Could there ever be a river or stream in which gold can be gathered if a net is placed propensity to the flow? I mean in the long term, getting substantial amounts of gold every day.
Short answer is: No!
Long answer is: No, not really
In order to be able to get any gold from a stream, there has to be gold particles in the stream, which means that you have to put your equipment near a placer deposit of gold.
What you would have to do would be the following:
- Set up several nets in succession with decreasing size of the net mesh.
- Allow the stream run over and through the nets while having a contraption to shake the nets. The shaking of the nets allow for both the sieving and the fractionating to work properly; the sieves will fractionate everything according to size, while the flow of the stream will fractionate everything according to weight.
- The heavier particles will then be localized more upstream on each net whereas the lighter particles will be further down (and preferably washed away entirely).
- Collect all of the heavier particles and send them for analysis or straight away for extraction.
What this result in is actually not a new invention. This is exactly how old rocker boxes work, with a potential efficiency improvement from the sieving (it might just as well be so that the nets get clogged constantly and never really help).
So, I would get some gold?
If there are any gold particles in the stream, then you have a chance to find them. However, since you are asking for "getting substantial amounts of gold every day", then the answer is still no!, simply because it's not lucrative enough compared to any investment made. While placer mining (gold panning) is a valid way to obtain gold and essential for prospecting, it is simply not worth the effort. All known deposits are already taken and usually use more advanced extraction methods which are more efficient. You would have to find a stream with gold dust which no one else would have noticed by now, and locating and buying the rights for one will most definitely eat up any profits you would make from the extraction.
On earth? In a river of water? Using a net made of some wire or rope mesh? No.
On some other planet, in a river of for example liquid metal, using a "net" that can cause gold to come out of solution and deposit on the net, sure. Gold can dissolve in mercury for example, which process was/is used to create gold paint. Brush the gold/mercury mix on something, wait for the mercury to evaporate, and you have a gold painted surface. I'm sure there are other ways to get the gold out of the mercury too than just heat and time, electrical?
But then you'd have a planet where humans are unlikely to be able to survive, certainly not without breathing equipment.