fluid dynamicsrenewable energy
OTEC (Ocean Thermal Energy Conversion) utilizes the temperature gradient between cold deep ocean water, and warmer water to do work. I understand the pressure in the depths may be as high as a couple of orders greater than surface atmospheric pressure.
I also remember, vaguely, that a fluid moves from an area of high pressure to low pressure; wouldn't a sealed pipe merely need valves at the top to control the flow? Does water need to be pumped up out of the deeps?
If we assume continuity, infinite speed of sound, no viscosity, and laminar flow, then the key is in Bernoulli's equation. In general the pressure variation is very complicated, but to get some ideas how it works we can consider the pressure variation a very simple system that can be calculated analytically.
I came up with this simple system:
Let's say somewhere in the water far from the surfaces, suddenly a cavitation bubble of radius $R$ with pressure $P_0-\Delta P$ is produced. Where $P_0$ is the atmospheric pressure, let's assume that the scale of the system we are playing with is small enough that the pressure of undisturbed water anywhere is equal to the atmospheric pressure. Because of the pressure drop, water will start moving radially to fill the bubble as shown in the picture. If the flow is continue and laminar then we have the following flux relation
$v 4\pi r^2= constant$
$v=\frac{C}{r^2}$..........................................(1)
Now Bernoulli's equation gives
$P_0=P(r)+\frac{1}{2}\rho v^2=P(r)+\frac{1}{2}\rho \frac{C^2}{r^4}$
Because $v=0$ at a point far from the bubble. Boundary condition at $r=R$ gives
$P_0=(P_0-\Delta P)+\frac{1}{2}\rho \frac{C^2}{R^4}$
Eliminating $C$ and $\rho$ we get
$P(r)=P_0+\Delta P \frac{R^4}{r^4}$
As expected $r\rightarrow \infty$, $P(r)\rightarrow P_0$. Thus the pressure change fades away as we go farther from the source of disturbance.
In a more general case where the above assumptions still hold, the velocity profile of the flow equivalent to our eq.(1) is quite complicated. Eq. (1) can be replaced with a general flux equation which holds along a streamline
$vA=constant$..................................(2)
Where $A$ is the cross sectional area of a streamline portion. A typical flow's streamlines caused by a moving object look like this
We can view eq.(2) as an equation that holds in the moving object's frame. As we can see in the picture above, initially the streamlines are uniformly separated. Let's denote the cross sectional area of each slice of stream line portion as $A_0$, from here we know that if the cross sectional area of a stream line portion equals to $A_0$ then its pressure is unchanged or $P_0$. We can see that the streamlines near the object are denser, which means that their cross sectional area are smaller than $A_0$. Thus from eq.(2) we realize that the water is moving faster there, and Bernoulli's equation says that the pressure there is lower than $P_0$. As we move perpendicularly to the flow, away from the moving object the streamlines' cross sectional area get more and more similar to that of undisturbed ones and so does the pressure there. Therefore it can explain how the pressure disturbance decreases over distance from the source.
Fluid power began with hydraulics and the fluid being water. Water cannot be compressed. Though other fluids can be compressable and some even into gasious states, some remain non-commpressable.
External force or pressure means anything protruding from the outside in being the pushing force creating the pressure. We need non-compressable fluids to make the hydraulics and other fluid powers to work in the ways in which they do today.
Keep in mind that even if the verbage of fluid power were to change, that the principles will continue to work the same as they exist today. To alter the verbage now and in todays society, would only confuse people more in this already confusing world.
Ask yourself this; is it worth the fight to chage laws of theroys for one mans different interiptations? Also, is this why our constituion is so insanely ammended because everyone seems to find a way to change it to how they see it to be?
I think you're over thinking this thing buddy. It's just meant to be used as a basic tool in understanding how fluid power works.
Thanks
Joe
Best Answer
Typically, yes, the water does need to be pumped up.
Because if it released energy by rising, it would already have risen to the surface.
OTEC depends on a high-enough temperature difference between the lower-depth water intake and the higher-depth one, for that temperature difference to do enough work to provide some surplus power, in addition to the power needed to pump the water up.
Tepco's OTEC plant on Nauru (1982-3) reportedly generated 120kW electricity gross, of which 90kW was needed to operate the plant. The surplus 30kW was fed into the grid.
More context: OTEC is estimated to be viable with a ${\Delta}T$ of 20 Kelvin, so definitely the tropics, and predominantly the western Pacific. Unsurprisingly, Japan has been particularly active in OTEC. The global harnessable resource is estimated at $10^{13}W$, which is the same order of magnitude as total global energy consumption.