First of all, there are two problems here one being hydrolics and static pressure to address loss of pressure. One formula you can use for volume is D squared divided by d squared, i.e.I f you increase from 1 inch to 1 25 1x1 equals 1 1.25x1.25 equals 1.5625 this is a 56 % increase in volume .Your next concern is to calculate the static pressure needed from your well to the out laying buildings. You want to maintain probably a forty five to 55 psi on the system farthest from the well. I AM GOING TO SEE IF I CAN FIND SOME FORMULA ON LINE , TO ACCOMPANY LOSS OF PRESSURE

The extra 350 ft of line will not be a problem for a 1" line. Your potential problem is not so much one of pressure, but of available volume.

1. Is your water supplied by a private well?
2. If so, what are the specs on your well and well pump?
3. What volume can your well deliver and for how long?
4. Well recovery rate?
5. Size of existing pressure tank?
6. How many and what type of fixtures will be installed in the two outbuildings?
7. What is your water supply pressure range?

Thank you for the questions. I apologize for my lack of information. We bought this property 3 years ago and have zero info on the well or pump. It has served us well without issue is all we know at this time.
We have a private well. The current pressure tank is about 20 gallons with 100 PSI max and a 30 PSI differential?
Fortunately, the usage at both external sites should be minimal - around 100 gallons per day together.
A water bib at the barn for a few goats and chickens.
A shower and kitchen sink only at the mini-cottage. I estimate a total of 100 gallons per day for both sites together.
Will adding additional pressure tank(s) address the loss of pressure throughout the system brought about by the added uses? If so where would be the best place to utilize one or two of them?

It is not possible to tell you whether or not you will have VOLUME (not pressure) problems without knowing about your well. However, I can tell you this. Do not put additional pressure tanks at the cottage and barn. This will result in water flowing back from the barn and cottage to the house. You could install backflow preventers or check valves, but that places wear-items in your water system that tend to fail when exposed to frequent low-flow incidents such as what happens every day in a house.

If you find that you have problems with insufficient water when fixtures in the house and cottage are used at the same time, your best bet would be to increase the size of your existing tank.

The first thing you ought to do is find out about your well. There should be a sticker or paper posted somewhere near it with the name of the company that drilled and/or installed the pump. Call them. They will have records of your well depth, draw-down test, pump, etc.

Thank you aliceinwonderland for your help. You have given me the answers I needed about the pressure tanks before I made that mistake.
We bought this property through a foreclosure and never met the owners. It will be difficult to find them or the company that installed the well. I will call some local companies just to be sure. Thank you for that idea.

There is no visible sign of the well on the property... All we know is there is a 1"PE leaving the basement at one corner with a power cable bound to it for the pump. That PE feeds the existing pressure tank.

One more question now that you said I should use the existing pressure tank. It is old and I should probably just replace it.
When we moved to this house there was no working water pipes. We installed 3/4 pex with 1/2 inch pex feeding most stations.
Can we go from 3/4 pex to a 1" or larger PE pipe at the place where the water leaves the house?
Or should I install the PE on a new pressure tank and run the house pex as a "T" off of the 1" PE?

Would you recommend installing back flow prevention devices and if so where?

Thank you in advance again!

I've run 1" pipe out over 600 ft with no noticeable issues with volume or pressure. We didn't use any pressure tanks or anything else, other than the tank at the wellhead.

Thank you aliceinwonderland for your help. You have given me the answers I needed about the pressure tanks before I made that mistake.
We bought this property through a foreclosure and never met the owners. It will be difficult to find them or the company that installed the well. I will call some local companies just to be sure. Thank you for that idea.

There is no visible sign of the well on the property... All we know is there is a 1"PE leaving the basement at one corner with a power cable bound to it for the pump. That PE feeds the existing pressure tank.

One more question now that you said I should use the existing pressure tank. It is old and I should probably just replace it.
When we moved to this house there was no working water pipes. We installed 3/4 pex with 1/2 inch pex feeding most stations.
Can we go from 3/4 pex to a 1" or larger PE pipe at the place where the water leaves the house?
Or should I install the PE on a new pressure tank and run the house pex as a "T" off of the 1" PE?

Would you recommend installing back flow prevention devices and if so where?

Thank you in advance again!

thank you for that rwiegand. That encourages me to go forward. This has been an excellent resource for me.
thanks again

"Or should I install the PE on a new pressure tank and run the house pex as a "T" off of the 1" PE?"

Do it that way.

I would not install backflow prevention devices. You won't have a back-pressure situation (unless your barn/cottage are significantly uphill from your house?) so there is no need.

When you replace your existing pressure tank, you may wish to go with one a bit bigger to account for the extra usage. The correct size is determined by well characteristics. I've linked some information to help you with that.

Here is a link that might be useful: Sizing a Pressure Tank

I'm planning a similar project as this (water out to a detached garage, and shed), and I was able to get all the well info off the original permit to put it in, which was on record with the local board of health.

All this stuff usually has to be documented by the county (drinking water safety is a big deal) and somebody probably has those documents.

thank you for that rwiegand. That encourages me to go forward. This has been an excellent resource for me.
thanks again

I plan to install a larger pressure tank with P.E. and the Pex "T" from there.
Still doing research on what size tank to get. What are the negatives of buying a over-sized tank (other than the cost).

It is difficult without the information about the well. We live in a rural area, house built in 1958, could even be a spring fed well for all we know... I will look into getting info on it.
Thank you aliceinwonderland for the responses you have given. I am studying the link you sent about pressure tanks.

I plan to install a larger pressure tank with P.E. and the Pex "T" from there.
Still doing research on what size tank to get. What are the negatives of buying a over-sized tank (other than the cost).

It is difficult without the information about the well. We live in a rural area, house built in 1958, could even be a spring fed well for all we know... I will look into getting info on it.
Thank you aliceinwonderland for the responses you have given. I am studying the link you sent about pressure tanks.