Centripetal force of rotating mass vs. flowing mass

  • #1
Hi, thanks in advance for any help and info. Have two conditions.

The first condition is a mass of water spinning as a fixed mass. Say we have a rectangular mass .25 inches tall, 2 inches long and .50 thick spinning at 3000 RPM with its center of mass at R = 2.00 inches. (Please see first attached jpg) The centripetal force of this mass is then F = m*V^2/R

To calculate mass the density is 1.94 slugs/ft^3. The volume is .25 X 2 X .50 = .25 in^3. The mass is then 1.94 slugs/ft^3 * ft^3/(12 in)^3 *.25 in^3 = .00028 slugs

The tangential velocity at R = 2.0 is 3000 REV/min * pi * 4in / (12 in/ft * 60s/min) = 52.4 ft/s

Therefore the centripetal force = .00028 slugs * (52.4 ft/s)^2/(2.0 in / 12in/ft) = 4.6 lbs.

For the second condition we open the ends of the rectangular tubes and place 90 degree elbows at the periphery as shown in the second attached jpg (similar to a lawn sprinkler)

Question is:
Is the centripetal force the same for condition two or does this change dependent on the mass flow out of the tubes?
 

Attachments

  • cent_frc_1.jpg
    cent_frc_1.jpg
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  • cent_frc_2.jpg
    cent_frc_2.jpg
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Answers and Replies

  • #2
816
1
Ok I won't deal with imperial units, and some of the inexactness... but the idea is basically this: the centripetal force to spin the water in the pipe is the same, but when the water is flowing you don't just spin, but you move water to the outside, on a spiral track (if you follow a small dust particle in a pipe). This would usually slow the wheel down, because you need energy to accelerate the water. Also the forces for a spiral are different from those of a circle.
When you attach bend ends you get a sprinkler effect. The water flows around the corner and carries away angular momentum, leading to a positive or negative acceleration of the sprinkler.
 
  • #3
Thanks OxDEADBEEF for the reply. Excellent point about the particles moving on a spiral track. My question came from working on a lawn sprinkler design and was confused on the stresses on the attached bends whether the force would increase with an increase in flow (not due to velocity but due to additional centripetal force). So does one need to calculate the velocity vector of a particle in the flowing stream to calculate the centripetal force? The velocity diagram I imagine would be similiar to the Euler formulas (velocity vector diagrams) for centrifugal pumps.
 

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