What is the maximum acceleration in horizontal direction without spilling water from the glass 4

[hungy_kid]

- Cup size : Bottom face Dia.50mm, Height 150mm, Top face Dia.100mm
- Fluid : water 0.5 kg

 

[electricpete]

Assuming it is a steady state acceleration (or ramp from 0 very slowly up to the final constant acceleration) with no transient sloshing around, then you can solve it as follows.

1 - For the stationary case (gravity force but no horizontal acceleration), determine what angle could you tilt the glass without spilling.
2 - What level of horizontal acceleration when vectorially combined with gravity "acceleration" will give a total acceleration in a direction that satisfies the angle of tilt calculated in part 1.

=====================================
(2B)+(2B)' ?

 

[rb1957]

acceleration applied at CG of fluid.

this isn't for work, right, so discouraged at the "for work" site.

another day in paradise, or is paradise one day closer ?

 

[hungy_kid]

No, I need to find out max acceleration on my conveyor mechanism.

 

[BrianE22]

Years of spilling stuff makes me think that "jerk" may be more important than acceleration.

 

[hungy_kid]

Jerk is a form of acceleration, isn't it? I am trying to figure out max acceleration to use in my specs.

 

[rb1957]

jerk is the time derivative of acceleration (d3x/dt3)

why do your specs care about water spilling out of a polystyrene cup ? unless you've calibrated your actual operation to water in a coffee cup ...

another day in paradise, or is paradise one day closer ?

 

[Strong]

Have you considered height of fluid compared to height of cup? Have you considered frequency range (F-min. and F-max.)? A quick experiment on my half-filled (or half-empty) coffee mug showed that tapping/impacting with my finger knuckle (closed fist) produced minor sloshing as compared to slight shaking of cup with my hand that produced considerable sloshing. I believe the g-level was much higher in the first case. I could measure it! Fluid in cup or tank has a sloshing natural frequency, so the frequency range of the applied acceleration along with amplitude should be considered.

https://www.bing.com/search?q=tak+f...8b811a175930af507&pglt=43&FORM=ANNTA1&PC=U531

Get a cup of coffee,
Walt

 

[IRstuff]

Often, spillage is from sloshing, which is non-trivial to calculate

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[hungy_kid]

What if I suddenly wanted to stop my conveyor? Wouldn't the speed and acceleration be detrimental to prevent spillage?

 

[IRstuff]

The same rationale applies. The change in direction of the jerk simply sloshes water in the opposite direction

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[LittleInch]

Are you actually transporting half full cups of water or just using that as an example.

Maybe look at what sushi restaurants do for their revolving conveyor of food....

Or restaurants when you place the tray on a moving conveyor.

I think though this is the sort of thing that needs some experimentation as there seem to be many variables involved (weight of the cup, friction, how full the cup is, whether a truly "smooth start / stop can be applied ( see flywheel issue below) final speed of the conveyor etc)

You probably need a big flywheel on the motor drive so that it can't accelerate or decelerate very quickly.

How fast does the conveyor go when it reaches max speed?

Is there an issue in doing this ramp up / down over 10 seconds, or 20 or 30?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[goutam_freelance]

If you know the static level of water and dimensions of the glass you can calculate the acceleration at which the water level reaches the brim.

Engineers, think what we have done to the environment !

https://www.linkedin.com/in/goutam-das-59743b30/

 

[rb1957]

for a steady acceleration ...
and the taper of the cup is going to mess things some (but nothing a bit of math won't solve)

another day in paradise, or is paradise one day closer ?

 

[hungy_kid]

yeah I am working on it now, but the calculations are taking much much longer as the shape of the glass is not as simple as a rectangular tank or cylinder.

 

[IRstuff]

I'm getting 2.75L for the cup and only 0.5L for water, so less than half full?

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[EdStainless]

As has been said, for this Jerk is what matters (rate change of acceleration)
Yes you will have a max acceleration, but how quickly it changes matters more in this case.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[goutam_freelance]

I got a_x=10.26 m/s^2. But somebody should check.

 

[rb1957]

for the cup volume I get .7L ... average 3" dia, 6" high = 42in3 = 700cc

what constrains the water to have the same CL when deflected ? is the volume above = the volume below the original water level ? doesn't look like it (if the center stays in the same place.

we know the initial freeboard, we know the initial empty volume of the cup. This is still the empty volume with the water tilted.

another day in paradise, or is paradise one day closer ?

 

[hungy_kid]

goutam_freelance , great work! I was able to calculate the height of the water, but nothing more. Could you please explain how you drove the equation you used to solve for tan (alpha)?