flood plains = science city, whatever economy you run.
In the early game, with low happiness cap, it's often good to farm 1 FP and cottage the rest. This way, you can grow a little faster to your happy cap and work the cottages faster. After that, if you want to run specialists, you may or may not (happy cap dependant) need to work the farm. But I can't see why you would need to work more than 1 farm for a loooong time:
- 2 FP cottages feed 1 scientist
- 1 farm feeds 1 scientist.
let's check the happy caps for a while :
happy cap at 1 : time to stop whipping

. no farm needed, no growth required. assign a scientist.
happy cap at 2 : working a cottage and assigning a scientist gives growth. Every now and then you can assign 2 scientists to avoid growth. No farm needed obviously.
happy cap at 3 : working a farm and assigning 2 scientists give no growth. 1 farm is enough. You could also work 2 cottages and 1 scientist for a better output but slower GPP generation.
happy cap at 4 : working 2 cottages and assigning 2 scientists give no growth. No farm needed.
happy cap at 5 : working 3 cottages and assigning 2 scientists gives growth. Assigning a third scientist (if available = caste system) once in a while will avoid growth. No farm needed. You could also work 2 farms and 3 scientists. but this requires caste system for a really small gain and really lower output.
After that, we enter the happy domain = above the usual early happiness caps. The choice here is between castes sytem and slavery. If you intend to run caste system, farms can be better.
happy cap at 6 : working 4 cottages and assigning 2 scientists gives growth. Assigning a third scientist (if available = caste system) once in a while will avoid growth. No farm needed.
You could also work 2 farms, 1 cottage and 3 scientists (sometimes 4). but this requires caste system for a really small gain and really lower output.
You could also work 3 farms (half the time 2), 3 specialists (half the time 4). We're entering SE domain here. If you intend to run Caste System and some SE enhancing civics (representation and/or pacifism) it may be good.
After that, we're entering a health problematic zone, let's assume no health issue.
happy cap at 7 : working 4 cottages and assigning 3 scientists gives no growth. No farm needed. If you don't run caste system, a priest or a merchant or an engineer or a plains hill mine can avoid growth. If needed, a good whip can bring down the pop if needed or building workers can make a good use of the food surplus.
You could also work 3 farms and 4 scientists. Not a lot better, if you ask me and a certainly lesser output even with representation.
happy cap at 8 : working 5 cottages and assigning 3 scientists gives growth. Assigning a 4th scientist once in a will avoid growth. No farm needed. If you're not running caste system, you're certainly in the perfect cottage heaven even if you have no hills to work: working the cottages and still producing (whip!) the necessary buildings (including the health bonus buildings, the research bonus buildings, the happy buildings).
You could also work 4 farms (sometimes 3) and 4 scientists, sometimes 5.
I won't go further, since after that we're not into reality. more than 5 FP and no health problems isn't very likely.
However, note that with only 4 FP and a happy cap at 9, you could work 4 farms and feed 5 scientists.