How to Calculate Gas Exit Velocity in a De Laval Nozzle?

[jslade]

Newby de laval nozzle ?

I am experimenting with de laval nozzles. I am trying to make a nozzle that operates at room temprature and moderatly low pressure.

This is the equation I have found for calculating area of throat.

At = (q / Pt) x SQRT[ (R' x Tt) / (M x k) ]

At= area of throat
q = gas flow rate
Pt= pressure at throat
R'= Universal gas constant x molecular weight
Tt= Temp at throat
M= gravity constant
k= gas specific heat ratio

How do I calculate the volocity of the gas that exits the throat? What is an ideal volocity,
is it relative to the speed of the rocket? Is it possible to work the above equation and end up with a low and therefor ineffective volocity? Do I have to set my pressure and flow rate
based on a target gas exit volocity?

Thanks for your time
jslade

 

[Achy47]

Hello jslade,

it is great to see that you are experimenting with de laval nozzles. These nozzles are commonly used in rocket engines to accelerate the exhaust gases to supersonic speeds, providing efficient thrust.

To calculate the velocity of the gas exiting the throat, you can use the following equation:

V = SQRT[ (2 x k x R' x Tt) / (k-1) x (1- (Pt / P) ^ ((k-1) / k)) ]

Where:
V = velocity of gas exiting throat
k = gas specific heat ratio
R' = Universal gas constant x molecular weight
Tt = temperature at throat
Pt = pressure at throat
P = exit pressure

The ideal velocity for a de laval nozzle is the speed of sound at the exit pressure. This is known as the critical velocity, and it is the maximum velocity that the gas can achieve in the nozzle. In order to achieve this ideal velocity, the pressure at the exit of the nozzle must be equal to the ambient pressure.

It is possible to calculate a low velocity using the above equation, but this would not be an effective velocity for a de laval nozzle. The purpose of the nozzle is to accelerate the gas to supersonic speeds, so a low velocity would not provide efficient thrust.

In order to achieve the ideal velocity, you may need to adjust the pressure and flow rate of the gas. The pressure at the throat and exit of the nozzle can be controlled by adjusting the geometry of the nozzle, specifically the area of the throat and the exit. The flow rate can be controlled by adjusting the amount of gas being fed into the nozzle.

I hope this helps with your experiments. Best of luck!