Lesson 4 - Principles of Fluid Mechanics 2

In many ways, the conservation of energy is an extension to the conservation of mass as it also deals with the ‘you get nothing for nothing’ scenario. This time, however, it is related to energy rather than mass.

The formal definition of the conservation of energy, which is based on the first law of thermodynamics, is:

Energy can be neither created nor destroyed but only converted from one form to another.

Conservation of energy has many applications in engineering and brewing; as we are considering fluid dynamics, we will restrict our attention to the application of the conservation of energy to three forms which are highly relevant to fluids:

• Gravitational potential energy

• Kinetic energy

• Pressure energy

Let us look at each of these in turn.

Gravitational potential energy

This is a form of energy which a fluid possesses when the fluid is at a vertical distance above a reference height. An increase in vertical distance increases the quantity of potential energy.

That may sound a bit confusing but imagine if you wanted to move a bucket of water from the ground floor of a building up to the first floor. To do so, you have to use some energy carrying the bucket up the stairs. Because energy is conserved, the energy you would have used would have been imparted to the bucket.

If you looked at the bucket, it would not obviously appear as if it had increased energy, but imagine the ways in which you could release this potential energy? These could include:

• If you dropped the bucket of water out the window, it would give up its gravitational potential energy on impact with the ground, or the unsuspecting person it hit.

• Being slightly more constructive, we could pour the water down a pipe and use the potential energy within the water to drive a small turbine or paddle.

Kinetic energy

This is a form of energy which a fluid possesses when it is moving with velocity. The higher the fluid velocity, the greater the quantity of kinetic energy.

Kinetic energy is comparatively easy to appreciate:

• A fast-flowing river has a high value of kinetic energy which nature uses to cut the path of the river into the earth.

• A nozzle placed at the end of a hose can be used to create a high-velocity stream of water, with a high value of kinetic energy which can be used to remove dirt from your car (think of a jet-washer).

Pressure energy

This is a form of energy which a fluid possesses when it is at an elevated pressure, i.e. the fluid is pressurised.

Again, this is quite an easy form of energy to appreciate:

• Inflate a balloon by increasing the pressure of the air in it, and its pressure energy increases. This can be converted into kinetic energy by releasing the balloon to let it fly around the room!

• Over pressurise a can of beer by shaking it excessively and then open it and you will get a very good feeling for pressure energy!