Velocity more efficient than volume?

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Discussion Overview

The discussion centers on the efficiency of using velocity versus volume in water-based energy generation systems, particularly in the context of hydroelectric power. Participants explore the mathematical relationships between kinetic energy, water velocity, and volume, while also considering practical implications and challenges in achieving high velocities through water depth and pressure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents equations suggesting that higher velocity yields nearly equivalent energy output compared to larger volumes of water, proposing that velocity may be more efficient due to its squared relationship in kinetic energy calculations.
  • Another participant agrees mathematically but raises practical concerns, noting that increasing velocity requires significantly higher water heights, which in turn increases pressure and poses material challenges.
  • A participant reiterates the initial equations and emphasizes the need for sufficient water height to generate pressure, questioning the feasibility of simply relying on ocean depth for pressure without additional energy input.
  • Another participant discusses the construction of high dams and the use of flumes in local hydroelectric systems, highlighting geographical advantages that allow for effective energy generation without the need for excessively high dams.

Areas of Agreement / Disagreement

Participants express differing views on the practicality of achieving high velocities through water depth and pressure. While there is some agreement on the mathematical efficiency of velocity, practical challenges and geographical considerations lead to unresolved debates about the best approach.

Contextual Notes

Participants acknowledge limitations related to the assumptions about water density, height, and the material capabilities required to withstand increased pressure. The discussion does not resolve these complexities.

drewman13
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Here are two equations showing a nearly equivelant energy output for a given volume and velocity of water. Using the formula:

EKin = M/2 x Vsquared

250/2 x 15.34m/s x 15.34m/s = 29,414 KW (requires 5 times more volume)

50/2 x 35m/s x 35m/s = 30,625 KW (requires only 2.3x more velocity)

Since the velocity is squared, isn't it better to look to use velocity over volume? IF velocity can be acheived through another means other than water pressure via water depth, wouldn't that be the most efficient way to go?
 
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Mathematically, yes, it is.

Practically?
[tex]v \propto \sqrt{h}[/tex]
where h is the height of the water and pressure
[tex]p \propto \rho g h[/tex]
This depends on desinty of water and height. If you want to double velocity, you'll 4x the height, which 4x the pressure...It'd be a challenge to find material that can withstand that...
 
drewman13 said:
Here are two equations showing a nearly equivelant energy output for a given volume and velocity of water. Using the formula:

EKin = M/2 x Vsquared

250/2 x 15.34m/s x 15.34m/s = 29,414 KW (requires 5 times more volume)

50/2 x 35m/s x 35m/s = 30,625 KW (requires only 2.3x more velocity)

Since the velocity is squared, isn't it better to look to use velocity over volume? IF velocity can be acheived through another means other than water pressure via water depth, wouldn't that be the most efficient way to go?

Water depth? You will still have to get the water to a sufficent height above the outlet in order to get the pressure. You will also have to refill this depth of water in order to maintain pressure. That means using energy to get all this water from the working level to the top.

Are you thinking that you can just put a hose deep in the ocean and water will flow up to land with the pressure from the depth? I hope not
:frown:
 
Why do you suppose they build dams as high as they can? The hydro electric system on the Umpqua river in Southern Oregon, does not have many high dams. They use a system of flumes to carry the water to top of a several hundred ft high cliff, then using huge pipes (8' to10' in diameter) drop the water at a high velocity into the generators and back into the river bed. This is a convenience of our local geography, and a relatively small river that drops rapidly from 5000' to near sea level in less then 50 mi.

http://www.outstandingrivers.org/northumpqua.asp
 
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