A 1,500 mile water pipe, connected to a large tank at the end?

Question

You open the valve. How long does it take before the level starts to drop?

Answer 1

The water level in the tank will start to drop immediately. The instant some small amount of water enters the pipe, the level of the tank will drop. This happens because the volume remaining in the tank will be reduced by the amount of water that has entered the pipe.

Depending on the dimensioning of the tank and the measuring accuracy, it may take a while for the drop to be detectable.

A taller tank with less surface area will show a drop more quickly than a shorter one with a larger surface area even though both have the same volume.

Answer 2

You don't have water pipes that long without pumps of some sort or other, which will change the flow rate.

Also, pipes that long can't be perfectly level, they have to go over hills and down valleys, all of which also change the flow rate.

So the answer is: how long is a piece of string.

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Answer 3

This obviously assumes that the pipeline is straight and level.

The tank also has a high water level.

The pressure in the pipeline is a Hydraulic Pressure and, water cannot be compressed. (Rephrased...water is considered to be incompressible for all normal intents and purposes. Under extreme high pressure, water will compress VERY slightly).

As the valve is opened, the pressure drop at the open valve will instantly be transmitted to the tank and the level will begin to fall.

And, where have I said I'm correct ????

My 'problem' is that, I refer to Web-sites as very little as possible and I depend upon my own vey deep and long Industrial experience, training and education.

Of course I'm also not in the 'Omega' club.

And, as to your questions in future, I wouldn't touch them with a barge pole.

Thank you to whoever gave the 'Thumbs Up'.

And, to Omega Jack. As I DID NOT give Remo the 'thumbs down', the deletion of your comment or an addition of an apology would now be in order don't you think ?.

Answer 4

Instantaneously.

Answer 5

1500 miles = 2400 km

Speed of sound in water = 1497 m/s

Time = d/v

t = 1600 s

Sound is just a compression, or in this case, a decompression wave.  This is the top speed.  If you get some cavitation, or you have air bubble, the speed of sound would slow down.

******

It is not instantaneous.  Not even light is instantaneous.  Furthermore, nothing is incompressible.  Water has a bulk modulus.  The speed of sound is simply sqrt(bulk modulus/density).

I presume that there is a valve at the end of the pipe.  The pipe is filled with water (all 1,500 miles).  The valve is opened.  Water starts to flow out.  This flow is powered by the existing pressure, which in turn is powered by the partial decompression of the water in the pipe as the decompression wave flows back to the tank.  You can figure this one out just using density and bulk modulus, but the end result is the speed of sound.

BTW: Can you bench 315?  Impressive.