Topic: Portable Water Turbine

Team Members:
Austen Greene
Bradley Anthony


Our project aims to analyze the practicality of a personal use, portable water turbine. Such a device would generate green, renewable energy for an individual, which could then be used any way they wished. Once constructed, the turbine would essentially generate free power, relying on the kinetic energy of the water instead of on fuel. We intend to look at the cost of constructing the turbine to get an estimate of the price a consumer would pay for one. We'll also look at the durability of the parts to guess its lifetime; when we put these estimates along with our calculations for power output, we should be able to determine whether it could be a realistic economical energy source.

How Turbines Work:

There are two types of water turbines: "impulse" and "reaction". Our design uses a reaction turbine, which uses the same design theory as a windmill, except that the working substance is water instead of air. The propeller is fully immersed, with the current flowing past the blades. The blades are designed so that water flows more quickly over one side than the other, which creates a pressure difference. This pressure difference exerts a force, which spins the blades. The blades are connected to a generator shaft, which then converts the mechanical energy into electricity.

To determine the power output:

external image 240c7ca1e55d2a02994866ce4bc13dad.png
  • η = turbine efficiency
  • ρ = density of water (kg/m³)
  • g = acceleration of gravity (9.81 m/s²)
  • h = head (m). For still water, this is the difference in height between the inlet and outlet surfaces. Moving water has an additional component added to account for the kinetic energy of the flow. The total head equals the pressure head plus velocity head.
    The velocity head is equal to external image fea8eeda954d010b0cf2abba68536486.png
  • external image 205e04657ce06ac57dfbcd408038a629.png= flow rate (m³/s)

Since gravity is a constant, and the density of water varies little from place to place, the key components which influence the power generation are the efficiency of the device, the flow rate through the propellers, and the the 'head' of the river. Head is defined as the water pressure, which is directly related to both the velocity of the water, and the height difference between the beginning and end of the river.

What this means is that if you want to get the most power out of your generator, you need a large propeller located in a fast moving body of water on a steep incline.

How ours is different:

Most water turbine systems are large, expensive, and immobile--dams being the most well known example. The hoover dam generates about 2GW of power, but was a massive project and had a substantial negative environment impact on aquatic life. Ours would be small and light enough to carry, with a much smaller power limit--about enough to recharge an electric car in a reasonable amount of time *is this realistic? How much power would that be?*. The ultimate goal would be to carry one in your car for a road trip, and be able to stop at a river, quickly unload it, recharge your car, then pick it up and leave. This would ideally all take less than an hour, and thus we can set that as our goal for power generation.
A 'standard' electric car needs about 10 hours to fully recharge off of a 1.5 kW outlet, meaning that if we want 1 hour of charging time, we need 15 kW *please show this calculation. I think you will be disappointed*.

The Shroud:

Turbines' power generation are normally limited by the surface area of the blades. The shroud is a duct surrounding the propeller, similar to those often seen in conventional aircraft which are used to improve the thrust of the propellers. It accomplishes this by directing the flow of a larger area in towards the blades, somewhat like a funnel. A well-designed shroud can effectively double the power output of the turbine by allowing the blades to affect a greater portion of the water--which is equivalent to an increase in the flow rate. Standard shrouds are made of solid materials, like plastic or metal; our design involves a light, flexible shroud which can collapse in it needs to be transported, or parachute out when it needs to pull in more water.


To be portable, we can require that the device weigh at most 15 kg, and fit in a 0.5 x0.5x0.5m box (= 0.125 m^3)
The turbine blades will be extend-able, in order to double the area covered to reach 1 m^2. The shroud should effectively further increase the size to 2 square meters of coverage.

Power Output Calculations

Given that the river will be relatively level, we can neglect the height difference and assume only velocity head.
To estimate, we will use the average river velocity of the Colorado river, of ~2 mph.[6]
Converting: 2mph * (1600 m/mile) *(1 hour / 3600 seconds) = ~0.9 m/s

Flow rate = velocity * area covered by propellors
0.9 m/s * (2 m^2) = 1.8 m^3 /s
Velocity head = (0.9 m/s)^2 / (2 * 9.81 m/s^2)
= 0.04 m

Density of water = 1000 kg / m^3

gravity = 9.81 m/s^2

efficiency = 90%

putting this all together:
P = (1.8 m^3/s) * (0.04 m) * (1000 kg /m^3) * (9.81 m/s^2) * (0.9)
= 635 kg*m^2 /s^3
= 635 W


With an average power conversion rate of 635 W, in 1 year the turbine will output
8760 h *0.645 kW = 5562.6 kW/h UNITS! (below as well)
assuming a lifetime of 50 years [7] In it's lifetime it will generate
5562.6 * 50 = 278,130 kW/h

At a high end turbine cost of $5000, this translates to an electricity cost of 1.8 cents per kilowatt-hour, extremely cost-effective.

Environmental Cost
Hydro-power is carbon free; The only carbon cost comes from the construction of the turbine itself, and once running the carbon intensity is 0. Additionally, while large scale hydro-electric dams can re-route rivers, harming nearby wildlife, killing fish, and disrupting any indigenous people, small-scale portable turbines have none of these effects.

*Please do some more calculations, design a device, and find references that are not wikipedia. Grade so far 50%*