy that can knock you off your feet while wading through a stream. To calculate this, we multiply half of the mass (M) of the water by the square of the velocity (V) (i.e. kinetic energy equals ½ M.V 2). The classic example of conversion of potential energy to kinetic energy is hydroelectric power generation, in which potential energy in an upstream reservoir is converted into kinetic energy as it flows down through the turbine. However, the interplay between the two occurs at all scales under natural circumstances.

It turns out that for purposes of most hydraulic analysis it is convenient to think not so much in terms of conservation of energy in general, but rather in terms of conservation of momentum which equals mass times velocity. To grasp why conservation of momentum is important, think about a river you know well. Where the channel is wide and deep, the water can appear to be almost stagnant: the velocity of the water is very low. Where the channel becomes narrow and/ or shallower, such as between bridge piers, the velocity picks up immediately.

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