11348

Linear Momentum Balance in Aerodynamic Thrust

The force generated by a jet engine on a static thrust stand is determined using Newton's second law of motion. For a fixed, nondeforming control volume with uniform and steady flow, the sum of the forces is equal to the net rate of linear momentum flow through each control surface. Use sliders to change inlet and outlet radii, inlet velocity and inlet pressure. The anchoring force is the force to keep the jet engine stationary. The inlet and outlet pressures are gage pressures ().

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]

DETAILS

The linear momentum balance for a nondeforming, stationary control volume is:
.
Since the flow is steady, the momentum balance simplifies to:
,
where
is velocity (m/s),
is the density of the fluid (),
represents the product of the component of velocity normal to the control surface,
is the differential area of the control surface ().
Application of the momentum equation to the contents of the control volume yields:
,
where
is velocity (m/s),
is gage pressure (kPa),
is the thrust force (N).
For one-dimensional flow:
.
Due to conservation of mass :
,
,
using the ideal gas law:
,
where
is the mass flow rate (kg/s)
is the density of air at the inlet (),
is atmospheric pressure,
is the ideal gas constant,
is temperature (K).
The continuity equation is used to determine the velocity of air exiting the turbine:
,
,
where and is the radius (m).
Solving for the thrust force:
.
Reference
[1] B. R. Munson, T. H. Okiishi and W. W. Huebsch, Fundamentals of Fluid Mechanics, 6th ed., Hoboken, NJ: John Wiley & Sons, 2009.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+