Reply To: Porta's Derivation of Lempor Theory
Broadly speaking, you have it about right, Chris.
In the case of a loco front end, the efficiency is actually miniscule when viewed as a pump. So any attempt at using energy as the main consideration means energy in is a large number – probably known. Losses are a large number but can be estimated (more or less!). The output is a small number, being the energy in minus the losses. However, any error in the other two terms will cause huge errors in the output.
Typical numbers for a Black 5, expressed in megapascals – 340 energy in. 30 out, hence losses in the order of 310.
One has a similar problem with the momentum approach, but are not faced with trying to estimate loss terms for sharp changes in velocity (Particularly Terms 2 & 3 of equation 1 in Porta’s 1974 paper). Here, momentum expressed in megapascals – 210 momentum in, about 30 out.
As far as I can see, the energy approach will give a smaller blast pipe orifice just running some typical numbers, but if you work it all back the difference between approaches is quite small (about 5% on diameter for the Black 5 example). Hence the reason why the Strahl / Porta approach “works”.