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Old Nov 16th 2016, 04:37 PM   #1
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Unhappy Funnel Design- Particular Flow

Hi all, I am a brand new member here so please excuse any breach of etiquette. I am having a really rough time with a fluid mechanics problem. For the problem, I am to design a special kind of funnel, no more than 9cm tall or 6cm in diameter. The funnel must have a very particular design. As the water flows it, it will fall two meters into a container on a scale. The trick is that the scale must read a constant number for the entire flow of 100ml. So, the force impacting the scale at the initial point of contact must equal the final weight of the scale (.98N when all the water has accumulated), with the applied force decreasing in exact proportion to the accumulating weight. I have already started trying to break down the problem using Bernoulli's and the beginnings of a mass flow analysis, but I can't seem to get to a point where I can solve for any of the variables. Any nudge in the right direction would be greatly appreciated!
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Old Nov 18th 2016, 03:09 PM   #2
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Some ideas that might help...

What you haven't got yet is the equation for the force of the water hitting the scales.
This will be given by the velocity of the water (meters per second) multiplied by the mass flow (kg per second).
The velocity of the water will obviously depend on the height of the funnel above the scales.
This means that there will not be a single answer,
you can get the same result for a small mass flow from a great height or a large mass flow from a small height.
For simplicity you might want to choose a height that results in a terminal velocity of 1 m/s, you then want to have an initial mass flow of .98 kg/s.
You also want to finish with .98 newtons or a tenth of a kg of water on the scales.
one litre of water masses 1 kg, so the volume of water is 1/10 litre,
this fixes the volume of the funnel, which means that if you choose an initial depth for the water in the funnel, the radius follows.
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Old Nov 19th 2016, 10:55 AM   #3
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New conclusions

Thank you so much for the response. So many times I overcomplicate these problems when I'm trying to solve them. I was getting caught up because, as you said, the variables for height and area are dependent on each other, but can't be found in the problem unless one of them is already determined. Based on the design specifications of the problem, I've concluded that a conic funnel shape is geometrically impossible, so I am trying to run calculations with a cylindrical shape.
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Old Nov 20th 2016, 04:16 AM   #4
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I had a vague suspicion that a simple cone would not work,
I would not be surprised if a simple cylinder was also found wanting.
I have a gut feeling that you might find that you require a more complicated curved bowl shape.
I think your best option is to build some mathematical models in EXCEL (or similar) and play with different parameters to see what happens.
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