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copria

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__Restrictions__:

- Water wheel must have a height of less than five feet
- The design of the water wheel cannot be changed

__Undefined variables__:

- Dimensions of water wheel
- Pipe diameter (can be changed from six inches)
- Length of pipe (as extended from initial pipe segment to increase distance between turbine and bucket of water)

__Dimensional Relationships__:

length of pipe + diameter of water wheel = 60"

diameter of pipe = radius of water wheel

My first thought is to make the diameter of the pipe as small as possible.

Pros

- Increased velocity due to gravitational acceleration
- Increased velocity due to Bernoulli's Principle

Cons

- Contact area between between water and pipe is increased (thus, reducing the velocity of the water)
- Mass flow rate decreases

How can I optimize my design according to the length and diameter of the pipe?