# Estimating head loss from pipe slope?

444 feet vertical, 126 gpm, 1kw? Double check your numbers.
Yes check your numbers, I think you are off by a factor of ten.

russ_watters
Mentor
Yes check your numbers, I think you are off by a factor of ten.
Where are you guys seeing 1kW? I see 5 kW in post #19. That seems reasonable based on 50% extraction efficiency.

Where are you guys seeing 1kW?

For the given conditions (126 gpm and 444 feet) I get ~10.5 kW. As @russ_watters alludes, the this would be a maximum theoretical value with real-world considerably less.

russ_watters
256bits
Gold Member
Per Bernoulli, they are all the same.
Thanks for answering, but it was mainly for @morrobay to think about in response to his question.

russ_watters
256bits
Gold Member
Case 4 converts gravitational potential energy into kinetic energy by allowing the water to accelerate through open air
Case 4 adds a vertical pipe. You are referencing case 1.
Since they are all gravity fed, the energy of the water is the same at the end of the 444 drop in elevation, barring, as I said, any friction loss in the pipes., which in the real world would have to be taken into account.
Your penstock could be of either .
A free falling column of water would be difficult to control onto the turbine buckets.

Beware of overpressure at the turbine end. Be especially aware of what will happen if you try to turn off the flow too fast. With 2689 feet of penstock the inertia is very big and rapid shut off will destroy all your equipment. You may even need a surge pipe with a blow-out diaphragm to protect against overpressure.

This is a good point, but I'm a bit confused about how a surge tank would be made. If I'm understanding correctly, the surge tank would need to be located at the bottom of the pipeline, and would need to be higher than the head, in order to prevent water from coming out during normal operation. In other words, if I have 444 feet of head, then my surge pipe would need to be greater than 444 feet tall. Would that even work? It seems like the 444 ft of head pressure in the surge tank would prevent it from rapidly absorbing pressure spikes. I must be missing something .

Perhaps a simpler option in this case would simply be to install a pressure relief valve?

Are you serious about the dimensions? 10" diameter and 2689 feet, 444 feet vertical, 126 gpm, 1kw? Double check your numbers. What is the total mass of water in the pipe? What is the velocity of the water?

Not sure where you got 1 kw from. Some of my earlier calculations were a little bit off, but I think my current numbers below are good. I'm seeing about 10 kw power available, of which the turbine will probably capture about 80%.

One thing I notice is that the water PSI is now 176 which exceeds the 150 PSI limit for PVC (and that's without taking into account pressure surges). Therefore, I would either need to use a steel pipe, or shorten the pipeline to stay safely below 150 PSI. During actualy construction, I would need to be careful to measure the PSI and see how close reality is to theory.

 Resource​ ​ Head(f)​ 444.32520​ Stream velocity(ft/sec)​ 1.00000​ Stream cross section(in^2)​ 45.00000​ Flow(gpm)​ 140.25971​ ​ ​ Pipeline​ ​ Pipe Length(f)​ 2,689.60000​ Pipe Diameter(inch)​ 10.00000​ Pipe cross section(inch^2)​ 78.53982​ Pipe Absolute Roughness (in)​ 0.00006​ Pipe volume (gal)​ 43,894.17240​ ​ ​ Constants​ ​ Fluid density(lb/f^3)​ 62.40000​ Fluid viscocity​ 1.10000​ ​ ​ Intermediate calculations​ ​ Re​ 40,307.88717​ F (Darcy friction factor)​ 0.02183​ ​ ​ Results​ ​ Head Loss(f)​ 35.91983​ Effective Head(f)​ 408.40537​ Water PSI​ 176.83952​ Water velocity through pipe (ft/sec)​ 0.57262​ Total pipe travel time (min)​ 78.28398​ Max power (kw)​ 10.79508​ Gallons per kwh​ 779.57561​ Rain barrels per kwh​ 15.59151​

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Just to be pedantic, you should know that in general pipe inside diameter is not the same as the nominal pipe size. Pipe comes in "schedules" which are different wall thicknesses. 10-inch pipe has an outer diameter of 10.750 inches. Normal or standard is schedule 40; for 10-inch sch 40 pipe the ID is 10.02 inch, transverse area is 78.86 in^2. So in this case you can get away with using 10 inch ID in your calculations.

I have never seen PVC in anything but schedule 40. You can look at the pipe manufacturer's website to see what they supply; they usually have useful tables of "Pipe Data" showing the dimensions for the various schedules in each nominal size. There is some ASME specification that defines the dimensions.

anorlunda
Staff Emeritus
If you have 176 psi working pressure, the burst pressure should be on the order of 800 psi. Then pressure relief valves and/or burst diaphragms should try to limit the pressure to 400 psi.

That much 10 inch steel pipe, I couldn't find the price, but at least several hundred thousand dollars.

