Backyard Aquaponics
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This post is about how to calculate the friction losses in pipes from the pump to where ever you are delivering water to. Understanding how big friction losses are is important in system design because it should play a big part in your selection of pump and layout of the various components.

I would advise that you have your pump in a sump (ST) and that the pump delivers water to your fish tank (FT) for a number of reasons but there are systems out there doing very well with their ST being their FT and the pump delivering water to their growing beds (GBs). If you are going to do this then the instructions below will need some modification which I'll talk about in another post called "Friction losses in drains (Moderate mathematics)".

Any time two surfaces interact there is always friction. In pipes as water moves through them there is friction between the water and the inner surface of the pipe and this friction resists the flow of water. The more friction the stronger your pump needs to be to overcome the resistance of the friction. As long as you as aware of this it is not a problem because you can design your system to reduce the friction.

The most important thing to understand about friction in pipes is that it increases in proportion to the square of the velocity water moving through the pipe. So when you double the speed of the water from a speed of 1m/s to 2m/s the amount of friction increase 4 times. Knowing this you can use it to your advantage because especially as you decrease the water velocity or speed below 1m/s.

Before you get started you need to know a number of things.

1. How much water per hour (flow) do you need to deliver to your FT?
2. How long is the pipe that will deliver the water to your FT?
3. How many fittings and of what type are they?
4. How high do you need to lift the water?

1. A standard value for this is figure is the volume of your FT or more per hour.

2. When you are doing your design you are going to place your FT and sump somewhere on your site. Once you have an idea of where they are relative to each other you can work out how long the pipe from the pump to your FT needs to be also...

3. you can work out what fittings you will need to get the pipe to your FT. The size at this stage isn't important but the types are. You need to make a list of all the bends valves connections, branches, etc.

4. The vertical height that you need to lift the water is from the water surface of the sump to the highest water surface that the pipe delivers water to. This is also called the static head.

If the end of the pipe is above the FT then the vertical height that the pump has to work against is from the water level in the sump to the pipe outlet.


If the pipe outlet is submerged in the FT then the static head is measured from the water level in the sump to the water level in the FT.


If the pipe has an opening along its length then the water level at this opening is the static head.


The tricky thing with working out the vertical height between the sump and the FT is that to a large degree this will be influenced by the height that is needed between the FT and the GBs to get the drains to work. I'll do another post on Drain design.

To give us some figures for a worked example here is a simple example.



In this simple diagram The pipe goes up from the pump into the greenhouse trusses, along a truss and then back to the FT.

Lets assume that the total length of pipe is 1m to get out of the sump, 2m to get to the greenhouse truss, 1.5m a long the truss to above the fish tank and then down 1.5m to the fish tank, for a total length of 6m.

In terms of fittings there is one pipe entrance into the pump, two 90 degree bends and one pipe exit.

Finally the static head is given as 1000mm in the diagram. This is a bit optomistic because the water level in the sump will go up and down. To be conservative we should probably use a larger value representing the sump at its lowest level. Most pond pumps require about 200mm of water coverage so we will assume a minimum depth of 400mm in the sump (200mm for the pump and 200mm of water covering the top of the pump).

We now have almost all the information to begin our calculations.

We also need to know the flow and the size of the pipe we are going to use.

For this example we will use a FT size of 5000L and calculate the friction losses for a number of different pipes.

When a pump is working it has to work against gravity to lift the water (static head) and against the friction in the pipe line (dynamic head) to get the water to move.

One of the easy formulas to use to calculate dynamic head is:

Z=(KV^2)/2g

Where:

Z=Dynamic head (m).
V=velocity of water in pipe in (m/s)
g=acceleration due to gravity =9.81 m/s^2
K=friction coefficient.

First calculation is to work out the velocity of the water in the pipe.

V = Q / A

Where:
Q=flow (m3/s)
A=cross sectional area of pipe (m2)

The flow should be at least one tank volume per hour so the value for Q should be 5000L/hr or 0.00139m3/s.

Let us assume we have a pump in mind that has an outlet that is 32mm diameter and that we are going to use pressure pipe for the first calculation.

The internal diameter of class 9 pressure pipe is 38.5mm.

So A will equal 0.0385 x 0.0385 x pi/4= 0.00116m2.

Therefore V= 0.00139/0.00116
=1.2m/s

The friction coefficient or K takes a bit more explanation.

It would be nice of plumbing fitting manufactures suppied if they supplied the K values for their products but generally they don't. Instead we have to use approximations. One such table of values can be found in Table 3.4 of the the Vinidex PVC manual http://www.vinidex.com.au/wp-content/uploads/2013/03/VIN014_PVC_Technical_Manual.pdf

By looking at table 3.4 we can see the K values for the various pipe elements.

We need to find the sum of all the individual K values.

The entrance can be ignored because that loss should already be accounted for in the performance curve of the pump.

The K value we use for the 90 degree bends in pressure pipe is 1.1 and there is also one exit (K=1).

So the K value of all the fittings is K=1.1*2+1=3.2.

We now just need to account for the losses in the pipes themselves.

The K value for pumps is:

L=4fL/D

Where:

L=length of pipe
D=internal diameter of pipe
f=friction factor.

To work out f there is a complex formula or you can use a Moody diagram of the fanning friction factors.


To use the moody diagram you first need to determine the relative roughness. Vinidex says that their PVC pipes have a roughness value of ε=0.003mm. Remember though that this value is for the clean, brand new pipe, once it has a bit of biofilm buildup the pipe will be rougher (and a little narrower as well). Unfortunately there are very few to no studies that have investigated pipe roughness in aquaculture pipe networks (Timmons and Ebeling et al. "Recirculating Aquaculture" 2007. I use a value of 0.1mm.

