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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 1^st law of thermodynamics:

No work is involved in nozzles and diffusers:

ΣW_j=0

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

 (e_pot)_out – (e_pot)_in≈0 → g∙(z_out – z_in)≈0

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

Furthermore, m_out=m_in because of conservation of mass.

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

q + (h_in +o.5∙c²_in) – (h_out+o.5∙c²_out) =0

q + (h_in –h_out) + 0.5∙ (c²_in – c²_out) =0

where

• q=heat transferred per unit mass

•  h_in= specific enthalpy of inlet fluid

•  h_out= specific enthalpy of outlet fluid

•  c_in= velocity of inlet fluid

•  c_out= 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:

ρ_in∙c_in∙A_in= ρ_out∙c_out∙A_out

where

• A= section area

• ρ=density

Another necessary equation is the law of ideal gas:

p= ρ∙R∙T

where

• 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 + (h_in – h_out) + 0.5∙ (c²_in – c²_out) =0

• The conservation of mass:

ρ_in∙c_in∙A_in= ρ_out∙c_out∙A_out

• The law of ideal gas:

p= ρ∙R∙T