When an individual of the male persuasion in an institutional circumstance (i.e. work, school, etc.) becomes sexually aroused, due to thoughts of past sexual exploits; the subsequent tightening of the groin area, due to the constriction of pants upon the hardened member, produces a penile-angular shift, which is almost perfectly horizontal in form, and points towards either the left or right. Thus the moniker, Side-Pipe.
Mosieur LePajonais: What, pray tell, is that tubular formation protruding from the side of your pantaloons?
Herr Schmidt: Why, my good man, tis my side-pipe!