Water Pipe System - Exploring Analogies & Calculations

[truewt]

Hey guys, I'm currently having some trouble regarding the water pipe systems. The problem arose as I was exploring analogies for the electrical circuit.

Alright firstly, in a water pipe, we need pressure difference for the water to flow, right?

Okay, not necessary, as long as initially the water is flowing, it can flow across pipes which are ideal and without resistance. Can this explain why current flow even in ideal wires of electrical circuits which do not have resistance? Or do we stick to the fact that in reality, wires have resistance, hence there is a potential difference between the 2 ends of the wire, hence current flows?

Does Poiseulle's Law for water flow rate applies when water in a pipe flows from a constricted section to a wide section and vice versa? If so, it seems weird that the flow rate is dependent on the pressure difference, by Poiseulle's Law, and the pressure difference is dependent on the flowrate, by Bernoulli's Law.

So how do we go about working out the calculations if we do indeed face problems regarding water flowing from one section to another which are of different radius?

 

[mgb_phys]

Alright firstly, in a water pipe, we need pressure difference for the water to flow, right?

It's a good analogy, Volts=pressure, Amps=flow rate.

Can this explain why current flow even in ideal wires of electrical circuits which do not have resistance?

Current flows for ever in superconducting wires which you could regard as pipes with no friction.

So how do we go about working out the calculations if we do indeed face problems regarding water flowing from one section to another which are of different radius?

Welcome to computational fluid dynamics http://en.wikipedia.org/wiki/Computational_fluid_dynamics

 

[truewt]

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

Here's a web link to the water analogy.

However, the more I think about it, the more I find that it is incorrect to use Poiseuille's Law to explain, because the change in pressure is due to Bernoulli's principle.

 

[Q_Goest]

Hi truewt,
The electricity analogy is valid, and it might be a good way of learning pipe flow. Once you’re doing pipe flow analysis in industry for a while though, you’ll probably think electricity is an analogy for pipe flow instead of the other way around.

If you pick up this PDF file, you’ll see how this is done in industry :
http://www.eng-software.com/products/methodology/pipe_flo.pdf

Check out equation 2. There’s something called a “resitance coefficient” which is designated by K. Values for resistance coefficient for various types of restrictions in piping systems such as expansions and contractions can be found in references such as this one and especially the Crane Technical paper, #410. See equations 12 and 14.

Bernoulli’s equation is not valid for determining pressure drop due to frictional flow, though it is used to determine overall pressure drop if frictional pressure drop is incorporated as shown in equation 15.

Note also, that the Poiseuille's Law isn’t used very much in industry. The standard frictional pressure drop equation used is the Darcy-Weisbach equation as shown in equations 1 and 2.

Regarding the use of comptational fluid dynamics, using such methods for pipe flow is overkill. They aren’t used except perhaps to determine a resistance coefficient of a newly designed part such as the Cv value of a valve.

 

[truewt]

So the weblink regarding the water analogy, is it correct or not?

I'm thinking that, if we have a parallel water pipe system, instead of the one in the link I gave, how do we introduce a change in pressure?

 

[Q_Goest]

So the weblink regarding the water analogy, is it correct or not?

The analogy is reasonable, but the Darcy-Weisbach equation is essentially an implicit equation as the flow rate depends on friction factor which depends on Reynolds number, which depends on velocity which depends on flow.

if we have a parallel water pipe system, instead of the one in the link I gave, how do we introduce a change in pressure?

Flow can be determined by equating those variables you know. For example, at the T where two parallel pipes separate, the pressure for the start of each leg is known. Similarly for the T where two parallel legs come back together, the pressure has to be the same. Knowing these two pressures, you can find flow through each leg.

 

[truewt]

But then again to induce a difference in water pressure, the pipe radius will have to change, am I right to say that? If we introduce a resistance in, the speed of water flow should decrease instead of increasing, right? but pressure drops, water speed increases, right?

 

[FredGarvin]

But then again to induce a difference in water pressure, the pipe radius will have to change, am I right to say that? If we introduce a resistance in, the speed of water flow should decrease instead of increasing, right? but pressure drops, water speed increases, right?

Are you thinking with or without frictional effects?

 

[truewt]

I'm thinking without frictional effects, to simplify matters.

But what happens if we take frictional effects into consideration? Does it complicate matters too much, or we will see a completely opposite observation?

 

[Q_Goest]

Hi truewt,

But what happens if we take frictional effects into consideration? Does it complicate matters too much, or we will see a completely opposite observation?

That's a good question, one of the most common points of confusion when learning about Bernoulli's equation and pipe flow.

Take a look at the link I provided here:
http://www.eng-software.com/products...y/pipe_flo.pdf

And go down to page 14. Start reading "System Fluid Pressure". Note that equation 15 is the Bernoulli equation without frictional loss. As they say,

Provided no work is done on the fluid, the energy of the fluid must remain the same throughout the piping system. The pressure at any point in the system can be found if the energy at one point is known and the velocity and elevation heads are known.

In other words, the total head (H in equation 15) will remain the same throughout the system. But of course, this isn't what happens in real life. There is a loss of pressure due to frictional losses. Equation 16 shows how you can modify the Bernoulli equation to take into account the pressure (total head) of the fluid in your system. This is as simple as factoring in the additional head loss due to frictional flow as determined from the Darcy Weisbach equation.

 

[truewt]

There isn't anything to view in the link; probably taken down?

But what happens if there isn't any friction to begin with. How do we bring the water pipe system as an analogy to the electrical circuit?

 

[Q_Goest]

I'll attach the file.

But what happens if there isn't any friction to begin with. How do we bring the water pipe system as an analogy to the electrical circuit?

If there isn't any friction in the fluid system, then you're not dealing with a real (water) system. In that case, the electric circuit analogy doesn't work.