# Estimating Potential Flow through a pipe, from tanks to outlet

I am working on a project for an amazing hot springs project in CA. As part of this project, the county is requiring that we provide our own fire suppression water. We have 3 tanks of 40,000gal each. These tanks will equally feed into a 6" PVC pipe. From the tanks, the 6" pipe will drop 172' of elevation, and run approx. 1400' with several bends and a few 90degree turns, terminating at a fire hydrant. The county has given us certain flow requirements which will be physically tested once the system is in place. I need to estimate the flow at that hydrant before we install this expensive pipe. If the estimate is considerably over our requirements, then I feel confident enough to begin the installation. If the estimate is close or below....then I have a problem. I understand the equations for determining flow, BUT they always need numbers that I don't have- specifically velocity! I know my pipe diameter (6"), but how can I estimate velocity? To find velocity I need flow, lol. And so on. Any help would be immensely appreciated!

Tanks- 3 tanks x 40,000gal = 120,000gal

Tank height to top= 20'

Pipe Interior Diameter= 6"

Elevation from Tanks outlet to Hydrant= 172'

Pipe length= 1400' (including approx. 5 x 45deg turns, 2 x 90deg turns)

• Draw a sketch of the physical situation. – MrYouMath May 24 '17 at 19:38
• What are their flow requirements? You can then do a balance of the pressure drop cf the mass flow rate. – Solar Mike May 24 '17 at 20:15
• You need to also find out at what tank level you fail to meet these requirements and see if that result is applicable. I can't imagine the setup you describe not providing enough flow for when the fire tanks are at capacity, but if the usage is large or frequent this system could run into a problem. – J. Ari May 25 '17 at 17:06

I'm pretty sure that you have all of the info that you should need to determine flow velocity using Bernoulli's equation.

Basically you can calculate the hydraulic pressure based on the elevation (don't forget to add what's in the tank), use that to determine your final velocity, and then use that to determine your flow rate based on your pipe size.

$$0=z_2-z_1+\frac{P_2-P_1}{\rho*g}+\frac{V_2^2-V_1^2}{2g}$$

I threw it into some hydraulic software and included the accounting for the fittings you listed. I made a couple of assumptions:

1. The water exits the tank at 0 ft in the tank.
2. The tanks are all at the same elevation (so it doesn't really matter how many 40,000 gallon tanks you have, that just determines how long the water will flow.
3. The tanks are essentially manifolded together and there is virtually no distance between the bottom of the tank and where you start counting the pipe run length.
4. I used the default spec for 6" Schedule 40 PVC pipe which actually has an ID of 6.065

It came up with 1676 gpm flow at the pipe outlet at 8.65 psig. Remember that as the tanks lose water, that pressure will drop slightly, though that is only 20 feet of the total 192 in elevation change.

• I answered this and am now working back through it. That flow rate seems ridiculous. – Secundus May 25 '17 at 1:25
• Hmm, what is the calculated pressure drop at this flow rate ? Any idea of the velocity necessary to achieve this flow rate?? – Solar Mike May 25 '17 at 4:43
• Pipe-flo crashed on me 5 minutes after I submitted that last comment and I didn't have a chance to recreate the model yet. I do remember the flow rate, however, and it was ~18 ft/s. That didn't seem terribly off base, though it is probably a little high for any sustained use of the system; it should be OK for an emergency system, though. What initially tipped me off was that when I went to 8 inch pipe, the velocity actually went up, rather than down. I suppose thinking about it now, there would be less pressure drop with larger pipe... – Secundus May 25 '17 at 4:49
• 18ft/s is not a flow rate, it is a velocity. You gave the flow rate as 1676gpm. – Solar Mike May 25 '17 at 4:57
• Yes, sorry, that was a typo. I was responding to your question about the velocity and typed flow rate. – Secundus May 25 '17 at 5:04

gives you a calculator BUT does not include any losses due to junctions, joints or bends. Losses due to all the junctions, joints, bends or any change in section will reduce this result which will / should be a maximum.

Note : I did not include the height of the tanks for this first run - you can enjoy tweaking the input !

If you have their expected flow rate then you can work backwards using continuity of mass etc.

I have included a picture of the results:

• Good resource! I was trying to find something like that because all of my reference books were at work. Looks like the numbers I got line up once the tank height is factored, at least when the tanks are near full. – Secundus May 25 '17 at 13:23
• Two methods, coming out very similar : excellent. I would still like to have the expected flow rate and work backwards... – Solar Mike May 25 '17 at 13:24