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Publication Title | Hydro Basics

Organic Rankine Cycle

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Hydro

Q =Ax V

Flow = cross sectional Area x Velocity

Area A

Figure 3: Flow

Ft3 2 Ft

Sec

= Ft x

Sec

Velocity V

Hydro Basics

John Cowdrey

©1994 John Cowdrey Hydroelectric power potential

depends of the basic physics of

falling water. While the concepts of head, flow, and pressure may seem esoteric, they are actually simple.

Where does the water pressure come from?

Pressure is generated by the weight of water due to a difference in elevation. Figure 1 shows that the 62.4 pound weight of a cubic foot of water exerts 0.433 pounds of pressure on one square inch. This means that for every foot of elevation, the static pressure increases 0.433 pounds per square inch (psi). Another way of saying this is that for every 2.31 feet of elevation, the static pressure increases one psi.

For a given flow, the equation can be written V = Q/A which means that the velocity is inversely proportional to the cross-sectional area A of the pipe. Figure 4 shows that for a given flow, the velocity of water in a pipe is inversely proportional to the square of the pipe diameter. This means that the friction losses rise dramatically as the pipe diameter is reduced because the velocity increases four times when the pipe diameter is reduced by half.

If the pipe is undersized, this friction loss can be substantial, and the available pressure is reduced. Another way of expressing potential hydraulic energy is by using the term “head”. Static head is the difference in elevation between the reservoir and the turbine. Friction losses cause loss of head over a length of pipe, making it appear that the reservoir is lower than it really is when the water is flowing, as shown in Figure 5.

Pressure head and velocity head

Besides the fluid energy due to pressure, water has energy due to its velocity, or kinetic energy. This is expressed in Bernoulli’s equation, which is studied in the field of fluid dynamics. The point we need to make here is that there is water energy due to both pressure and flow. It is convenient to express the velocity energy in feet of head, which is called velocity head. Mathematically, the velocity head is: V2/64.4, where V is the velocity of the water in cfs. One type of turbine works better on high pressure, and one is better for higher flow applications, as is discussed below.

If the pipe diameter is reduced by half, the velocity increases four times

V2 d12 (4)2 16

V 4V = = = = 4:1

V1 d22 (2)2 4

Figure 4: Velocity vs. pipe diameter

One cubic foot of water weighs 62.4 pounds

Pressure on one square inch =

62.4 lbs 144 in2

= 0.433 pounds per square inch

Figure 1: Each foot of elevation gives 0.433 psi pressure

12"

12"

Area = 144 square inches

3 ft

Pressure decreases 97 ft

Figure 5: Loss of head (pressure) due to flow of water

Pressure and flow

Static pressure means the pressure when no water is flowing. From the previous section, you can see that 100 feet of elevation will produce a pressure of 100 feet x 0.433 psi/ft or 43.3 psi.

When water begins to flow, there is some friction between the water and the wall of the pipe, which reduces the available pressure. Flow in a pipe is designated by the letter Q. As shown in Figure 3, flow equals cross sectional area times velocity, or Q = A x V.

Static head = 100 feet

If static head is 100 feet, the gauge reads 43.3 psi

Figure 2: Static pressure

34 Home Power #42 • August / September 1994

Loss 3 ft/1000 ft at 10 cfs

1000 ft

Image | Hydro Basics



hydro-basics
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