Help with hydro maths needed!

Hi there permies!
We've come to realise that our feeble 50w solar setup is no longer keeping up with our needs.
We are situated directly down hill from a spring fed water tank, I've been told (but yet to confirm) that we can connect a pipe to the overflow on the tank.

Here's where it gets a little bit crazy....
I've paced it out to approx. 600m of pipe from the tank to the highest point of our property, say another 100m to get from there to a sensible place for a battery shed.

Google maps puts the head height at around, wait for it..... 400m, or 1300ft

If I put a holding tank at the top of our property we'd have about 30m of head, over 100m of pipe which is probably ample but a bit boring.
I have a background in engineering, and a pretty sound understanding of how stuff works, so I kinda want to go full "mad scientist" on this and see if i can harness the power of 400m of head.
But! I need some help getting my head around the maths of it all.
If I were to run a 700m length of 1" pipe, with a head of 400m, what sort of pressure and flow rate would I be looking at? I'm struggling to find any reasonably accurate figures. Most of the reference tables I've found stop at 200psi!

I'd also like to build this setup using an infinitely available resource, the humble car alternator! I know they get a bad rep for low efficiency and short lifespan but I have 4 sat in my workshop already, and they're a damn site cheaper to replace than a "proper" unit. They also have the bonus of a built in voltage regulator and a 12v dc output to keep the wiring simple. I think with the head I have available it should be quite easy to get it spinning fast enough to produce more power than it consumes without having to build up an overly complicated gearing system.

I know it's mad, crazy, unnecessary, insert derogatory term here, but that's just how I work. If anyone equally nuts wants to help me out regardless of how likely this is to blow up then I would very much appreciate your input!

It is roughly 1/2 a Pound per Square Inch per vertical feet of head, so you would have around 650 pounds per square inch of pressure (44.81 bar)

In metric units this is pretty easy: 10m of water height ≅ 1bar.
As for pressure loss, there are various calculators online. (one example)

The fun part will be getting pipes that can handle 40bar with plenty of reserve if you are not extremely careful with changes in water flow.
Also, I'd rather not have one burst in the same room as me.

I have a few questions?
Dam elevation =??m
Alternator/Generator Elevation = ??m
Height = Dam Elevation - Alternator Elevation = ?m

Flow of the stream = ??L/s

Output = Flow X Height X 5 = ??W


So lets say
Flow=0.1L/s
Height = 400
Output = Flow X Height x 5= 0.1 x 400 x 5 = 200W
If efficiency was at 50% then the actual output would be 200W X 50% = 100W
Which is 2.4KWH per day enough to power all your LED lights + Computers/Tablet/Laptop/Phone/Electronics + TV + Fridge.

If only there was a way to extrude all 700m of pipe onite as one single thing with no joints.

Let’s look at some typical microhydro system efficiency numbers:
Penstock (pipeline) efficiency = 95%
Nozzle and runner efficiency = 80%
Permanent-magnet alternator efficiency = 90%
Wiring and control efficiency = 98%
0.95 × 0.80 × 0.90 × 0.98 = 0.67
By the time the water has moved through this example microhydro generator system, only 67% of its initial potential energy has been converted to electricity. In fact, this would be considered very good performance—typical systems are about 55% efficient.

Seems you got most of the answers you need; i will try to add just some information to consider before building it.

40 bar = (400 m water) is just de standing still working pressure. You must include also water hammer effect the same  thats allows the watr hammer pump to work.

Here are some calculations: https://www.engineeringtoolbox.com/water-hammer-d_966.html to help you estimate

I think you will need to go with steel for this; I have seen it work with theathed pipe just be sure is rated accordinly (welded pipe is better if you have the expertice).


I havent seen any equipment with a energy recovery that high for hidraulic although havent work with that many; i would consider it to be closer to 30%; This summer i will start my serius research on household size pelton units; please let me know your results.

Hugo

Am I understanding you correctly in that you expect the overflow from the tank to run uphill 30 meters?  That seems highly unlikely.

How much overflow (in gallons per minute) do you get from the tank.  

Roughly speaking, for every gallon of water per minute at 400 m head, you'll get about 15-20 watts (assuming a high efficiency turbine coupled to a low efficiency car alternator)

P = m x g x Hnet x η
Where:
P = Power, measured in Watts (W).
m = mass flow rate in kg/s (numerically the same as the flow rate in litres/second because 1 litre of water weighs 1 kg)
g = the gravitational constant, which is 9.81m/s2
Hnet = the net head. This is the gross head physically measured at the site, less any head losses.
          To keep things simple head losses can be assumed to be 10%, so Hnet=Hgross x 0.9
η = the product of all of the component efficiencies, which are normally the turbine, drive system and generator

Firstly, i must apologise! I have learnt my lesson and shall no longer attempt to read topographical maps after a couple of glasses of vino...

