Along a smoothly flowing stream, the total mechanical energy per unit volume, made up of pressure, motion and height, stays constant. If the pipe narrows and the fluid must speed up to keep the same flow rate, it can only get that extra speed by giving up some pressure. This trade-off between how fast the fluid moves and how much pressure it carries is exactly what Bernoulli's equation expresses. Heat and work belong to thermodynamics, stress and strain to mechanics of solids, and diffusion and temperature to kinetics, none of those pairs describe flowing fluids. So Bernoulli's equation relates pressure and velocity.