Figures I've seen for number of searches on Google daily (not clear whether US or worldwide) are between 3.3 billion to 3.5 billion. Going with 3.3 would probably not be excessive.
Wonder how much of that is real traffic vs. bots used by SEOs and other tools that constantly hit their servers all day long. Not all traffic is valid traffic when it comes to accurately assessing the true size of the actual search market.
I'm guessing automated calls which have zero value probably make up at least a percentage point or two of those visits, mostly thanks to headless browser technology like PhantomJS, it's really hard to sort out fake traffic these days.
Don't even say you can tell by the UA or headers, anyone worth his salt can fix that with a couple of lines of code and make it spotlessly anonymized and hidden from suspect, assuming equal care is taken with the IPs being used.
I say all this with a reasonable amount of certainty because we're all still scraping Google to make ranking reports daily without being stopped.