So, my potential head from the tank is around 80m, not 400m. Turns out those little lines represent 20m intervals and not 100m. Feeling slightly stupid now, but also a little glad I don't have to deal with skin stripping water pressure!

Anyways, to answer your questions.
The damn height I'm guessing would be the elevation of the tank? Approx 600m, hydro setup would be situated at around 500-530m depending on where I decide to put it.

Flow of the "stream" would be dictated by the size of pipe, I'll be plumbing into a spring fed concrete tank, the only place it flows to is over the edge because they haven't sizes the overflow correctly (2" inlet, 1.5" overflow. Genius)

So according to some chart I've found, 80m head will give approx 115psi at the bottom. For a gravity feed in a 1" pipe this works out at around 1l/s

So, flow x height x 5 = 1x80x5 = 400
Assuming 50% efficiency for arguments sake, 200w over 24h = 4.8kwh of potential energy

Assuming another 50% efficiency of the hydro setup would bring the power down to approx 2.4kwh which would still be ample.

And no, at no point would any pipework be running up hill, there is a dirt track up to the tank with a pretty consistent gradient, i plan on digging a trench and dropping the pipe along the track. The 30m mentioned is the potential head on our property if i we're to build a holding tank at the highest point of our property and feed down to a battery shed in a sensible location

I'm still a bit confused, do you have 80m of head or 30m?
Is the holding tank from the spring at the high point on your property?  If not, how are you going to get the water from the holding tank up to the high point?

While you can calculate MAXIMUM flow rate based on pipe diameter, the continuous flow rate is based on what the spring will deliver, unless it can deliver more than the pipe can handle.  
How many gallons per minute of overflow do you get from the spring?  Is it higher than the maximum flow rate the pipe will handle?

The flow rate of a river and of a tiny spring is not the same.
One can visually see that there is a huge difference in the volume of water passing per second.

So when I ask for the flow rate I am asking what the flow rate would be if we had the 'biggest' possible pipe that did not limit the amount of water that was flowing

if you were somehow able to pool/collect all the water that is currently flowing in the stream how long would it take to fill a 5galloon (20L) bucket.

The tank I will be connecting to is Not on our property,  it is situated at the top of the hill, giving approx 80m of head to where I would place the hydro setup.

I also have the option of placing a holding tank at the highest point of our property, 50m below the spring fed tank, giving me approx 30m of head to the hydro setup IF I chose to run at a lower psi.

The spring fed tank puts out a ridiculous amount of water, it has a 1.5" overflow pipe that isn't capable of getting rid of all the water. Even after a dry summer the water is still spilling over the edge of the tank.
So, if i I were to run a 1" pipe, it's pretty safe to assume that pipe will be supplying it's full capacity 24/7 except in exceptionally dry years.

Clear as mud

I have a request, can you put a bucket under the 1.5" overflow pipe and tell us how long it takes to fill the bucket and how many gallons/liters the bucket holds? The bigger the 'bucket' the better. Here is a $70 flow meter that you can buy too https://www.dakotainstruments.com/6b0100-h20?gclid=EAIaIQobChMIrumhreu_3gIVRUCGCh315wMKEAQYAyABEgKmYvD_BwE

None of the formulas that these stupid scientist came up with uses diameter of pipe to calculate flow, for some strange reason they all say liters/second or gallons per minutes.
So can you share it in the common language that all these scientist seems to be using, I know it might be extra work on your part.

Tony ; I have been living with micro hydro / solar for 20 years now.  
Here is my nickels worth... for what its worth.
Forget a holding tank on your property. no matter how large it will drain out in moments if its inflow stops.You want all that water flowing directly to your hydro. Your losing head if you stop it at the top of your property.

Use as large a pipe as possible. Directly from the upper tank . There is a magical thing known as line loss . Start with a 1/2" pipe at the top and depending on the distance you will get literally nothing out the bottom. So if you think 1" is what you need then buy 1.5 "or 2"  you will never regret going large ... you will Definitely regret not going large enough. If cost is stopping you from going with larger pipe than the other way to defeat line loss is to start down the hill with 1" after 100' switch to 1.25 for several hundred then back to 1" this will eliminate the friction.

Now on to micro hydro's, personally I use a Harris but there are many choices.  My only strong suggestion ... ONLY use a permanent magnet alternator...  do not use a standard alternator with brushes !!! Brushes last apx 6 months before needing changed...  if you don't change them soon enough , you destroy your commutator .. requiring an even larger repair....  don't use one...

Now last but certainly not least .. what is your plan for the waste water ?  It has to go somewhere... have a plan or be prepared to get wet.  

One last tidbit of info for you.   Running water does not freeze ....it regularly goes below zero here, hydro never freezes ...  UNLESS you turn it off when temps are below freezing.... if it freezes up during winter...  bad deal.

 

Running water WILL freeze...if it get's cold enough.  Running water is "resistant" to freezing, but it can still freeze.