# Calculating Force on a Sphere with 1 Bar Pressure

• cheekibreeki

#### 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?

cheekibreeki said:
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.

Thanks, that makes things a whole lot easier!

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.

## 1. What is the formula for calculating force on a sphere with 1 bar pressure?

The formula for calculating force on a sphere with 1 bar pressure is F = PA, where F is the force in Newtons, P is the pressure in pascals, and A is the surface area of the sphere in square meters.

## 2. How do you convert pressure from bar to pascals?

To convert pressure from bar to pascals, you can use the conversion factor 1 bar = 100,000 pascals. This means that if you have a pressure of 1 bar, it is equivalent to 100,000 pascals.

## 3. Can you calculate the force on a sphere with a different pressure?

Yes, the formula for calculating force on a sphere with pressure can be used for any given pressure. Simply plug in the value of the pressure in pascals into the formula along with the surface area of the sphere to calculate the force.

## 4. What is the significance of calculating force on a sphere with 1 bar pressure?

Calculating the force on a sphere with 1 bar pressure is important in understanding the amount of pressure being applied on an object. This can be useful in many scientific and engineering applications, such as designing structures that can withstand certain pressures or determining the force required to move an object.

## 5. How does the force on a sphere change with different pressure?

The force on a sphere will increase as the pressure increases. This is because pressure is directly proportional to force, meaning that as pressure increases, so does the force. This relationship is described by the formula F = PA, where a change in pressure will result in a proportional change in force.