A Pipe in the Water in the Sea
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From: Green on 19 Jul 2010 06:08 Suppose I have a vertical pipe, 10 feet in diameter, mounted rigidly on legs to the bottom of the sea. Both ends of the pipe are open. The top end of the pipe never gets covered with waves and the bottom end of the pipe is always submerged. Suppose the current wave height is 10 feet and the full wave cycle is 10 seconds long. Suppose in the first configuration, the bottom of the pipe is just below the surface as the wave troughs. Then as the wave rises around the pipe, the water inside the pipe also rises - nearly as high as the outside wave height. Suppose in the second configuration, the bottom of the pipe is 5 diameters (50 feet) below the wave trough. In a third configuration, the pipe is 10 diameters (100 feet) below the wave trough. Fourth, 20 diameters (200 feet). And so on. Is there a way to estimate how far above the wave trough the water inside the tube will rise and then fall in each configuration? Is there a depth for the bottom of the pipe at which there will be no rise or fall of the water level inside the pipe? Thanks.
From: Greg Neill on 19 Jul 2010 07:52 Green wrote: > Suppose I have a vertical pipe, 10 feet in diameter, mounted rigidly > on legs to the bottom of the sea. Both ends of the pipe are open. > The top end of the pipe never gets covered with waves and the bottom > end of the pipe is always submerged. > > Suppose the current wave height is 10 feet and the full wave cycle is > 10 seconds long. > > Suppose in the first configuration, the bottom of the pipe is just > below the surface as the wave troughs. Then as the wave rises around > the pipe, the water inside the pipe also rises - nearly as high as the > outside wave height. > > Suppose in the second configuration, the bottom of the pipe is 5 > diameters (50 feet) below the wave trough. In a third configuration, > the pipe is 10 diameters (100 feet) below the wave trough. Fourth, 20 > diameters (200 feet). And so on. > > Is there a way to estimate how far above the wave trough the water > inside the tube will rise and then fall in each configuration? > > Is there a depth for the bottom of the pipe at which there will be no > rise or fall of the water level inside the pipe? > > Thanks. It looks to me as though it might be modelled as a forced damped oscillator, similar to a spring-mass system, where the mass is the mass of the water column in the pipe. Below what is called the "wave base", the pressure variations due to all the waves above are averaged out and the effect of the individual wave passing overhead is essentially nil. The wave base is generally taken to be at a depth of a half wavelength. This also is the demarcation between "shallow water" and "deep water" conditions. It sounds like your waves are moving in deep water conditions, so you can determine the wavelength accordingly and then see how deep the bottom of the pipe can be before there is no forcing pressure variations at the bottom opening.
From: Cwatters on 19 Jul 2010 09:55 "Green" <GreenRite(a)yahoo.com> wrote in message news:f85840d4-77c0-4548-85f8-602a530964a7(a)k19g2000yqc.googlegroups.com... > Suppose I have a vertical pipe, 10 feet in diameter, mounted rigidly > on legs to the bottom of the sea. Both ends of the pipe are open. > The top end of the pipe never gets covered with waves and the bottom > end of the pipe is always submerged. > > Suppose the current wave height is 10 feet and the full wave cycle is > 10 seconds long. > > Suppose in the first configuration, the bottom of the pipe is just > below the surface as the wave troughs. Then as the wave rises around > the pipe, the water inside the pipe also rises - nearly as high as the > outside wave height. > > Suppose in the second configuration, the bottom of the pipe is 5 > diameters (50 feet) below the wave trough. In a third configuration, > the pipe is 10 diameters (100 feet) below the wave trough. Fourth, 20 > diameters (200 feet). And so on. > > Is there a way to estimate how far above the wave trough the water > inside the tube will rise and then fall in each configuration? > > Is there a depth for the bottom of the pipe at which there will be no > rise or fall of the water level inside the pipe? > > Thanks. Perhaps first approach is to simplify the problem to ignore the mass and friction of the water in the tube eg so the height of the water in the tube depends only on the pressure at the bottom of the tube. Google found this book with info on how to work out the pressure at any depth under waves... 4.3 Pressure field under a progressive wave http://books.google.co.uk/books?id=9-M4U_sfin8C&pg=PA83&dq=pressure+field+under+a+progressive+wave&hl=en&ei=C1hETK6UNdG6jAf5y-FX&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q=pressure%20field%20under%20a%20progressive%20wave&f=false Once you have an equation for the pressure then use that as the driving force for water oscillating in the tube.
From: Androcles on 19 Jul 2010 10:28
"Cwatters" <colin.wattersNOSPAM(a)TurnersOakNOSPAM.plus.com> wrote in message news:6cidnQFlteauxNnRnZ2dnUVZ8radnZ2d(a)brightview.co.uk... | | "Green" <GreenRite(a)yahoo.com> wrote in message | news:f85840d4-77c0-4548-85f8-602a530964a7(a)k19g2000yqc.googlegroups.com... | > Suppose I have a vertical pipe, 10 feet in diameter, mounted rigidly | > on legs to the bottom of the sea. Both ends of the pipe are open. | > The top end of the pipe never gets covered with waves and the bottom | > end of the pipe is always submerged. | > | > Suppose the current wave height is 10 feet and the full wave cycle is | > 10 seconds long. | > | > Suppose in the first configuration, the bottom of the pipe is just | > below the surface as the wave troughs. Then as the wave rises around | > the pipe, the water inside the pipe also rises - nearly as high as the | > outside wave height. | > | > Suppose in the second configuration, the bottom of the pipe is 5 | > diameters (50 feet) below the wave trough. In a third configuration, | > the pipe is 10 diameters (100 feet) below the wave trough. Fourth, 20 | > diameters (200 feet). And so on. | > | > Is there a way to estimate how far above the wave trough the water | > inside the tube will rise and then fall in each configuration? | > | > Is there a depth for the bottom of the pipe at which there will be no | > rise or fall of the water level inside the pipe? | > | > Thanks. | | Perhaps first approach is to simplify the problem to ignore the mass and | friction of the water in the tube eg so the height of the water in the tube | depends only on the pressure at the bottom of the tube. | | Google found this book with info on how to work out the pressure at any | depth under waves... | | 4.3 Pressure field under a progressive wave | | http://books.google.co.uk/books?id=9-M4U_sfin8C&pg=PA83&dq=pressure+field+under+a+progressive+wave&hl=en&ei=C1hETK6UNdG6jAf5y-FX&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q=pressure%20field%20under%20a%20progressive%20wave&f=false | | Once you have an equation for the pressure then use that as the driving | force for water oscillating in the tube. | It isn't that simple: http://en.wikipedia.org/wiki/Thermocline |