# Estimating head loss from pipe slope?

• yahastu
In summary, the head loss equation takes into account only friction losses in a horizontal straight pipe without bends or diameter changes. You need to calculate additional friction loss due to diameter changes, entrance loss, bends, fittings, and static head. Good search terms are Moody chart and friction loss pipe fittings. Those additional losses are added to the friction loss for the straight pipe. Friction is friction, and is dependent only on velocity, pipe properties, and fluid properties. It does not depend on horizontal or vertical pipe. The equations do assume that the pipe is running full.
gmax137 said:
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
anorlunda said:
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.

anorlunda said:
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
gmax137 said:
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​

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.

jrmichler said:
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!

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

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