Why does the diffuser section generate thrust in a jet engine? I am studying the thrust distribution of jet engines.
But I'm now a bit confused.

In Rolls-Royce's "The Jet Engine" book,

http://aeromodelbasic.blogspot.com/2012/05/thrust-distribution-distribution-of.html


  At the start of the cycle, air is induced into the engine and is compressed. The rearward accelera- tions through the compressor stages and the resultant pressure rise produces a large reactive force in a forward direction. On the next stage of its journey the air passes through the diffuser where it  exerts a small reactive force, also in a forward direction


I understand the first part of the paragraph that the compressor is providing forward thrust, as it is pushing (so compressing) air rearward. But why is the diffuser also providing forward thrust?
And also why the nozzle is providing rearward thrust?

The similar conculsion is also shown here:
http://www.pulse-jets.com/phpbb3/viewtopic.php?t=2183, that the diffuser is providing positive thrust by calculating the pressure force.

From my understanding of basic fluid mechanics,
shouldn't a nozzle be providing forward thrust, like the sprinkler in the garden or a fire hose?
And shouldn't a diffuser be providing rearward thrust, as the outlet speed is slower than the inlet speed, and so m dot X (v - u) is negative?

What's wrong with my understanding?
But why is the diffuser also providing forward thrust?


The diffuser slows down the flow to ease fuel-air mixing and combustion a bit later. If you only focus on entry and exit speeds, there would be no thrust.

However, if you look at the pressures on the diffuser walls, a different result emerges. Slower flow means higher static pressure, and the total pressure right at the compressor exit is already the highest within the whole engine. The pressure on those widening diffusor walls does indeed push the engine forward because of the forward slant of the pressure vector (which acts perpendicularly to the diffusor walls). Your linked pulse jet page explains this quite well.

Of course, no thrust would result if the flow were not heated and thus accelerated further downstream. So the diffuser all by itself will not create thrust; this happens only when it is placed inside a working jet engine.


  And also why the nozzle is providing rearward thrust?


This is not always the case, but here the nozzle has a converging shape which helps to accelerate the subsonic flow and converts the remaining pressure to speed. The walls now have a backward-facing slant, so the pressure vector on them will contribute a backward-facing component. In addition, the high flow speed along the large nozzle walls causes some friction, which needs to be considered, too.

For a comparison, look at the cone behind the turbine wheels. Its thrust contribution only stems from the forward-facing pressure acting on it.