I see 10-inch sch 40 PVC online at about $13 per foot, so there's$35,000. Plus 150 pipe couplings, glue, supports, etc... The turbine, the controls, wiring back up to the house...

our neighbor who owns property next to the road wasn't willing to give us 5 ft of easement onto a tiny corner of their 200+ acre property that we needed for the power line clearance region.
Maybe you can resume negotiations with the neighbor. Grid power at about 20 cents a kW-hr is a bargain.

anorlunda
Staff Emeritus
I see 10-inch sch 40 PVC online at about $13 per foot, so there's$35,000
Far too small pressure rating. He needs steel pipe.

Edit: Something like in this picture. My guess is that the picture shows something like a 10 inch pipe with 10 inches of insulating jacket. But it's hard to get accurate size from the picture. Just laying bare pipe on the ground would cause dents and dents become weak points.

yahastu
Far too small pressure rating. He needs steel pipe.

No argument there.

Maybe the OP can live with reduced power, then they could locate the turbine higher on the hill, reducing turbine inlet pressure and pipe length.

As interesting as the hydro project is, it will be costly and require work and  to maintain.

Far too small pressure rating. He needs steel pipe.

PSI is approximately 0.433 times head (ft). Therefore, if PVC can sustain up to 140 psi working pressure, then I can use PVC for the first 140/0.433 = 323 feet of head (a bit longer actually, due to head loss). That would be approximately 80% of the length of the pipeline. Then I only have to use steel for the bottom 20%.

Here I can find 10" PVC for about $12/ft: https://pvcpipesupplies.com/10-x-20-schedule-40-pvc-pipe-h0401000pw200b.html I have not searched around to find prices on steel pipe yet, but this looks promising.. https://www.alibaba.com/product-det...ferlist.topad_creative.d_title.1c0616c3k7evwI Maybe you can resume negotiations with the neighbor. Grid power at about 20 cents a kW-hr is a bargain. Even if I got the easement, it was going to cost$70k for the electric hookup. I can actually build a pipeline to give me free energy for less!

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Well it sure is interesting!

I don't know what kind of permitting is required for an installation like that. Have you checked your creeks for snail darters?

I work in a heavily regulated industry so part of my job is being able to come up with an endless stream of objections, reasons why plans / ideas will not work. We need to think of all that stuff ahead of time. Sorry if I come off as a wet blanket. I just can't help it

russ_watters
I don't know what kind of permitting is required for an installation like that.

Yeah, I have begun the less fun process of investigating the various pathways for permitting such a project. There are a few different ways...and eligibility depends a lot on the system design. It's much easier to get it permitted if I do it as a Run of River project (ie, no dam, and no upstream storage allowed)...which is another reason why large diameter pipes are preferred!

Just walked around to scope out some new spots today, took some more flow rate measurements. I have concluded that my method of measurement, which consists of dropping a styrofoam ball into the water and timing how long it takes to travel, is a really terrible way of estimating average stream velocity. So many eddies, currents, the surface moves differently than the undertow...yeah. I'm going to need to find a more accurate way to do that, but I don't want to shell out the cash for this thing...
https://rickly.com/usgs-type-aa-current-meter/

Here's the proposed pipeline path:

And some new numbers. A little bit lower than before, because I decided to change my pipeline path to try to optimize more reliable and streams, rather than to maximize peak power output.

 Resource​ ​ Head(f)​ 312.25928​ Stream velocity(ft/sec)​ 1.00000​ Stream cross section(in^2)​ 45.00000​ Flow(gpm)​ 140.25971​ ​ ​ Pipeline​ ​ Pipe Length(f)​ 4089.832​ Pipe Diameter(inch)​ 10.00000​ Pipe cross section(inch^2)​ 78.53982​ Pipe Absolute Roughness (in)​ 0.00006​ Pipe volume (gal)​ 66,745.90679​ ​ ​ Constants​ ​ Fluid density(lb/f^3)​ 62.40000​ Fluid viscocity​ 1.10000​ ​ ​ Intermediate calculations​ ​ Re​ 40,307.88717​ F (Darcy friction factor)​ 0.02183​ ​ ​ Results​ ​ Head Loss(f)​ 54.62005​ Effective Head(f)​ 257.63923​ Water PSI​ 111.55779​ Water velocity through pipe (ft/sec)​ 0.57262​ Total pipe travel time (min)​ 119.03939​ Max power (kw)​ 6.80999​ Gallons per kwh​ 1,235.77010​ Rain barrels per kwh​ 24.71540​ Pipeline fill time (hours)​ 7.93123​

jrmichler
Mentor
There is something wrong with your calculations. The lowest flow rate in my copy of Cameron Hydraulic Data for 10 inch Schedule 40 steel pipe is 180 GPM, where the head loss is 0.022 feet per 100 feet, so the total friction head loss is ##0.022 * 40.89 = 0.9 feet##. The head loss that you are getting at 140 GPM is very close to the head loss of 4 inch pipe at that flow rate. Your system just got a lot more affordable.

