Worr Angel
02-13-2004, 03:59 PM
So I am getting really tired of everyone pretending they know the laws of physics and fluid flow by saying that different guns shooting the same 280 fps will have the same accuracy and distance assuming the paint to barrel match is the same. This is so far from the truth and I will use mathematical equations from the books “Fundamentals of Momentum, Heat, and Mass Transfer by James Welty, Charles Wicks, and Robert Wilson”, “Flow of Fluids by Crane”, and “Perry’s by Robber Perry and Don Green” to prove it. I wouldn't consider myself an expert, but I did graduate from college with a chemical engineering degree. Also, I reviewed this with three coworkers that went to different colleges and we all agreed on the following content. So don't try to attack me or my school. I don't think four different chemical engineers would miss the boat on this one. So here goes….
The analysis is for fluid (in this case air, nitrogen, CO2) in pipes, which means your barrel.
Laminar Flow is defined as a flow in which the streamlines remain distinct from one another over their entire lengths (Perry’s 5-6). This means for a given amount of fluid the velocity for every molecule is exactly the same and the molecules are traveling informally and not crossing each other. The air is flowing straight down the barrel.
Turbulent Flow is defined as a flow in which eddies generated in the fluid spread rapidly throughout the fluid, thereby producing a disruption of the entire flow pattern (Perry’s 5-6). This means for a given amount of fluid the velocity varies for the molecules and their direction changes as well. Eddies are areas of reverse flow, which creates excess friction and reduced results.
Reynolds Number is the transition from Turbulent Flow to Laminar Flow as the velocity is reduced (Perry’s 5-6) Generally speaking, for flow in pipes, the fluid is considered turbulent for Reynolds Numbers greater than or equal to 2300. Reynolds numbers less than 2300 are considered laminar. The Reynolds number is dimensionless.
Re = Drv/m
Re = Reynolds Number
D = the pipe Diameter
r= the density of the fluid
v = the velocity of the fluid
m = the viscosity of the fluid
The velocity of a compressible fluid (air or nitrogen) is defined as follows (Crane’s 3-4)…
v = 8.75Y/Sg sqrt(((P1-P2)r)/K)
v = velocity
Y = expansion factor; basically a constant dependent on the pressure drop
Sg = specific gravity; density of the fluid as compared to air, so for this case it is the density
sqrt = square root
P1 = inlet pressure; pressure released into the barrel
P2 = outlet pressure; pressure at end of the barrel (atmospheric pressure)
r= density
K = resistance coefficient; similar to friction
In our velocity equation, several variables are basically constants; they are Y, Sg, P2, r, and K. Thus the velocity is proportional to the square root of change in pressure.
v ~ sqrt(P1-P2) ~ means proportional
Based on the same analysis as above (all variables but velocity are mostly constant regardless of pressure), you can quickly reduce the equation for calculation of the Reynolds number to…
Re ~ v
Taking this one step further gives the following…
Re ~ v ~ sqrt(P1 – P2)
Remember, P1 = inlet pressure and P2 = outlet pressure
Or P1 is the pressure from the LPR and P2 is atmospheric.
Thus, as the pressure from the LPR increases, the velocity increases, and so does the Reynolds number.
Because the velocity and Reynolds number are directly proportional, you prefer lower air velocities impact the paintball so you have laminar flow being the motive force on the paintball. With this type of flow, you get a more uniform force on the ball. Since the force is more uniform you also get less deformation of the paintball and this helps it move through the barrel more uniformly.
In contrast to this is turbulent flow. The air impact on the ball for this flow is everything but uniform. You will have areas of high velocity and areas of low velocity. Because of eddies (reverse flow; looping flow) you can even have area’s of negative or reverse velocity. All this adds up to lost force on the paintball and even deformation of the paintball that not only affects its movement in the barrel but also once it has left the barrel. Imagine the paintball being deformed so that instead of going straight down the barrel it bouncing of the walls of the barrel. This action is what leads to reduced accuracy and distance. This is true even though the ball velocity is adjusted to be the same from gun to gun.
