Hydrostatics

Is there kids around that dam? Just asking because if you put the dam wheels to close together they might get caught in between!

How much overflow do you guarantee?

Why did you not ask us to calculate the height of the dam. Was that not part of your work?

This sounds like a silly oversimplifed artificial school book type problem set by someone who has ignored most of the variables and has probably never seen a waterwheel.

Which is fine... but in those situations the solution is to build a quick prototype or scale model and test it. Bad maths is worse than no maths, which is why the silly UK push for teaching better maths in schools is doomed... what is needed is to teach better understanding and privide the mathematical tools to apply to the problem.

Simplifed problems are fine if there is some discussion about the assumptions made and why...

Maths is a tool...
Del

ya can't fix stupid no matter how much you throw at it

Actually... maybe it's a clever question designed to make you think.
Here are some questions to help you think.
1. What is the driving force for water flow?

2. How far does the water drop over the 1000meter?

3. How much power is generated in that 1000meter drop?

4. How far does it drop in 500 meter?

5. How much power is generated in each 500 meter drop?

6. How may wheel can you physically fit along that length of channel? Is this at all relevant?

Please Sir please Sir I know the answer.
Del (jumping up and down waving paw)

The loss of head at each wheel multiplied by the volumetric flowrate at each wheel represents the maximum amount of power obtainable at each wheel. However, no energy transfer process is 100% efficient so expect rather less than the maximum.

Bear in mind that, as more and more water wheels are encountered in this hypothetical situation, the head drops to the point where it is useless.

How the depth is maintained at 4 meters is open to speculation, as is the friction loss to the water as it flows in this channel.

There are numerous studies on waterwheels and a Wikipedia search will reveal links to practical information.

"Any missing data can be assumed"

Assume the channel is empty, no work will be done.

I'm even questioning the title.

Should this have been "Hydrodynamics" instead.

There is no mention of static water anywhere in the request.

That's why the question should have been how high is the dam!

Not very high if the exit velocity is only 1 m/s.

Kinetic energy E_k = mv²/2; power = E_k/t; all in compatible units.

As the teacher how to properly phrase a dumb question to trick people into answering it.

• The Easiest Ways to Cheat on Your Test (20 pics) - Izismile.com
  
• 50 Ways Technology Can Help You Cheat in School | Complex
  
• Top 8 ways students are cheating today - Higher Ed Morning

5.28

If the wheel depth and width is the same as the width and depth of the channel the wheal will not turn. It is jammed on the sides and bottom of the channel. I suggest you reduce the width and depth of the wheel in the channel, have a clearance of 300mm each side and on the bottom and then the wheel will turn. The wheel, based on your assumptions, will be approximately 16m high. And, how much of your wheel is in the water, 25%, 33%?

All of them water wheels that fit the channel can be installed.

The last one will not generate power!

I want a price for coming back and being smart!