Finding Maximum Thrust: Flow Rate, Velocity, Area & Pressure

[GiTS]

I've been thinking about how to calculate how to find maximum thrust. But I can't find any equations for flow rate and pressure and area. I know that thrust is a force and force is mass x acceleration. But I don't know how id get an acceleration. There's an exit velocity at the nozzle of the rocket but there's no acceleration. The acceleration stops at the nozzle.
I also know that the higher the exit velocity, the higher the thrust. And the way to increase exit velocity is to increase the pressure and the way to increase the pressure is to decrease the nozzle cross-sectional area. But decreasing the nozzle cross sectional area decreases the volumetric flowrate thereby decreasing the mass flow rate which decreases the mass part of the force equation and the thrust. I need equations relating flow rate, flow velocity, area, and pressure.

 

[Danger]

I'm not in a position to offer you any formulae right now, but keep in mind that the most effecient way to increase your thrust at a given flow rate is to increase the combustion temperature.

 

[FredGarvin]

You need to look at it in terms of momentum rate. You have your mass flow rate and you have the exit velocity. That will give you the main component of thrust. There can be additional thrust if the nozzle allows for the proper expansion. In that case you then have a pressure thrust acting over the area of the exit plane of the nozzle and the two components are added.

Here's a pretty good link:
http://www.grc.nasa.gov/WWW/K-12/airplane/rktthsum.html

 

[rcgldr]

The alternative to decreasing nozzle size is to increase the burn rate of the fuel. Although the thrust is directly related to mass x acceleration, a close enough approximation can be made by just using the velocity of the expelled matter.

The main fact about higher velocity, is that the higher the velocity, the more efficient the engine, more thrust for the same amount of fuel.

Also the acceleration continues past the nozzle, as the exhausted gas continues to expand, especially in space.

Flow rate versus pressure would depend on the fuel, it's surface friction and viscousity.

 

[Astronuc]

Try NASA's Glenn Research Center website - Index of Rockets and Propuslion
http://exploration.grc.nasa.gov/education/rocket/shortr.html

 

[GiTS]

to keep the high pressure exhaust from stopping fuel flow, the fuel lines would have to have a small area, smaller than the nozzle are.

but I'm doubting my previous logic. because if the pressure in the fuel tank was less than the pressure in the combustion chamber, the fuel would not flow into the combustion chamber because movement is alwys in the direction from high pressure to low pressure. or am i wrong?

 

[FredGarvin]

because if the pressure in the fuel tank was less than the pressure in the combustion chamber, the fuel would not flow into the combustion chamber because movement is alwys in the direction from high pressure to low pressure. or am i wrong?

No. You are correct. That is why there are huge turbopumps (boost pumps) in between to create that flow. Take a look at what the space shuttle's main engines use for that: http://www.boeing.com/defense-space/space/propul/SSME.html

Just as an aside, I like looking at this page every once in a while:
http://www.boeing.com/defense-space/space/propul/SSMEamaz.html

Notice the subsection in the table on pump output pressures.

Again, you need to look at the momentum rate out the back of the engine. That is not the same as saying f=ma which assumes a constant mass. If you look at Astro's (under Ideal rocket equation) or my link above, you will see that every term in the main equation, including the statement of Newton's 3rd law, is in terms of change of momentum.

 

[pervect]

I've been thinking about how to calculate how to find maximum thrust. But I can't find any equations for flow rate and pressure and area. I know that thrust is a force and force is mass x acceleration. But I don't know how id get an acceleration. There's an exit velocity at the nozzle of the rocket but there's no acceleration. The acceleration stops at the nozzle.
I also know that the higher the exit velocity, the higher the thrust. And the way to increase exit velocity is to increase the pressure and the way to increase the pressure is to decrease the nozzle cross-sectional area. But decreasing the nozzle cross sectional area decreases the volumetric flowrate thereby decreasing the mass flow rate which decreases the mass part of the force equation and the thrust. I need equations relating flow rate, flow velocity, area, and pressure.

You might take a look at

http://members.aol.com/ricnakk/th_nozz.html

Given the temperature and pressure in the combustion chamber, and the exit pressure at the nozzle (the atmospheric pressure), this allows you to calculate the theoretical exhaust velocity for an idealized nozzle and an idealized exhaust.

The next web (click next) or see
http://members.aol.com/ricnakk/th_thrst.html

calculates thrust, but you'll need the info on the first webpage to interpret the results.

Note that as other posters have remarked, you DO need powerful (but light!) turbopumps to make continuous flow liqiud fuel rockets work - that's why it's "rocket science"

The earliest designs, like the V2 pulse rocket, avoided this by having the combusion occur in spurts, with valves in the fuel line to allow for pulsed operaation. Fuel was fed into the chamber only when combustion was not occurring and the pressure was low.

The pulsed approach leads to a lot of mechanical and other problems, though, so the turbopump approach replaced the pulse rockets when the technology was developed.