Nozzle and Diffuser

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

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

The 1st law of thermodynamics:

+ + ∙ ℎ + 2 + ∙ = ( ∙ + + )No work is involved in nozzles and diffusers:

ΣWj=0

The change of potential energy of fluid flowing into and out of nozzles and diffusers is negligiblebecause 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:

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∙c2

out) =0

q + (hin –hout) + 0.5∙ (c2in – c2

out) =0

where

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 isusually taken into consideration in order to solve the problems:

ρin∙cin∙Ain= ρout∙cout∙Aout

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 + (hin - hout) + 0.5∙ (c2in – c2

out) =0

The conservation of mass:

ρin∙cin∙Ain= ρout∙cout∙Aout

The law of ideal gas:

p= ρ∙R∙T