Thread: Head loss by pipe friction

I have discussed with my friend about the head loss issue. Assume you have a water tank with full water inside (height = H). Then, connect a pipeline (with length = L) at the side of tank (at bottom level). This connecting pipe has no slope (0%). Once, when we open the valve, the flow start. I know that flow velocity will be varied with the distance from starting point (say, x) and time (t).


So, if we can say V is function of flow distance and time or V(x,t).
The pipe friction loss formula = (fL/D)(V²/2g)


In this case, can we say there will be a distance L that the flow can stop due to the balance between the pressure head (tank) and total head loss in the pipeline.Please advise. Thank you.


Sorry if my English is not clear.

No. If the flow stops completely, then velocity goes to zero and there is no longer any pipe friction loss. There will be an equilibrium condition where the head loss due to pipe friction is exactly equal to the level in the tank.

What do you mean by this? "I know that flow velocity will be varied with the distance from starting point (say, x) and time (t)." If the pipe is full of water, flow velocity is the same throughout the length of the pipe. This is just because mass is conserved and the water is not compressible. If you mean the velocity will vary if you use different lengths of pipe, that's true because a longer pipe will have more friction. Or are you referring to the fact that velocity will decrease with time as the tank drains and level decreases? Please define the problem a little better.

I am met37818's friend whom he discussed with, I would like to clarify more detail that the water tank is not closed roof. It is open roof or let say it is the water reservoir.
The quantity of water is more than enough, then the water level may assume constant through time. Then we wonder the certain distance of pipe length is the water full flow within the pipe can be determined by head loss. Beyond that length the water flow may change to open channel type. Finally the water flow can not overcome the friction of inner skin of the pipe. Water stop flowing at certain distance, if we can determined.

Hope we can have a clue. Thanks a lot.

Akus

If the water level is constant then, as I wrote before, there is no length of pipe that will stop the flow of water. As the length of pipe increases, the flow resistance also increases and the flow decreases. However, it will never get to zero with a finite length of pipe. Also, the flow rate does not decrease along the length of the pipe. It is the same throughout. If the flow were slower further along the length of pipe, that would mean the water is being compressed, and water is incompressible, or nearly so.

By the way, the formula given by met37818 is called the Darcy Weisbach formula.
http://www.pipeflow.co.uk/public/art...ch_Formula.pdf
In the example you have given, the head loss is constant. It is just equal to the pressure difference between the tank and the outside air which is constant when the level is constant. f is the friction factor, D is the pipe diameter, g is the acceleration due to gravity. So if you solved for velocity V, you would find that it is inversely proportional to the square root of the length of pipe L. This function will approach zero at high values of L but never reaches zero.