# Diffuser Impact on mass flow

## Main Question or Discussion Point

Change in gas velocity and pressure entering and exiting a duct or pipe expansion section (diffuser). Looking for a formula to determine velocity, pressure and density of a gas as it exits a duct or pipe diffuser section based on the entrance area to exit area ratio. Ambient temperature, subsonic, subcritical flow.

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Im pretty sure this has to do with the Steady Flow Energy equation from thermodynamics.

This equation can equate velocities, pressures, mass flow rates, heat input/output and work input/output, enthalpy's and physical changes in height.

for enthalpy use,
h = c(p) dt

For the density of the gas, assuming it is a perfect gas use
P(pressure)*Velocity=m(mass)*R*T(temp in kelvin)

where R=(Universal Gas constant = 8.315)/M ... (M is the molecular mass of the gas)
keep in mind the units of universal gas constant its in "k" or thousand

good luck

Sorry ive made a mistake ..

that second equation is meant to be

P * V(volume) = m R T

note that m /v is density so P/RT = density

hope that helps

Thanks for the tips and equations. Yes I believe that maybe correct also related to Bernoulli's "conservation energy equation only modified for compressible flow. Now I have to figure out how to apply them to solve for the ratio of area expansion to change in velocity or pressure. Gravity does not appear to be a factor so I can ignore it. Once I get one the rest should all follow.

Thanks for the tips and equations. Yes I believe that maybe correct also related to Bernoulli's "conservation energy equation only modified for compressible flow. Now I have to figure out how to apply them to solve for the ratio of area expansion to change in velocity or pressure. Gravity does not appear to be a factor so I can ignore it. Once I get one the rest should all follow.
Gravity can only be ignored if u have a single datum line. This means that the mass flow rate coming into the diffuser is leaving it at the same physical level(height) with respect to a reference plane. If the datum line changes(ie. change in distance from reference plane to the centroid of the diffuser inlet/outlet) between input and output, gravity does become a factor in the steady flow energy equation.

Q_Goest
Homework Helper
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Expansion of an incompressible fluid through a diffuser can be modeled as Ksum mentions, simply using Bernoulli’s equation (less the ideal gas equation). However, for a gas, it’s not quite so simple. The gas is expanding isentropically, so you have to account for this. See attached.

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Yes, for now the flow is subsonic yet above M.3 so it is compressible. In the future it maybe supersonic in which case as I see diffusing/converging have opposite effects. Sounds simple yet gets very complex. Appreciate the assistance very helpful seems to confirm what I was thinking.

If the angle is to wide the flow will separate and you will have a total pressure loss hence the flow is not isentropic anymore and bernoulli does not nessesarily aply anymore.