Water flow 2

[zaphod1]

Can anyone direct me to a table or calculation regarding flow of water, impelled only by gravity, through a pipe or channel?
I would like to determine the nominal flow rate of water flowing through a 1" (I.D.) pipe, with no other pressure than just gravity. The vertical drop from the tank is approximately 10' with approximately 3' of water in the tank. Thanks in advance.

 

[ElSid1]

Manning equation. Look it up

 

[MiketheEngineer]

Get a hydro book and Manning's

 

[bimr]

Here are some online calulators:

http://irrigation.wsu.edu/Content/Calculators/General/Pipe-Velocity.php

 

[katmar]

If you have a pipe (and not a channel) and the pipe suction is flooded (as seems to be your case) then the fact that the driving force is gravity and not a pump makes no difference. This means that you can use the standard pipe fluid flow correlations and calculators. You simply transform your height difference into a pressure difference. 13 ft of water is equivalent to 5.6 psi. With the pressure drop and pipe length and diameter known you can calculate the flow rate. If the height drop was more than 30 ft then there could be a risk of vaporizing the water in the pipe, but this complication can be ignored in your case.

If your pipe length is short the entrance and exit losses can be a significant fraction of the overall pressure drop. If your pipe in this case is vertical with a length of just 10 ft then ignoring the entrance and exit losses would increase the calculated flow rate by about 15%. As the pipe length increases the impact of ignoring these losses will decrease.

If you have a channel, or a pipe that is running only part full, then the advice given by the others to use Mannings formula is the right way to go.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[cvg]

it is very possible that flow is controlled by the inlet not by pipe hydraulics. the pipe may not run full. if so, orifice equation may give your answer.

 

[bimr]

Here is a link to another online calculator that shows you will get approximately 3 gpm.

http://www.calctool.org/CALC/eng/civil/hazen-williams_g

 

[cvg]

just using friction loss you could get over 40 gpm. assuming inlet controls and the pipe does not flow full, you get about half that. assuming the pipe is vertical, unlikely it will flow full, so just use an orifice equation at the inlet

 

[katmar]

cvg, how do you model a 1" orifice in a 1" line? The usually used equations will tell you that the pressure drop is zero. You can tweak the situation and pretend that the you have a 1" orifice in a 2" line and this will tell you that for a 3 ft head you will get 25 gpm. Or you could take the line as 3" and get a flow of 22 gpm. It is all just guesswork trying to find a representative model.

The losses through a square entrance are well known to have a resistance coefficient (K value) of 0.5. Why not just use this established methodology? This is low enough for the line (in this case) to run full if it is vertical. If the line is modeled as a square entrance plus 10 ft of 1" ID steel pipe plus an exit loss, with an overall driving force of 13 ft the flow rate would be 33 gpm.

I suppose that it depends on whether you want an accurate or a conservative estimate.

A side note - the reason bimr's calculated flows are so much lower than cvg's or mine is that bimr used an ID of 1 cm and not 1".

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[cvg]

so you are saying a larger pipe results in less flow?
I migt agree with pipe flow hydraulics if you could convince me the pipe was running full, but I am not convinced

 

[bimr]

Correction to my earlier post.

The corrected calculation shows you will get approximately 32 gpm. However, I would expect the flow rate to be below that. That flow rate requires a full pipe which would imply some type of pipe exit control.

If the drain pipe is vertical, the drain pipe will not remain full. Empirical testing on building drains has shown that the downward velocity tends to be self limiting to about 10 ft/sec which equates to about 25 gpm.

You also have other issues such as the pipe diameter will varyies slightly with the different pipe materials, the pipe roughness or fouling, and other minor losses.

 

[katmar]

@cvg: A 1" orifice will have a higher permanent pressure drop in a 3" line than in a 2" line (for the same flow rates) so if your assertion that the orifice is controlling the flow then yes - there will be less flow in the larger pipe than in the smaller one. But there are no 2" or 3" pipes in this scenario and I was only asking how you calculated the pressure drop for a 1" orifice in a 1" line. You have not explained how you calculate your orifice limited flow rate.

The requirements to keep a drain flooded are described by PD Hills in his Chem Eng 1983 article that is frequently cited in this forum. For a 1" outlet at 33 USgpm you need less than 3" above the outlet and the OP said he has 3 ft. I have no doubt that the 10 ft of pipe in this case will run full of liquid. If it is not full of liquid, where does the air come in?

A vertical 1" ID pipe has a maximum flow of water under gravity alone of 36 USgpm (assuming a roughness of 0.05 mm). This occurs when the head due to gravity is exactly matched by the pressure drop due to friction. It does not matter if the pipe is 10 ft or 50 ft long - provided the water can enter the pipe at this flow rate the pipe will reach an equilibrium between the driving force due to gravity and the head consumed by friction. The pressure drop through a 1" square edged entrance at a flow rate of 36 USgpm is about 1.8 ft of water so there is no problem initiating this flow into the pipe with the 3 ft available in the current case.

Once the pipe is full we have to take the overall system as the entrance, plus the pipe plus the exit loss and the the flow rate would settle out at about 33 USgpm.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"