The turboprop engine combines a turbojet engine that drives a propeller. These are the engines of choice for general aviation aircraft in the small category (< 50 passengers). The turbine now drives the compressor, the utilities, and the propeller (power turbine). The thrust obtained by the nozzle is not a big fraction of the overall thrust. The turboprop engine is rated in terms of power delivered to the propeller shaft - shaft horse power. Usually the propeller axis is parallelto the compressor/turbine axis and offset to accommodate a gearbox.
The turboshaft engines are usually employed in helicopters. The turbine drives a shaft which then drives the rotors(main and tail) of the helicopter. The shaft takeoff is usually at right angles to the turbine/compressor axis.
Actual Engine
GE T64 Turboprop
Schematic
Ideal cycle
Cutaway
Cutaway
GE T 58 turboshaft
The turboprop engine drives the propeller through a gear box because of the limitation of the rotational speed due to the propeller.. The turbines typically rotate at 35,000 rpm. The maximum rpm is restricted by sonic conditions at the blade tip
Since there is a limit on the gear reduction, these ratios require multistage gear reduction. The helicopter specially requires multistage gear reduction. For the mechanical engineer, the helicopter gear box is a thing of beauty
The simple fluid mechanics model is not very effective here since the jet exhaust does not provide much of the thrust.