Styrofoam balls do not work well for measuring stream flow velocity. Much better is a piece of wood, preferably one that is wet enough to float low in the water. If you want even more accurate measurements, use a weir: https://www.openchannelflow.com/weirs. The weir can be a simple piece of plywood jammed into the streambed, with sand and gravel shoveled up against it to hold it in place. Search weir flow measurement calculation to find how to calculate flow rates. They work much better than trying to estimate flow from stream bed size and velocity.

There is something wrong with your calculations.
I think @jrmichler is right. For 10-inch sch 40 pipe, I get v=0.5707 ft/sec, Re=44,000, and f=0.022. L/D = 4900. Then head loss is ~0.55 ft.

@jrmichler @gmax137

Hmm...I'm having difficulty finding out the source of the discrepancy. I would like to know if the fundamental equations I'm using or wrong, or if I'm just misapplying them or what.

I am using the exact equations from here:

I first entered the values used in the example on the above website:
Q (gpm) = 400 gpm
L (ft) = 100
d (inch) = 4.026
episolon(in) = 0.0018

Using those numbers, I get:
Re = 285,524.45468 (pretty close to what they got but not exact)
f = 0.01809 (again close)

For the final head loss calculatation (hL), it looks like their arithmetic is incorrect:
https://www.wolframalpha.com/input/?i==0.0311*0.018*100*400^2/4.026^3

Ie, using their own numbers, they should be value of 137.9 feet for head loss, rather than 8.46.

However, it looks like the units are inconsistent in their equation. L is given in feet, d is given in inches...so maybe there is a units conversion error?

The units are all wrapped up into the leading 0.0311 factor. These can be tedious to unravel. My Crane book shows this with the d^5 not d^3 (shown in your link), that explains maybe why you're getting values much higher.

Crane 410: h = 0.03111 f L Q^2/d^5

L in feet
d in inches
Q in gpm

I think the d^5 is correct and the d^3 is a typo

yahastu
yeah the velocity is flow/area and area is ~d^2

so the v^2 gives you d^4

and the L/d gives you "another" d, so you have d^5

so you see a small change in design diameter gives a big change in head loss (d to the 5th power). so doubling the diameter will reduce the loss by a factor of 2^5 = 32. This is not perfectly true since the diameter comes into the friction factor via the Reynolds number. But for turbulent flow it makes a small effect.

Nice, thanks for spotting that @gmax137!

Styrofoam balls do not work well for measuring stream flow velocity. Much better is a piece of wood, preferably one that is wet enough to float low in the water. If you want even more accurate measurements, use a weir: https://www.openchannelflow.com/weirs. The weir can be a simple piece of plywood jammed into the streambed, with sand and gravel shoveled up against it to hold it in place. Search weir flow measurement calculation to find how to calculate flow rates. They work much better than trying to estimate flow from stream bed size and velocity.

Thanks for the suggestion :) I constructed a couple simple weirs yesterday. I opted for a V-shaped design, since I read that it provides a more accurate flow measurement than other profiles. Here is a pic installed:

Installing the weir was a bit challenging due to the conditions, because the ground is frozen and the only dirt I had available to pack around it was loose rocks and gravel from the streambed. Unfortunately I was not able to stop all the flow from going underneath and around the sides of the weir in my initial attempt. I think I managed to capture somewhere in the range of 50% to 90% of the flow.

I measured the head over the V-notch to be 1.5" and 2" respectively at two different streams, which implies much lower flow rates on the order of 7-13 gpm...less than 10 times what I had estimated before using the velocity method. As a result, I'm now estimating 400 to 800 watts per stream, so that is certainly disappointing, but it's still a decent amount of energy...ie, more energy than consume in our current house on avg. However, it won't be enough to run the proposed heating system (geothermal heat pump) and charge EVs that we need. Fortunately this does not kill the project, because there is a near inifinite supply of water at the bottom of the hill, so it just means that I may need to rely more on using solar power to pump water up to the top into the pipeline in order to maintain higher rates of flow.

As for pipe diameter, it's awesome that head loss is so much lower than I originally thought. Even a 2" pipe would be sufficient for this native flow rate. However, since the plan is to use the hydro for retrieval of pumped storage energy, I really need to size the pipe based on the max power that I would want to deliver. It looks like, if I want my max hydro power to be able to ramp up to about 20 kw, then I should have at least a 8" pipe. I still might want to boost that up to 10" for the extra storage capacity in the pipe, if I cannot get the permit for a dam.

jrmichler
anorlunda
Staff Emeritus
How much volume at the top of the hill do you have to store pumped water? That too may become a permitting issue.