How does an inertial force affect water movement in an open channel?

[FloridaNick]

I am working on a project where I have to calculate the affected water movement in an open channel. What I mean by affected water movement is the gallonage moved by an inertial force such as a stream of water discharged under pressure.

For example:

A 1" pipe is discharging 10 GPM into an open water body parallel and just below the water surface. For the example there is no wind or restrictions. What I know is that the water is flowing at 10 gpm which displaces 10 gpm at the discharge. now I need to know the effect that discharge has on the water around it. All assumptions are the water is the same temperature, no wind, fresh water etc..

Supposed to be a straight forward calculation but I can't wrap my head around it.. Anyone out there that can offer a solution?

Thanks

 

[Cleonis]

I am working on a project where I have to calculate the affected water movement [...]
A 1" pipe is discharging 10 GPM into an open water body parallel and just below the water surface.

In the form presented here the problem is insufficiently described. There are too many scenario's, you cannot possibly cover all possible scenario's in one swoop.

It seems the only way to do any work is to narrow down the setting, to a form so symmetric that it lends itself to calculation.

For instance, let the open water that receives the inflow be a circular swimming pool with vertical walls. Let the inflow be in horizontal direction, parallel to the perimeter. Then the momentum of the inflowing water will induce circular motion, and you can calculate how much circular motion. Then you are in a position to try and put in estimations of friction. (Gyrating water in a swimming pool comes to a halt pretty quickly, so friction is a significant factor.)

 

[FloridaNick]

Sorry about being so vague but the problem is for open water systems like lakes and ponds. Trying to determine the flow rates for different aerators and circulators. To determine the proper flow rates you have to figure out how much water is moved by moving the water.

To try and simplify the question... If I pour a gallon of water into a large body of water, how much water does the gallon move?

I can assume that 1 gallon of water will displace 1 gallon of water. The inertia from the displacement of 1 gallon of water will continue for 3 seconds (just a number for the sake of argument) slowing to a stop. So what is the best way to figure out the total movement in Gallons.

I could argue that 1 gallon of water when poured in a water body will move 4 gallons of water ( a gallon per second plus the first gallon moved) plus the initial gallon so that would make a total of 5 gallons moved. So for every gallon pumped in or moved I can count 5 gallons of movement.

That is a total guess and is probably wrong. So I am looking to find someone who might be able to provide a proven formula for this type of movement or energy.

Thank you for the reply and I hope this explanation helps.

 

[cesiumfrog]

I guess you have known input of momentum, and also by the Poiseuille equation (laminar friction in the channel) known output of momentum.. you might also need to account for the slightly varying heights of water around the channel circuit.. as a rule though, turbulance (mixing) is one of the more difficult things to try to calculate. You might get better estimates from engineers than physicists.

 

[FloridaNick]

I have the initial input of water at 16 GPM (6 ft/sec) via 1 inch discharge into an open water body. The Poiseuille equation is for flow inside a pipe.. This is more of the after effects of water discharge. It does not have to calculate to the end of the inertia, just the first few seconds.

I can calculate the weight and velocity but it is all speculation nothing quantifiable. I can guess with the best of them but I don't think that is what physics is all about.

The argument could be made (with much speculation) that throwing a pebble into a lake will move every gallon over time but that is quite silly.

I have searched and searched for proven formulas but cannot find them.

Thank you to everyone who has posted so far. I truly appreciate the brain power... Please keep em coming