Remember this analysis is about the air velocity on the ball, NOT the ball velocity. Lower air velocity gives you better ball performance. Lower air velocity is reached with lower internal operating pressures.
Hopefully this has not added to the confusion. Feel free to ask me any questions you have.
Edit, This is why I have now bought an angel. They are now operating on low pressure that rivals cockers. Because of this, I believe the A4's are every bit as good of cockers.
The analysis is for fluid (in this case air, nitrogen, CO2) in pipes, which means your barrel.
Laminar Flow is defined as a flow in which the streamlines remain distinct from one another over their entire lengths (Perry’s 5-6). This means for a given amount of fluid the velocity for every molecule is exactly the same and the molecules are traveling informally and not crossing each other. The air is flowing straight down the barrel.
Turbulent Flow is defined as a flow in which eddies generated in the fluid spread rapidly throughout the fluid, thereby producing a disruption of the entire flow pattern (Perry’s 5-6). This means for a given amount of fluid the velocity varies for the molecules and their direction changes as well. Eddies are areas of reverse flow, which creates excess friction and reduced results.
Reynolds Number is the transition from Turbulent Flow to Laminar Flow as the velocity is reduced (Perry’s 5-6) Generally speaking, for flow in pipes, the fluid is considered turbulent for Reynolds Numbers greater than or equal to 2300. Reynolds numbers less than 2300 are considered laminar. The Reynolds number is dimensionless.
Re = Drv/m
Re = Reynolds Number
D = the pipe Diameter
r= the density of the fluid
v = the velocity of the fluid
m = the viscosity of the fluid
The velocity of a compressible fluid (air or nitrogen) is defined as follows (Crane’s 3-4)…
v = 8.75Y/Sg sqrt(((P1-P2)r)/K)
v = velocity
Y = expansion factor; basically a constant dependent on the pressure drop
Sg = specific gravity; density of the fluid as compared to air, so for this case it is the density
sqrt = square root
P1 = inlet pressure; pressure released into the barrel
P2 = outlet pressure; pressure at end of the barrel (atmospheric pressure)
r= density
K = resistance coefficient; similar to friction
In our velocity equation, several variables are basically constants; they are Y, Sg, P2, r, and K. Thus the velocity is proportional to the square root of change in pressure.
v ~ sqrt(P1-P2) ~ means proportional
Based on the same analysis as above (all variables but velocity are mostly constant regardless of pressure), you can quickly reduce the equation for calculation of the Reynolds number to…
Re ~ v
Taking this one step further gives the following…
Re ~ v ~ sqrt(P1 – P2)
Remember, P1 = inlet pressure and P2 = outlet pressure
Or P1 is the pressure from the LPR and P2 is atmospheric.
Thus, as the pressure from the LPR increases, the velocity increases, and so does the Reynolds number.
Because the velocity and Reynolds number are directly proportional, you prefer lower air velocities impact the paintball so you have laminar flow being the motive force on the paintball. With this type of flow, you get a more uniform force on the ball. Since the force is more uniform you also get less deformation of the paintball and this helps it move through the barrel more uniformly.
In contrast to this is turbulent flow. The air impact on the ball for this flow is everything but uniform. You will have areas of high velocity and areas of low velocity. Because of eddies (reverse flow; looping flow) you can even have area’s of negative or reverse velocity. All this adds up to lost force on the paintball and even deformation of the paintball that not only affects its movement in the barrel but also once it has left the barrel. Imagine the paintball being deformed so that instead of going straight down the barrel it bouncing of the walls of the barrel. This action is what leads to reduced accuracy and distance. This is true even though the ball velocity is adjusted to be the same from gun to gun.
Remember this analysis is about the air velocity on the ball, NOT the ball velocity. Lower air velocity gives you better ball performance. Lower air velocity is reached with lower internal operating pressures.
Hopefully this has not added to the confusion. Feel free to ask me any questions you have.
Edit, This is why I have now bought an angel. They are now operating on low pressure that rivals cockers. Because of this, I believe the A4's are every bit as good of cockers.