How do link juice and PR flow in a Link pyramid?

No one can give an answer to this question.

Google simply says the link juice will be passed on to the target site. It does not say how much ? Or what is the process ?

So , you can not calculate the link juice weight.

What you can be sure of is, if there are quality ( high PR) back links to a site, the link juice will be higher . Thats all. The exact quantity no one knows.

I think that the link pyramid is not needed for top ranking at Google. Enough the 1st tier. Focus on high quality backlinks from authority sites only.

I agree with what Anil said, even if you knew Google's complex formula for calculating PageRank, it would still be impossible for any human to calculate.

There's that many different factors than effect the PageRank of links which are linking to your site within a pyramid, for example a PR0 link on a page on a PR7 domain site will usually deliver more juice than a PR0 link on a PR6 domain site for the most part, although that's not certain either, it depends on many factors.

There's an endless amount of factors that will effect the juice that comes from that PR0 page, such as outbound links, inbound links, amount of juice passed down on the home PageRank, which could also change daily depending on how many new pages are created on the site, which could potentially drain PageRank from other pages of the site. PageRank of pages on most websites (particularly large authority sites used in link pyramids) will fluctuate daily, it's just that Google only shows us these updates when they are calculated at the time of updating toolbar PageRank.

Personally I don't worry about calculating what PageRank to expect from the links I build to my sites. I just focus on analyzing the results they bring in the SERPS and increase/decrease the amount of links I build accordingly. Obviously if you try to build higher PageRank links then it will do more for your rankings but I wouldn't worry about the calculations.

I agree with Jonny. Focus on SERPs not PR, rank will follow. If you can manage to get links from high authority site on your money site then you don't have to worry about tiering but in case you don't then use automated tools to send links to lower tiers that point to your money site and let your SERPs rise.