Calculating Force on a Sphere with 1 Bar Pressure

[cheekibreeki]

Hey people, first post, I'm sorry if I'm posting this in the wrong place.

How do you calculate the force exerted on a sphere? I'm building a pneumatic air rifle, and I'm trying to figure out how fast an airsoft bb accellerates with a certain pressure.

The projectile is 6mm in diameter, so that makes the surface on which the air pressure works 1/2 * (4 * pi * 3^2) = 1/2 * 113.1 = 56.5 mm^2 = 5.65 * 10^ -5 m^2.

What is the force on the projectile if the difference in pressure is 1 bar?

 

[Bystander]

surface on which the air pressure works 1/2 * (4 * pi * 3^2) = 1/2 * 113.1 = 56.5 mm^2 = 5.65 * 10^ -5 m^2.

It's an attractive notion to use the area of the hemisphere, an it's also incorrect. The area on which the pressure acts is the cross-sectional area of the projectile, period. Force then is pressure times area of the bore.

 

[cheekibreeki]

Thanks, that makes things a whole lot easier!

 

[Nathanael]

Just in case you're curious:
The force from the pressure acts perpendicular to the surface, so if you were to use the surface area of the hemisphere, you would have to use only the component of force that acts along the barrel. If you do the math it reduces to using the cross-sectional area.

 

[pmacias]

To calculate the force exerted on a sphere, you will need to use the formula F = PA, where F is the force, P is the pressure, and A is the surface area of the sphere. In this case, the pressure is 1 bar and the surface area is 5.65 * 10^-5 m^2. Plugging these values into the formula, we get F = (1 bar)(5.65 * 10^-5 m^2) = 5.65 * 10^-5 N. This is the force exerted on the projectile by the air pressure.

However, it is important to note that this calculation only takes into account the force exerted by the air pressure. There may be other factors that affect the acceleration of the projectile, such as air resistance and the weight of the projectile itself. It is also important to make sure that your calculations are accurate and that you are using the correct units for pressure (in this case, bar).

I would recommend consulting with a physics expert or conducting further research to ensure the accuracy of your calculations and to better understand the factors that may affect the acceleration of your projectile. Good luck with your project!