In the Garden Centre The Lad saw a display of a pump for emptying the water from the garden rainwater butt; it takes the place of a tap at the bottom of the butt emptying into a watering can.
Versus the tap it seemed an example of inappropriate technology. This is a subject exercising his mind lately but as it will be a subject of another post shortly, we can move on.
Anyway, the display had one buzzing and pumping away sitting in the bottom of a water butt covered by only few centimetres depth of water. The pumped water went up a length of straight garden hose about a meter and a half and poured out of a garden hose gun in a straight stream under gravity down back into the bottom of the water butt. As he walked by, The Lad let the water stream from the tap wet his fingers and he came to an abrupt halt as he noticed that the water was quite warm. Not hot, you understand, but quite warm enough to to make a really comfortable hand wash.
He pondered on where the heat energy came from and thought that there were several phenomena causing it. He found that they were easy to envisage but were difficult to imagine in the form of the calculation of each contribution to the total heat of the water in the little [almost!] closed system. There would be heating from the shear flow of the leakage round the centrifugal impellor; there would be the friction of the flow against the walls of the hose as it rose up it; then there would be the heat generated as the water jet splashed into the bottom of the butt [the Joule Honeymoon effect according to The Lad – look it up!].
Then he realised that from the point of view of the water in the butt the net sum of velocity and displacement is [apart from the small amount of swirl in the butt] zero. This simple version says that , apart from the bit of swirl in bottom of butt the total power of the pump is changed into net zero velocity and displacement. It only turns into heat. So all the separate sources of heat can be sidelined by this overall calculation.
The summary version of the calculation in its simplicity is enough for us here. It also shows that a suitable insight can simplify estimates. But it is also true that in real engineering, where they have hot oil or hot water coolant flowing in a closed system, there is a need to control the heat flows and to ensure adequate cooling. Then they will have to calculate or experiment or, almost certainly, both to work out what are the contributions of every source of heat generation and sink of heat radiation, convection or conduction. Now that’s what real engineers working on engines or machine tools have to do and do do.
“Work is Heat and Heat is Work” is one version of the First Law of Thermodynamics. There it was – in the Garden Centre.