First, let's make it clear that plowing a field for cultivation breaks up the soil and does make it more susceptible to erosion. What is important to remember is that any serious erosion by water requires a significant drop in elevation. This is why many societies that must cultivate hillsides to survive have developed terrace farming. Along with the drop in elevation, the flow must be channeled to focus the water's power. A broad, flat expanse of heavy soil, even with a slope of 200 feet per mile, will erode very little unless channels are allowed to form. Even then, it must get to a natural stream to ever have any hope of getting very far. Most of the tillable land in the Minnesota River watershed is nearly flat, and almost level, until it reaches the banks of River Warren or its bluff-lined tributaries. Then the elevation drops, very quickly, about 200 feet.
The basic principles involved during erosion are: the first law of thermodynamics, which deals with conservation of energy; the work of kinetic energy, which is the energy of motion; the force of gravity; and the action of friction. These are the same principles involved in grinding grain or generating hydroelectric power.
One cubic foot of water equals 7.5 gallons and weighs 62.5 lbs. Gravity is measured as acceleration and is about 32 feet per second each second. Water runs downhill for the same reason that a rock, thrown straight up, must come down.
Kinetic energy is computed by multiplying half the mass (we'll settle for weight) times the square of its velocity. If you throw a rock into the air and allow it to hit you coming down, you will experience the transference of kinetic energy from the rock to your head. Furthermore, that energy will be roughly equivalent to the energy you expended in throwing the rock. Any apparent loss of energy has been dissipated by other forces, such as friction with the air. This is conservation of energy. Energy is never lost. It is just converted to another form or transferred to another body. Any mass not at the Earth's center of gravity has stored kinetic energy proportional to its distance from the center.
For most practical purposes when dealing with surface erosion by water, the applicable stored energy in a cubic foot of water is determined by the elevation of the water in relation to the elevation at sea level. At 1,000 feet above sea level, one cubic foot of water contains usable stored energy equal to about 62,500 foot pounds. A continuous flow from this height at a rate of one cubic foot per second will deliver 114 horsepower for as long as the flow continues. Needless to say, anything at the bottom will take serious pounding. If you reduce the drop, the energy expended is reduced accordingly. A one cubic foot per second flow with a drop of one foot equals .114 horsepower.
Water flows in a stream or river because gravity is pulling it downhill. Most of the time the water travels much farther horizontally than vertically. Movement across the surface of the ground has an energy cost roughly equal to .15 horsepower per mile per cubic foot of water. This means, in general, when the elevation of the stream surface changes by less than 1.5 feet per mile, all the usable kinetic energy is dissipated just moving the water. Erosion begins when the drop in this elevation exceeds 1.5 feet per mile and the flow of water is restricted to a definable channel. Channelization creates deeper, swifter flows that produce more kinetic energy than is needed to move the water over the ground. It is this excess energy that transports soil downstream.
The basic situation is that any mass, including a rock or a pound of water, has potential usable kinetic energy relative to its height above sea level. This potential decreases as the mass gets closer to sea level. Along with this, any lateral movement requires spending energy, either potential, or artificially induced. Water flowing along a slope of 1.5 feet or less per mile will generally spend all the energy released in the drop to cover the mile. A rock, on the other hand, will not roll or slide along such a slope and requires much more energy to move.
So why does it cost energy to move across the ground? It's mostly due to friction accentuated by the pull of gravity. Separate energy costs accrue by lifting up against gravity to escape friction.
Friction, the rubbing together of two masses, converts kinetic energy into either heat or work. With flowing water, this is mostly work. The miller's wheel, a hydroelectric turbine, and soil erosion are prime examples of flowing water releasing its pent-up energy by performing work. The fundamental action of work is moving something. Work is commonly measured in horsepower.
Soil doesn't float. Just as you must give away energy to pick up a rock and carry it across town, so must the river. The energy you use is just the amount required to move you and the rock to the new location. The river expends just what it takes to get it and the rock from point A to point B.
When water flows down a slope steeper than 1.5 feet per mile, it doesn't necessarily cost less energy to move across the ground. Instead, the water is getting closer to sea level with less horizontal movement. More potential energy is released at a faster rate. This increase in energy presents itself as increased velocity. The water moves faster. When the potential horsepower exceeds that needed to maintain the flow, the excess must go somewhere. If it is not somehow captured, it usually goes toward tearing up the land and carrying it away.
A foot pound is the work produced by dropping one pound one foot. A flow of 550 foot pounds per second equals one horsepower. If you know the flow rate in a stream or river, you can estimate the potential horsepower contained in that flow.
So, let us examine the Minnesota River.
A straight shot from Mankato to Fort Snelling is nearly 70 miles. The River Warren traversed about 100 miles from the great bend at Mankato to where the rivers join. The Minnesota snakes its way through the old bed flowing twice that distance. During normal flows, the surface elevation of the river at Mankato is less than 75 feet higher than the surface elevation at the mouth. The slope of the river is less than .4 feet per mile. The slope of the floodplain is less than .8 feet per mile. About the only reason the Minnesota River flows at all is because tributaries like Blue Earth and Cottonwood Rivers provide much of the water that is the Minnesota River. The water from these tributaries falls an extra 150 or more feet within a few miles of entering the Minnesota. This additional horsepower provides the energy needed to maintain the flow.
As these tributary flows rush quickly down to the Minnesota River, some energy is converted to work and digs away at the soil. More energy is spent to carry it downstream. When the silt-laden water hits the flat of the River Warren bed and joins the sluggish Minnesota, it gives up much of the energy that was carrying the silt. Most of the suspended dirt then settles to the bottom.
Now let's see what happens when heavy snows and/or torrential rains precipitate a flood.
A flow of 60,000 cubic feet per second at Mankato is certainly a flood, but it is not a record. This much water quickly overflows the Minnesota's banks and begins following the River Warren channel. Most of this water is coming from about 1,000 feet above sea level and within 150 miles of the Mississippi River. The elevation at the mouth of the Minnesota is just below 700 feet.
60,000 cfs(flow rate) x 62.5 lbs(weight) x 300 ft(drop) = 1.125 billion ft-lbs/sec. Divide this by 550 to get 2.045 million horsepower. Of this, .15 horsepower per cubic foot per mile is required for the water to flow.
60,000 cf x .15 hp x 150 miles = 1.35 million horsepower. Subtract this from the total horsepower to get the excess kinetic energy.
2.045 million - 1.35 million = 695,000 horsepower.
This is a rough approximation of potential continuous output at the mouth. At Mankato it would be right around a million horsepower. Picture an endless army of advancing bulldozers, 350 horsepower each, 2,000 per row, a continuous wave of unstoppable, earth moving power. This doesn't come close to describing what actually happens. Look at it this way, if this 60,000 cfs flow were captured, as much as 750 Megawatts of continuous power could be generated. Instead, this energy goes toward carrying away our state. And it comes from the ever-eroding stream banks, not the nearly flat table lands.