NASA Logo - Web Link to

+ Text Only Site
+ Non-Flash Version
+ Contact Glenn

Computer drawing of gas turbine schematic showing the equations
 for pressure ratio, temperature ratio, and exit velocity for a nozzle.

Most modern passenger and military aircraft are powered by gas turbine engines, which are also called jet engines. There are several different types of jet engines, but all jet engines have some partsin common. All jet engines have a nozzle which produces the thrust as described on the thrust equation slide. The nozzle also sets the total mass flow rate through the engine as described on a separate slide. The nozzle sits downstream of the power turbine and, while the nozzle does no work on the flow, there are some important design features of the nozzle.

Because the nozzle does no thermodynamic work, the total temperature Tt through the nozzle is constant. Referring to our station numbering, the nozzle entrance is station 5 and the nozzle exit is station 8. Tt8 divided by Tt5 is 1.0

Tt8 / Tt5 = 1

The total pressure pt across the nozzle is constant as well:

pt8 / pt5 = 1

The static pressure at the exit of the nozzle is equal to free stream static pressure, unless the exiting flow is expanded to supersonic conditions. A convergent-divergent nozzle will have supersonic exit flow, a simple convergent nozzle will not. The ratio of the nozzle total to static pressure ratio is called the nozzle pressure ratio NPR.

NPR = pt8 / p8 = pt8 / p0

Considering the energy equation for the nozzle, the specific total enthalpy ht is equal to the static enthalpy plus the square of the exit velocity divided by two.

ht8 = h8 + V8 ^2 / 2 / nn

An efficiency factor nn has been included here to account for all the losses in the nozzle, but its value is normally very near 1.0. With a little algebra which you learned in middle school, and using the definitions shown on the slide, you can solve the energy equation for the exit velocity Ve = V8:

V8 = sqrt(2 * nn * cp * Tt8 * [1 - (1 / NPR)^((gam -1 ) / gam)] )

Using this velocity, and the mass flow rate through the engine, we can solve the thrust equation for the amount of thrust produced by the nozzle.

As shown on this slide, the exit velocity depends on the nozzle pressure ratio and the nozzle total temperature. The nozzle pressure ratio depends on the exit static pressure and the nozzle total pressure. We can determine the nozzle total pressure from the free stream conditions and the engine pressure ratio, EPR. EPR depends on the pressure ratio of all the other engine components. We can also determine the nozzle total temperature from the engine temperature ratio , ETR. ETR depends on the temperature ratio of all the other engine components. With this information, we can solve for the thrust developed by a jet engine.

The nozzle performance equations work just as well for rocket engines except that rocket nozzles always expand the flow to some supersonic exit velocity. You can explore the design and operation of turbojet and rocket nozzles with our interactive nozzle simulator program which runs on your browser.


Guided Tours
  • Button to Display Previous Page EngineSim - Engine Simulator: Button to Display Next Page
  • Button to Display Previous Page Nozzle: Button to Display Next Page
  • Button to Display Previous Page Thrust Equation: Button to Display Next Page
  • Button to Display Previous Page Nozzle Simulator: Button to Display Next Page

Navigation ..

Button to Display Aerodynamics Index Button to Display Propulsion Index Button to Display Model Rocket Index
Beginner's Guide Home Page


     First Gov Image

+ Inspector General Hotline
+ Equal Employment Opportunity Data Posted Pursuant to the No Fear Act
+ Budgets, Strategic Plans and Accountability Reports
+ Freedom of Information Act
+ The President's Management Agenda
+ NASA Privacy Statement, Disclaimer,
and Accessibility Certification


Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: May 13 2021

+ Contact Glenn