Flow Rate through Smooth Bore Hose 2

[Chairs]

I assumed this was easy but I'm having difficulty finding the right equation. I need to calculate the flow rate in GPM of a smooth bore hose. The diameter is 3/8", length is 100 ft, inlet pressure is 250 psi and outlet is atmospheric (14.7 psi). The rest is unknown

 

[Latexman]

Chairs,

Buy yourself Crane's Technical Paper 410. It's online and cheap. It's the best, concise fluid flow manual there is, IMO.

Btw, what's the fluid and conditions?

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[racookpe1978]

Hoses are not "smooth" .... The flow will be less than that of an equal sized "normal" straight pipe, but (unless lined with Teflon or the like) not catastrophically less. Compare, for example of rougher or corrugated flex hose.

Also, there will be some loss due to bends.

 

[Chairs]

Its water under normal conditions (70F). And to make it simple we can assume its straight.

 

[Latexman]

Finally found it! The answer is, it's the Darcy–Weisbach equation. You crunch the numbers and we'll check it.

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[MikeHalloran]

For realistic results, you also need to model the interior of the end fittings, which are almost never smooth and flush to the lumen, and usually have an ID considerably smaller than the hose itself.




Mike Halloran
Pembroke Pines, FL, USA

 

[Chairs]

I looked at the Darcy–Weisbach, I figured if I could solve for the velocity then from there the flow rate would be easy. The problem was finding the head loss. And I'm just trying to figure out the basic formula without fittings right now

 

[MikeHalloran]

It's still an iterative process, but closure comes faster if you compute a Cv for each element in a flow system using an arbitrary flow, then use Kirchoff's rules to assemble the system model.



Mike Halloran
Pembroke Pines, FL, USA

 

[Latexman]

Crane TP410 will make it easier. It has a whole chapter of worked examples. Your company may even pay for it.

Btw, I do NOT work for Crane.

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[MikeHalloran]

I have both 410 and 410M, somewhere.
Well worth the modest investment.
Do work the examples.
Do put them in a spreadsheet and beat on them some more.




Mike Halloran
Pembroke Pines, FL, USA

 

[Artisi]

Try Google " friction loss in smooth bore rubber hose" seems like plenty of nfo there.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[katmar]

Rubber hoses like fire hoses or hydraulic hoses have a roughness very similar to commercial steel pipe. A value of around 0.0018 inch should give you realistic answers. Spiral wire reinforced hoses are a different story and the roughness could be 0.04 inch.

A potential problem with high pressure rubber hoses is that the diameter actually increases during operation. This is taken into account in evaluating fire hoses.

The nozzle at the end of the pipe should have very little influence in this case.

The Darcy-Weisbach formula is set up to calculate the pressure drop and not the flowrate. You therefore have to guess a flowrate and calculate the pressure drop and compare the result with you actual pressure drop. On the basis of this you refine your guess for the flowrate and calculate the pressure drop again. Keep doing this until the flowrate change from one guess to the next is insignificant.

You can speed up the guessing by noting that the pressure drop is roughly proportional to the square of the flowrate. For example, if your hose is smooth and you neglect any fittings a flowrate of 4 GPM will give you a pressure drop of 96 psi. Your actual pressure drop is 235.3 psi (250-14.7). Your second guess for the flowrate will therefore be 4 x (235.3/96)^0.5 = 6.26 GPM. Using this flowrate gives a pressure drop of 229 psi. Your third guess is therefore 6.34 GPM and this is probably as accurate as you can be within all the other assumptions.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[racookpe1978]

Oh come on Kat! You're making it too easy!

We were trying to make him do the work so HE would learn! We know you already know how. 8<)

 

[katmar]

@racookpe1978 - in principle I agree with you and I mostly ignore posts that blatantly ask "can you calculate this for me". It's a judgement call in the end. I had the lucky situation in the early part of my career of working in a very supportive and mentoring environment. I don't think it is like that for most engineers these days and in a way I feel that I should give something back to the profession in return for all the support I was given way back then.

There have been many times when I have simply referred the poster to Crane. But in all honesty Crane is not the most user friendly book in the world. I know I struggled with it initially. There is nowhere in the discussion section that describes how to solve a problem where the pressure drop is known and you need to calculate the flowrate. You have to read all the way to Example 4-6 near the back of the book before this problem is mentioned, and even then it is just illustrated with very little reasoning. For us who know the book we can get to Example 4-6 very quickly. A beginner has to start on page 1.

Perhaps in this instance I should only have outlined the method and not done the first few iterations. The way I took the situation is that Chairs is not looking to learn everything there is to know about pipe flow calculations. He has a once-off need for an answer and it would not be worth his while to read the whole of Crane to come to grips with the problem. He seemed to have made some effort and come unstuck so I decided to help. Like I said, it's a judgement call and we will all have different opinions of who should be helped and by how much.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Chairs]

Thanks I appreciate the help. I'm a new engineer (and the only one in my division); that being said your solution makes a lot of sense and I dont know why it never occurred to me. I started reading Crane 410 but it looks like it'll take me a while to get through it so this method will definitely help me out in the meantime.

 

[Latexman]

Chairs,

There is a button for that.

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[Chairs]

Ok this is the calculation I used but I'm getting a different answer. Is this approach correct?

Darcy - Weisbach
deltaP = Df * (Length/Diameter) * ((Density * Velocity^2)/2)

deltaP = 250 - 14.7 psi = 33,883.2 psf
Df=.0018 (Darcy Friction Factor for smooth bore rubber)
Length = 100 ft
Diameter = .375 in = .03125 ft
Density = 1.936 slug/ft^3

I solved for velocity and got V = 77.95 ft/s
then I used Q=VA to get 26.834 GPM.

 

[Latexman]

Not splitting hairs on whether the 250 psi is absolute or gauge, yeah that looks right.

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[Latexman]

No! I used the roughness for the friction factor. Did you do the same?

My spreadsheet confirms katmar's 6+ gpm number.

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[Chairs]

You're right I did do that. How do you calculate the Darcy's Friction factor if you don't have the velocity?