Short Answer:

The energy line (E.L.) is a line that represents the total energy of the fluid per unit weight at different points along the flow. It is obtained by adding the pressure head, velocity head, and elevation head at each point.

The hydraulic gradient line (H.G.L.) represents the sum of pressure head and elevation head at various points in a flow. It shows the level to which the liquid would rise in piezometer tubes connected along the pipeline. The energy line always lies above the hydraulic gradient line by a distance equal to the velocity head  .

Detailed Explanation:

Energy Line and Hydraulic Gradient Line

In fluid mechanics, when a fluid flows through a pipe, it possesses energy in different forms — pressure energy, kinetic energy, and potential energy. The variation of these energy components along the length of the pipe can be represented graphically using Energy Line (E.L.) and Hydraulic Gradient Line (H.G.L.).

These lines are used to visualize the energy distribution and energy losses due to friction or other resistances in fluid flow systems. They are very important for designing pipe systems, ensuring proper pressure levels, and avoiding cavitation or backflow.

1. Energy Line (E.L.)

The Energy Line represents the total energy head of the fluid at different points along the pipe. It is drawn by plotting the total head (sum of all three energy heads) above a fixed reference line, usually the centerline of the pipe.

Mathematically,

where,

•  = Pressure head (due to pressure energy)
•  = Velocity head (due to kinetic energy)
•  = Elevation head (due to potential energy)

Thus, the Energy Line (E.L.) represents the height of the total head above the reference line. It indicates the total mechanical energy of the flowing fluid per unit weight.

Characteristics of Energy Line

1. The Energy Line shows the variation of total head along the pipeline.
2. It always slopes downward in the direction of flow due to energy losses caused by friction.
3. The slope of the energy line becomes steeper when the rate of energy loss is higher.
4. In the case of steady flow without losses, the energy line remains horizontal.
5. The vertical distance between the energy line and hydraulic gradient line equals the velocity head  .

Example of Energy Line

Consider water flowing through a horizontal pipe from a tank. At the tank surface, the velocity is almost zero, so the energy line and hydraulic gradient line start from the same level (equal to the water surface).
As the fluid moves along the pipe, energy is lost due to friction, so the energy line gradually drops with distance.

2. Hydraulic Gradient Line (H.G.L.)

The Hydraulic Gradient Line (H.G.L.) represents the variation of the piezometric head (sum of pressure head and elevation head) along the pipe. It shows the level to which water would rise in piezometer tubes placed along the length of the pipeline.

Mathematically,

Hence, the H.G.L. represents the line joining the heights of piezometric heads above a fixed reference line.

Characteristics of Hydraulic Gradient Line

1. The H.G.L. indicates the energy available due to pressure and elevation at different points in the flow.
2. It also slopes downward in the direction of flow due to head losses.
3. The vertical distance between the Energy Line and the H.G.L. is equal to the velocity head  .
4. If the flow velocity is high, this distance becomes larger.
5. The H.G.L. should always be above the pipe centerline; if it falls below, negative pressure or cavitation may occur.

Example of Hydraulic Gradient Line

In a water supply pipe fitted with piezometers, the water level in each tube represents the pressure head plus elevation head at that point. When these levels are connected by a smooth curve, the line formed represents the H.G.L. As the fluid moves along the pipe, the water levels in the piezometers gradually decrease due to frictional losses, showing a downward slope in the hydraulic gradient line.

3. Relationship Between Energy Line and Hydraulic Gradient Line

The Energy Line (E.L.) and Hydraulic Gradient Line (H.G.L.) are closely related because they both represent energy heads but in different forms.

• The Energy Line includes all three energy heads — pressure head, velocity head, and elevation head.
• The Hydraulic Gradient Line includes only pressure head and elevation head.

Hence, the Energy Line always lies above the Hydraulic Gradient Line by a distance equal to the velocity head.

Mathematically,

In slow-moving or stationary fluids, the velocity head is very small, so both lines almost coincide. In high-velocity flows (such as through nozzles), the difference becomes significant.

4. Importance of Energy Line and Hydraulic Gradient Line

These two lines are extremely important in practical fluid mechanics and hydraulic engineering:

1. Design of Pipelines:
   They help in determining pressure variations and energy losses along pipelines, which is essential for proper pipe sizing and pump selection.
2. Avoiding Negative Pressure:
   By ensuring the H.G.L. stays above the pipe centerline, engineers can prevent cavitation and pipe collapse.
3. Flow Analysis:
   They visually represent energy distribution, making it easier to understand and analyze fluid flow systems.
4. Locating Pumps and Turbines:
   They help decide the placement of pumps or turbines in hydraulic systems by showing energy availability and requirement.
5. Detection of Head Loss:
   The slope of both lines indicates the rate of energy loss due to friction and fittings.

5. Typical Behavior in Flow Systems

• In a horizontal pipe: Both E.L. and H.G.L. are parallel but slope downward due to head loss.
• In a rising pipe: Both lines drop sharply as elevation increases.
• In a falling pipe: Both lines may rise slightly due to elevation drop, but total energy still decreases due to friction.
• At sudden expansion or contraction: Both lines experience an abrupt drop due to additional head loss.

Conclusion

In conclusion, the Energy Line (E.L.) and Hydraulic Gradient Line (H.G.L.) are graphical representations of the energy distribution in a fluid flow system. The E.L. shows the total energy head, including pressure, velocity, and elevation heads, while the H.G.L. shows only the piezometric head (pressure plus elevation). The Energy Line always lies above the Hydraulic Gradient Line by a distance equal to the velocity head. These lines are vital tools in fluid mechanics for analyzing head losses, ensuring safe design, and maintaining efficient operation of pipelines and hydraulic systems.