Fluid mechanics & pump sizing (pseudo parallel pumps)

[mw11]

TL;DR

fluid mechanics, pump sizing (pseudo parallel pumps). Three wells each pump 20 gpm to a combined header. What is the correct way to size pumps 1, 2, and 3 (with respect to head, flow) considering this configuration shown in sketch?

Three wells each pump 20 gpm to a combined header. What is the correct way to size pumps 1, 2, and 3 (with respect to head, flow) considering this configuration shown in sketch?

 

[Baluncore]

What is the correct way to size pumps 1, 2, and 3 (with respect to head, flow) considering this configuration shown in sketch?

The header section may be profiled to handle the different flow volumes, at the same fluid velocity. The system appears to be low pressure with an open outlet.

I would expect all three pumps to have the same specification.

 

[berkeman]

What is the correct way to size pumps 1, 2, and 3

Is this question for schoolwork?

 

[mw11]

real life application. Trying to conceptualize to start things off before looking at real flows and real header distances / head losses. For example, does P.1 need to just be able to do 40 gpm and the total head from P.1 to Pond, P.2 needs 40 gpm and total head from p.2 to pond, P.3 needs 40 gpm and total head from P.3 to pond, or is the approach different?

 

[mw11]

The header section may be profiled to handle the different flow volumes, at the same fluid velocity. The system appears to be low pressure with an open outlet.

I would expect all three pumps to have the same specification.

thanks for the reply, i added more info / a question below in the thread.

 

[mw11]

Is this question for schoolwork?

thanks for the reply, i added more info / a question below in the thread.

 

[erobz]

+

Start with this, and you'll see how it develops.

Apply "Energy Equation" from fluid mechanics for an incompressible flow in the network :

$$ \frac{P}{\gamma} + Z +\frac{V^2}{2g} + h_p = \frac{p}{\gamma} + z +\frac{v^2}{2g} + \sum {h_l} $$

Branch $1$ to $a$ is in parallel with $2$ to $a$ (or the head of pump 2 $h_p$ in this case), and both in series with head loss from $a$ to $b$.

$k$ in the diagram generically characterizes the head loss. Pretend it's a constant independent of flow velocity for now i.e. $h_l = k\frac{u^2}{2g}$

You have to satisfy the energy equation at/between nodes, so we have to apply the equation above around the system.

If you have questions about the notation I just conjured (being lazy), ask.

Considering a system without losses is pretty much a waste here IMHO (in the cases dealing with applications of pumps). I can push whatever flow I want through a needle at no pressure if it's over idealized. Reality is quite different.

 

[mw11]

+View attachment 351572

Start with this, and you'll see how it develops.

Apply "Energy Equation" from fluid mechanics for an incompressible flow in the network :

$$ \frac{P}{\gamma} + Z +\frac{V^2}{2g} + h_p = \frac{p}{\gamma} + z +\frac{v^2}{2g} + \sum {h_l} $$

Branch $1$ to $a$ is in parallel with $2$ to $a$ (or the head of pump 2 $h_p$ in this case), and both in series with head loss from $a$ to $b$.

$k$ in the diagram generically characterizes the head loss. Pretend it's a constant independent of flow velocity for now i.e. $h_l = k\frac{u^2}{2g}$

You have to satisfy the energy equation at/between nodes, so we have to apply the equation above around the system.

If you have questions about the notation I just conjured (being lazy), ask.

Considering a system without losses is pretty much a waste here IMHO (in the cases dealing with applications of pumps). I can push whatever flow I want through a needle at no pressure if it's over idealized. Reality is quite different.

Think that makes sense, please see sketch to see if I am interpretating correctly:

 

[Flyboy]

What pressure are we talking about here? Below 20psi?

 

[Lnewqban]

real life application. Trying to conceptualize to start things off before looking at real flows and real header distances / head losses. ..., or is the approach different?

What type are those pumps, reciprocating or centrifugal?

 

[mw11]

What pressure are we talking about here? Below 20psi?

assume in the range of 40 to 60 psi.

 

[mw11]

What type are those pumps, reciprocating or centrifugal?

assume submersible centrifugal pumps, in water wells

 

[Lnewqban]

assume submersible centrifugal pumps, in water wells

Then, each of the pumps will self-adjust the delivered flow of water according to the actual resistance or pressure at each point at which each pump is discharging.
All you can do is to estimate that discharge pressure for each pump and use a diagram that the manufacturer should provide to estimate the corresponding flow or gpm.
The discharge pressure should be influenced by three main things:
*Head or height difference between the water surface of the well and point of your choice.
*Friction in pipes.
*Back pressure from the other two pumps.

 

[erobz]

Think that makes sense, please see sketch to see if I am interpretating correctly:

View attachment 351574

Are you familiar with the equation, do you have question about the variables are etc...? There is much to investigate if you already aren't familiarized with it.

I was hoping you would just start with the sub-system like I suggest. Once you understand the application of the "Energy Equation (s) - multiple applications" to that system you can extend it further on your own.

Write out the energy equation as it applies in going from what I have labeled $1$ to $a$. Fill in missing key details of pipes sizes, lengths, elevation changes... as variables. This confirms what you understand about it, what you might not. See what you are left with as unknown variables, rinse, and repeat. You have to put a flag in the ground somewhere to begin the computations.

You are also going to use continuity (since we are working under the assumption of steady- uniform- volumetric flow of in incompressible fluid) $Q = V A$ .

Please use the math formatting LaTeX Guide available on the site to present your mathematics. I don't like reading the handwriting-this is volunteer work-make it easy for us.

 

[erobz]

All you can do is to estimate that discharge pressure for each pump and use a diagram that the manufacturer should provide to estimate the corresponding flow or gpm.

We can work our way through this system without too much difficulty to find the required head for each pump (that's why I hope for them to just cut it back a bit to understand the method with post #7). We have the desired/spec flowrate, the OP just needs to say what variables are known.

As far as estimation goes, I'm not sure exactly you mean. The individual pump selected for each position would have to meet the required head calculated from the solution to the system of equations developed at the spec flowrates. As far as I can see, this is the problem as stated, and is the easier one to solve. It's really only a few lines of algebra - and some practical understanding of friction factors if I could just get someone to stick around long enough!

If you are talking about it being an estimation based on selecting two identical pumps to see how it pans out with the flowrates, it's a different beast. However, we can usually write the head of the centrifugal pump as a function of the flowrate via the manufactures data. It's my experience that most fit a quadratic of the form $h_p = C - \beta Q^2$ pretty well? This function can be used in the developed system of equations with numerical techniques (Hardy Cross) and some iteration for the friction...a good bit more involved, but not hopeless with help of a computer.