Pumps, Fans, and Turbines – Horsepower

The Engineering Toolbox – Electrical

As the water is brought down by gravity, it can turn the mass of turbines to produce work. Except for losses due to friction, the amount of energy you get out of those turbines is exactly the same as the amount of solar energy needed to evaporate that water and lift it up against gravity to that reservoir. Energy is neither created or destroyed, just shifted from one form to another.

Energy locked up in hydrogen nuclei in the core of the sun is released by fusion, travels through space to earth as light where it causes water to evaporate and float into clouds, where it rains onto a lake, where it then falls on a turbine, turning a mass of metal against a magnetic field, which produces an electric potential, which can be used to operate an appliance, etc.

You will note the amount of energy in the water available to do work has nothing to do with the properties of water, it has to do with its mass and how high the water is relative to the turbines.

Work has to be done to lift a mass against gravity, giving that mass potential energy. If the mass drops, that potential energy is available to do work.

The amount of potential energy in an elevated mass is Ep = mgh, where m is the mass, g is the acceleration of gravity (at the earth’s surface, 9.8 M/s**2, the upper-case M is “Meters”), and h is the height.

As the mass drops, velocity v increases and h decreases. The kinetic energy available to do work the mass gains as it loses potential energy is Ek = 1/2mv**2. At any time during the fall, the total energy of the mass is whatever Ep it has left plus whatever Ek it has gained, Ep + Ek = whatever mgh you had when you started.

So at the beginning of the fall, Ep = mgh (the original value of h you had when you started), and Ek = 0. At the end of the fall, Ep = 0 (because h is now also 0) and Ek = 1/2mv**2. And at any time during the fall, Ep + Ek = mgh. The “h” here being the original h you had when you started falling. Remember, in a falling body problem, h, v, Ep and Ek are always changing, and m and g are always the same.

With these relations, and a bit of simple algebra, it is possible to calculate all sorts of neat facts about falling objects. For example, the speed of any falling mass is equal to the square root of twice the acceleration of gravity times the height it has fallen, v = SQRT(2gh). The mass terms cancel out when you set 1/2mv**2 = mgh, so the velocity of a falling object has nothing to do with its mass, a fact Galileo had to prove experimentally.

These equations have to hold for anything to be possible. However, a lot of times the equations will hold but the the activities are not possible. The reason is that other equations also have to hold, involving concepts we haven’t talked about yet, like momentum (mv), force (ma, where a is acceleration) and action (Et). And of course, there is always the “jerk”. The jerk doesn’t have a formal name or units, but is mathematically defined as the third derivative of the distance with respect to time, the second derivative of the velocity, or the first derivative of the acceleration. The jerk is used by rocketeers, because rocket mass and acceleration change drastically as propellant is consumed, even if the engine thrust remains constant. Tom can probably explain “jerk” better than I can, he’s the rocket scientist here.

In all mechanical reactions, the energy and momentum are always conserved, the action is minimized, and the forces always add up to zero.

I’ve often wondered about the way the gearing compared to the size and pitch of the blades are calculated.

In remote Argentina I saw vanes connected directly to generators and alternators charging car batteries outside a house. The “gearing” was effected by pulleys. The vanes were generally fans from cars or small trucks. Seemed to work for them, but they were in a very windy area.

a Watt is a Joule per second, because a Joule is a unit of energy. I say this because some people use power and energy interchangeably, which is not correct.

So if you have a 60 Watt bulb, it consumes 60 Joules of energy every second.

Sometimes you’ll hear watts multiplied by time, which gives you energy. So for example,

1 kiloWatt-hour = 1000W x 3600 seconds = 3,600,000 Joules.

http://www.unitconversion.org/power/watts-to-horsepowers-conversion.html

So 1000W = 1 kW = 1.34102209 HP
or going the other way,
1 HP = 0.74569987kW = 745.69987 W

If you forget, just Google “convert watts to horsepower”