Table Top Fire Flow Calculation 1

[oshead]

Hello,
I am trying to determine the velocity that a pipe can achieve with a given pressure. I know this value will depend on what the system can provide, system conditions, etc. I am just trying to do a table top analysis to set up a spreadsheet to refine down the road once I can complete hydrant testing.

My approach/thinking was to take the Bernoulli equation and the Hazen Williams head loss equation and solve for the V2 velocity. The v2 velocity would be the velocity within the headloss equation. I have all the other variables within the equation to solve for V2. Utilizing excel solver, I have solved for v2. My findings do not appear to be accurate for shorter runs of pipe.

My assumptions/givens:
P1= 276.92 ft of head; P2= 46.15 ft of head; 0.5' diameter pipe; length of 500'; C=150; V1=0

I solved the equation to 230.77'=(v[sup]2[/sup]/2g) + 0.3158v[sup]1.85[/sup]

I found it odd that I cant find any solvers or much discussion on solving for available velocity given pressure taking into account pressure losses. Am I missing something?

 

[bimr]

There are many solvers online:

Link to calculators

 

[hydrae]

EPAnet
it is still free...

 

[LittleInch]

Normally you want to know flowrate and then check velocity as it is a simple volume per second / area calculation.

There are many solvers but normally you want to limit the water velocity to around 3m/sec and generally no more than 5m/sec

Your head calculations look very precise versus the other numbers.

You appear to have a very high pressure drop for such a short pipe - 6 bar in 130 odd metres is not realistic and you're going to get very high velocities. I calculate about 17m/sec. That is not a good idea.

But for pipe friction losses forget Bernoulli is my advice. Just use the standard pipe friction loss equations.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[oshead]

Thanks for the replies. The example I provided is really not my intent for using this. My intent was more for a system where there is only about 35 to psi to work with. Using a residual pressure of 20 psi, there is only 15 psi to convert to velocity. I have not been able to find any solvers that take pressure or head and convert it to velocity while taking into account headloss.

I know this can be easily modeled. Its nice to understand what the computer is doing on the back end to justify/understand the results and their accuracy.

 

[LittleInch]

I've got an app on my phone which does this so I don't think you're looking very hard...

Your terminology is a bit strange though. You have to have a pressure or head difference from one end to the other to obtain flow (head loss). flowrate is directly convertible to velocity once you know your ID (Volume per second / cross sectional area = velocity per second.

They normally use hazen williaam or colebrook white formula.

Accuracy for liquid systems is about 5%, but there are multiple inputs which impact this, especially internal roughness and actual ID, vs nominal ID.

"I have not been able to find any solvers that take pressure or head and convert it to velocity while taking into account headloss."

Sorry but this just doesn't make sense. Can you look again and figure out what it is you're not getting here?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[oshead]

Using the Bernoulli equation velocity can be determined from a pressure and/or from a head due to elevation difference. With a known velocity, the Hazen Williams equation can then be used to determine the headloss in the pipe. If you were to write out the Bernoulli Equation with the Hazen Williams equation, you would end up with a Velocity unknown for V2.

Essentially I am trying to determine what velocity a 15 psi of pressure differential between two locations (assume the same elevation for simplicity) taking into account the head loss with known pipe properties.

(Z1) + (P1/γ) + (v1[sup]2[/sup] / 2g) = (Z2) + (P2/γ) + (v2[sup]2[/sup] / 2g) + Headloss

I believe this is typically done by equating the pressure differential to the headloss, and solve for V. This approach does not take into account the V2. Is this done just for simplicity? Thinking about the conservation of energy, the engergy produced by the pressure differential head will equal the velocity head + the headloss.

 

[LittleInch]

All you need to worry about is the head loss and any elevation change.

In a pipe of the same size V1 = V2.

If you know your pressure difference, diameter of pipe, length of pipe, elevation difference, you calculate head loss based on Hazen Williams or similar and iterate until the head loss equals your pressure difference for a given flow / velocity.

Velocity head is usually neglected as it is a minor component of the pressure loss.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[1503-44]

Without considering head loss, there is no difference e in 15psig at any location or elevation. 15 psig is 15 psig at 1, 10, 100, or 1000 ft elevation in New York, or California.

15 psig converts to an equivalent velocity of v= (2gh)^0.5
Water density is 62.4 pcf, so
15 psig x 144 / 62.4 = Head, h

Use whatever flow loss equation to find Headloss.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."