Optimize Conservation of Energy with Water Wheel

[copria]

A five gallon bucket of water is placed five feet above the ground. The initial diameter of the pipe leading from the bucket is six inches. Energy from the falling water is captured by a water wheel. Optimally, there should be a complete transfer of energy from the water to the water wheel.

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?

 

[jbsteele]

First, the pipe should be designed to maximize the water's velocity. The diameter of the pipe should be as small as possible to decrease the contact area between the water and the pipe, which will help increase the water's velocity. However, too small of a pipe diameter could cause turbulence and decrease the efficiency of the system. The length of the pipe should also be taken into consideration. Increasing the length of the pipe will give the water more time to accelerate before it reaches the turbine, thus increasing the energy transfer from the water to the turbine. The dimensions of the water wheel should also be considered. The height of the water wheel should be as low as possible to keep the total system height below five feet. The diameter of the water wheel should be as large as possible to maximize the force applied to the turbine blades.