Nozzle and Diffuser

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For more analyses of compressible flow through nozzles and diffusers, click the topic “Gas Dynamics” please: Gas Dynamics

A nozzle is a device which accelerates fluid. During this process, velocity of fluid increases with decreasing pressure.


A diffuser is a device which slows down fluid. That means, velocity of fluid decreases with increasing pressure.


The 1st law of thermodynamics:

1 hauptsatz

No work is involved in nozzles and diffusers:


The change of potential energy of fluid flowing into and out of nozzles and diffusers is negligible because of almost no height change.

 (epot)out – (epot)in≈0 → g∙(zout – zin)≈0

Nozzles and diffusers are also regarded as steady-flow engineering device, so the term at the right-hand side equals zero:

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Furthermore, mout=min because of conservation of mass.

So now we obtain a simplified expression for nozzles and diffusers:

q + (hin +o.5∙c2in) – (hout+o.5∙c2out) =0

q + (hin –hout) + 0.5∙ (c2in – c2out) =0


  • q=heat transferred per unit mass
  •  hin= specific enthalpy of inlet fluid
  •  hout= specific enthalpy of outlet fluid
  •  cin= velocity of inlet fluid
  •  cout= velocity of outlet fluid

We notice that velocity appears in the equation of energy balance, so the conservation of mass is usually taken into consideration in order to solve the problems:

ρin∙cin∙Ain= ρout∙cout∙Aout


  • A= section area
  • ρ=density

Another necessary equation is the law of ideal gas:

p= ρ∙R∙T


  • p=pressure
  • R=specific gas constant
  • T=temperature
So usually we need three equations to solve the problems related to nozzles and diffusers:
  • The conservation of energy:
q + (hin – hout) + 0.5∙ (c2in – c2out) =0
  • The conservation of mass:
ρin∙cin∙Ain= ρout∙cout∙Aout
  • The law of ideal gas:
p= ρ∙R∙T