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Old Jan 29th 2015, 05:26 AM   #1
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Force of a fluid on an object

Hello.

Ive been trying to calculate the force air has on some cylinders that are transported in a production line using air. They move along some guides but the transportation is caused by compressed air all along the guides.

I can obtain the velocity of the air, área of the cylinders. I thought I could use the equation of quantity of motion to calculate this, but I am not sure.

How would you do it?

Thank you for your time.
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Old Jan 29th 2015, 07:53 AM   #2
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It's possible to estimate the force for either of two conditions:

1. The pressure of the air behind the cylinder is greater than the pressure n front of the cylinder - in this case the force is the difference in pressure times the area of the back of the cylinder. You should use this if the cylinder completely fills the tube it's moving in.

2. If the cylinder is in open air with wind blowing past it at a known velocity, then the force can be calculate based on an assumption of the cylinder's coefficient of drag.
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Old Jan 29th 2015, 08:04 AM   #3
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Originally Posted by ChipB View Post
It's possible to estimate the force for either of two conditions:

1. The pressure of the air behind the cylinder is greater than the pressure n front of the cylinder - in this case the force is the difference in pressure times the area of the back of the cylinder. You should use this if the cylinder completely fills the tube it's moving in.

2. If the cylinder is in open air with wind blowing past it at a known velocity, then the force can be calculate based on an assumption of the cylinder's coefficient of drag.
It is definitely option 2. I had thought about this, by using the equation of drag D=rho*v^2*cd/2, and then assuming it is equal to the force of the air since it's not accelerated. However, there is some friction included whose value I ignore. The ideal way to find it is to calculate both drag and the force of the air independently if possible, and the difference would be the friction. What do you suggest?
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Old Jan 29th 2015, 08:30 AM   #4
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I think you're on the right track. If you know the velocity of the forced air (call it v_a) and the velocity of the cylinder (v_c) on its track, and assuming the air in front of the cylinder has zero velocity, then the net force of the air acting behind and in front of the cylinder is:

F_net = (1/2) rho C_d A ((v_a-v_c)^2 - v_c^2)

= (1/2) rho C_d A (v_a^2 - 2 v_a v_c)

This net force must equal friction between the cylinder and the supporting structure. This assumes that the track is horizontal (i.e. we can ignore any force needed to go up or down hill). Note that if there is no friction F_net is zero if v_c = (1/2)v_a.
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Old Jan 29th 2015, 09:38 AM   #5
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Originally Posted by ChipB View Post
I think you're on the right track. If you know the velocity of the forced air (call it v_a) and the velocity of the cylinder (v_c) on its track, and assuming the air in front of the cylinder has zero velocity, then the net force of the air acting behind and in front of the cylinder is:

F_net = (1/2) rho C_d A ((v_a-v_c)^2 - v_c^2)

= (1/2) rho C_d A (v_a^2 - 2 v_a v_c)

This net force must equal friction between the cylinder and the supporting structure. This assumes that the track is horizontal (i.e. we can ignore any force needed to go up or down hill). Note that if there is no friction F_net is zero if v_c = (1/2)v_a.
I am happy that I am on the right track. However, I have to admit I am a Little lost on the difference of sq(va-vc) and vc square. Which two forces are you considering? Drag and maybe the pushing force?

I only need to know the force air is applying to the bottles to move them.

Thank you so much for your help.
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Old Jan 29th 2015, 10:01 AM   #6
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The force on the back end of the cylinder pushing it along is dependent on the relative velocity of the air to the cylinder, which is v_a - v_c. If the air is moving at 10 m/s, and the cylinder is moving at 8 m/s in the same direction, then the relative velocity of air to cylinder is 2 m/s, and hence the force applied by the air is (/2) rho C_d A (2 m/s)^2.
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