How can we determine the thrust generated?

[Chris Michos]

Homework Statement

How can we determine the thrust/ propulsive force generated?
We know that:
There is C02 inside a given Volume V and we know the mass M of the gas inside the volume. We know that we release the gas from a hole of diameter 1.6 mm.

Homework Equations

PV=nRT
∑F= dp/dt
∫u(t) dt = dx

The Attempt at a Solution

I tries using the law of ideal gases to calculate the pressure inside the chamber but then figured out that C02 is not a perfect gas. I can't figure out how to solve it no matter how much I have googled.

This question is for a competition called F1 in Schools. Basically, we are trying to find a way to predict the time that it will take for our car to finish a 20-meter track given some other parameters. We have figured out a function that when we integrate, we can find the time it takes, but there is a part of the equation missing, which is what I am asking above. In case you want to learn anything more regarding this competition, feel free to send me an email. If you help us with this problem, you can get a shout out on our Competition engineering portfolio

 

[DLeuPel]

Homework Statement

How can we determine the thrust/ propulsive force generated?
We know that:
There is C02 inside a given Volume V and we know the mass M of the gas inside the volume. We know that we release the gas from a hole of diameter 1.6 mm.

Homework Equations

PV=nRT
∑F= dp/dt
∫u(t) dt = dx

The Attempt at a Solution

I tries using the law of ideal gases to calculate the pressure inside the chamber but then figured out that C02 is not a perfect gas. I can't figure out how to solve it no matter how much I have googled.

This question is for a competition called F1 in Schools. Basically, we are trying to find a way to predict the time that it will take for our car to finish a 20-meter track given some other parameters. We have figured out a function that when we integrate, we can find the time it takes, but there is a part of the equation missing, which is what I am asking above. In case you want to learn anything more regarding this competition, feel free to send me an email. If you help us with this problem, you can get a shout out on our Competition engineering portfolio

F = ma So you need to know how much mass escapes and with what acceleration. Regarding acceleration, when the thrust begins, time the moment it begins until the molecules start escaping and measure the velocity with which they escape. I recommend doing it in a cold place where CO2 will be visible to the naked eye and with a good camera you can measure its velocity. When done so you take into consideration the distance that the molecule traveled until it escaped and the time you measured until it did. Of course, many of these things depend on how the thrust mechanism works and what stages to the molecules go through until they escape. Unless you don’t post it as well I guess it will be up to you n case it doesn’t work with the equation written at the bottom.

Let’s divide F = ma into the “a” part and the “m” part
a : It is just simply x = 1/2 at² . Both x and t measured how I explained before

m :
The diameter of a molecule of CO2 is 232x10^-12. To know the area of this molecule, treating it a small an approximate circle is (232x10^-12/2)²pi since r²pi is the area of a circle. To calculate the amount of CO2 molecules in that 1,6 diameter you just divide the total area of the hole with the area of a CO2 molecule, which is (232x10^-12/2)²pi/pi(1,6x10^-3)² . Next, knowing already the quantity of CO2 molecules you just multiply the mass of one CO2 molecule ( 7.30x10^-20) times the quantity of CO2 molecules to know the total mass. This will have to be multiplied by the rows of CO2 forming a column until the top of the tank taking into account the molecules on the sides as a part of the colum but i’ll
skip that since it is just one extra thing to add.
Combining both we have ( not taking into account what I stated before ) :
V/t x (232x10^-12/2)²pi/pi(1,6x10^-3)² ( 7.30x10^-20) = F that will be exerted on the car.

Hopefully it was of help,
Good luck.

 

[Andrew Mason]

Homework Statement

How can we determine the thrust/ propulsive force generated?
We know that:
There is C02 inside a given Volume V and we know the mass M of the gas inside the volume. We know that we release the gas from a hole of diameter 1.6 mm.

Homework Equations

PV=nRT
∑F= dp/dt
∫u(t) dt = dx

Hi Chris. Welcome to PF!

The first thing you have to do is determine the number of moles of gas you have. Then, assuming you know the temperature of the gas (in K not °C) you can determine the initial pressure of the gas (ie. before you open the valve letting it out). CO₂ behaves almost like an ideal gas so you can use PV=nRT.

When you know the initial pressure, you can then determine the initial force pushing on the gas (hint: it depends on the pressure difference and area of the hole.). How is that force related to the acceleration of the car? [Note: you can also determine the speed at which the gas escapes using Bernoulli's law: $\frac {1}{2}\rho v^2 = \Delta P$ and determine force by tbe rate of change of momentum).]

That should get you on the right track

AM

 

[DLeuPel]

An easier way is to measure the acceleration the car has and then multiply it by its mass.