The relative roughness is:

r=ε/D

where:

ε = roughness (mm)
D= Diameter (mm)

So in this case r=

r=0.1/38.5
=0.0026

The second thing you need to work out is the Reynolds number:

R=VDρ/μ

Where:

V=water velocity (m/s)
D=pipe internal diameter (m)
ρ=density of water (~1000kg/m3)
μ=viscosity (@20C =1.002*10^(-3)Ns/m2)

R=1.2 * 0.0385 * 1000 / 0.001003
~46,000

Using these values (r=0.0026 and R=46,000)to look up the f value we get f~0.025.

So the K=4fL/D
=4 x 0.025 x 6 / 0.0385
=15.6

Total K= 3.2 +15.6
=18.8

So using this value the head loss will be:

Z=(KV^2)/2g
=18.8 * 1.2 * 1.2 / 2 / 9.81
=1.38m

So after all the that the Total Dynamic Head that the pump has to work against is (Dyanmic Head + Static Head) almost 2.4m.

As you can see more than half the work the pump has to do is just overcoming the friction from the pipe.

Most people when they chose a pump see that they have to raise the water 1m and will choose a pump capable of lifting the water at the required level of flow to 1m. Looking at the pump that we had in mind the Laguna at first blush seems fine because it can pump more than 6000L/hr at 1m of height.



Since effectively the pump in this example has to lift the water to an equivalent of 2.4m we can see that this pump is not up to the task:



Now we could say that 4000L/hr was close enough but the rule (guideline) is to turn over your FT at least once per hour and this setup is not going to do that.

So one solution is we can get a bigger pump. The Laguna 9000 is just a tad too small but the Laguna 11000 will do the trick:



This will cost you an extra $71 up front and over 3 years (pump warranty) and an roughly an extra $328.5 in electricity.

Watts of L 7500 =75w
Watts of L 11000 =125w
Difference = 50w

Extra power usage= kW *hrs * days * years * $/kwhr
= 25/1000 * 24 * 365 * 3 * $0.25/hr
=$328.5

Can no longer edit the post above so here is the correction for the calculations. I changed the diagramms before getting lock out but the changes I made of the text got lost some how:

Another approach is we can increase the size of the pipe and that will decrease the velocity and hence the friction. Also we can use DWV pipe the fittings of which are designed to reduce the friction at the fittings.

So what we will do is run the calculations again but this time with 50mm DWV pipe.

A =piD^2/4
=3.1416 * 0.0516 * 0.0516 / 4
=0.00209m2

V= Q/A
=0.00139 / 0.00209
=0.665m/s

In this example we are using DWV. DWV pipe has bends with a radius to diameter ratio r/D of 1. This is pretty much an ideal radius to make a bend to reduce the friction losses and so the 90 DWV bends have a K value of 0.5 or even less. This changes the sum of the K values for the fittings to:

K=0.5 + 0.5 + 1
=2

Since the velocity has changed the friction factor and reynolds number will also be different:

R=0.665 * 0.0516 * 1000 / 0.001003
~34,000

Looking up f for relative roughness of 0.0026 and R of 3.4 x 10^4, f = 0.034

K(for pipe)=4fL/D
=4 * 0.034 * 6 / 0.0516
=15.8

So:

Z=(KV^2)/2g
=(2+15.*0.665*0.665/2/9.81
=0.4m

We also have to add an enlargement. This makes the calculation a little trickier because when you calculate the losses for an enlargement or a contraction you need to use the velocity of the smaller pipe.

We are going from the 32mm pump outlet to 50mm as quickly as we can so the losses from the 32mm pipe can be ignored but the loss from the enlargement (k(32/50=0.29) is equal to:

Z=(KV^2)/2g
=0.29 * 1.2 * 1.2 / 2 / 9.81
=0.02m

When considering choice of pipe and pump this is otherwise known as "stuff all" but when are working on drain design and you have a FT close to overflowing 2cm can make a big difference

So the total loss is:

Z1+Z2=Zt
=0.42m

If we go back to the pump curve of the Laguna 7500 then we can see that using a larger pipe allows us to use a smaller pump.



You may have to spend a bit more on fittings if you use this approach but you will likely save money on your pump.

I hope all that makes sense but due to the edit rules I can no longer fix of any of

If anything needs clarification please ask.

great post!

want to put it in excel for us numpties??

Great post Stuart, and a lot of effort on your part it's just a pity that I'm a dumbass when it comes to those types of equations (Moderate Mathematics) fortunately for me my system is small and the pump is large enough to expand my system somewhat.

When it comes to sizing the pipe from your pump to your FT, in terms of water flow, bigger is always better.

You don't need to know the above because you can follow the guidelines in the other post I did:

http://www.backyardaquaponics.com/forum/viewtopic.php?f=8&t=21045&hilit=xtutex

I was trying to demonstrate how much the size of your pipe influences the performance or choice of pump. People often site the expense of bigger fittings as they reason they went with a smaller size of pipe bu the above example gives one example where it would clearly be better to go for the larger pipe.

Now when new people ask about pump pipe sizing they can take our word for it and size their pipes to make the water velocity less than 1 or better yet less than 0.5m/s or they can do the calculations themselves.

Unfortunately when it comes to drains you either need to get lucky, copy someone else's that works or know how to design them.

A few more things I want to cover because these questions get asked a lot.

1. The pipe outlet on my pump is only (insert size here) will I damage my pump by using a larger pipe?
2. The pipe outlet on my pump is only (insert size here) won't using a larger pipe get it to work harder?
3. The pipe outlet on my pump is only (insert size here) won't using a larger pipe use more electricity?
4. The pipe outlet on my pump is only (insert size here) won't ...

No.

xtutex

lost me on the last post

All will be revealed Bawahahaha.

Who put the smiley face in my calculations

Put a space between the 8 and the )