What is total energy line (TEL)?

Short Answer:

The Total Energy Line (TEL) is a line that represents the sum of pressure head, velocity head, and elevation head of a flowing fluid at any point along a pipeline or channel. It shows the total energy possessed by the fluid per unit weight and helps in analyzing energy losses and flow behavior.

At any point in the flow, the height of the TEL above a reference line indicates the total head of the fluid. The TEL always slopes downward in the direction of flow due to energy loss caused by friction, but it rises at pumps and drops at turbines where energy is added or extracted.

Detailed Explanation:

Total Energy Line (TEL)

The Total Energy Line (TEL) is a graphical representation used in fluid mechanics to show the total energy available in a fluid at different points along a pipe or channel. It helps visualize how energy changes due to flow conditions such as friction, elevation differences, and added or extracted energy from pumps or turbines.

In a flowing system, the total energy per unit weight of the fluid is given by the sum of three components:

  1. Pressure head (p/ρg) — energy due to pressure,
  2. Velocity head (V²/2g) — energy due to motion, and
  3. Elevation head (z) — potential energy due to height above a reference level.

Thus, the total energy head can be written as:

The line representing this total head along the length of a pipeline is called the Total Energy Line (TEL).

Representation of Total Energy Line

The TEL is drawn by plotting the value of  at several points along the pipeline and joining them with a smooth curve.

  • The height of the TEL above the reference line (usually the pipe centerline or datum) represents the total head at that point.
  • The slope of the TEL shows the head loss due to friction or fittings.
  • The TEL always slopes downward in the direction of flow, since energy is continuously lost as fluid moves through the pipe.
  • At points where a pump adds energy, the TEL rises suddenly.
  • At points where a turbine extracts energy, the TEL drops sharply.

Expression for Total Energy

At any section in a flowing pipe, applying Bernoulli’s equation, we have:

Where,

  •  = head loss due to friction or fittings.

The term on the left-hand side of the equation represents the total head at section 1, and the right-hand side represents the total head at section 2. When these heads are plotted along the pipeline, they form the Total Energy Line (TEL).

Hence, the TEL helps in visualizing how the total energy reduces from one point to another due to head losses.

Relationship Between TEL and HGL

The Hydraulic Gradient Line (HGL) represents the sum of pressure head and elevation head, i.e.:

The TEL includes one more term — the velocity head (V²/2g). Therefore,

Hence, the vertical distance between the TEL and the HGL at any point is equal to the velocity head of the fluid at that section.

  • If the velocity of the fluid changes, the vertical distance between the TEL and HGL also changes.
  • In a uniform diameter pipe with constant velocity, this distance remains constant.
  • The TEL always lies above the HGL by a distance equal to .

Characteristics of Total Energy Line

  1. Downward Slope:
    • TEL always slopes downward in the direction of flow because of energy losses.
  2. Distance from HGL:
    • The vertical distance between TEL and HGL equals the velocity head ().
  3. Rises at Pumps:
    • The TEL rises suddenly where energy is added to the fluid by a pump.
  4. Falls at Turbines:
    • The TEL drops sharply where energy is removed from the fluid by a turbine.
  5. Parallel to HGL:
    • For constant velocity flow, TEL and HGL are parallel since the velocity head remains constant.
  6. Pressure Relation:
    • The relative position of the TEL above the pipe centerline indicates the pressure condition — if TEL is above the pipe, pressure is positive; if below, it may indicate negative pressure.

Importance of Total Energy Line

  1. Visualizes Energy Distribution:
    • TEL helps engineers understand how total energy changes along the length of a pipe or channel.
  2. Design and Analysis of Pipelines:
    • Used to determine head losses, energy gradients, and efficiency of fluid systems.
  3. Pump and Turbine Analysis:
    • Helps in selecting pump head or turbine settings to maintain required flow conditions.
  4. Detection of Flow Problems:
    • TEL helps identify zones of high head loss or abnormal energy drop.
  5. Flow Efficiency and Safety:
    • By comparing TEL and HGL, engineers can ensure sufficient pressure to prevent cavitation or pipe collapse.

Example Explanation

Consider a pipe connecting two reservoirs with a pump placed in between.

  • The water level in the first reservoir represents the total head at the inlet.
  • As the fluid flows through the pipe, friction causes a gradual loss in energy, represented by a downward-sloping TEL.
  • At the pump location, energy is added to the fluid, so the TEL rises sharply.
  • After passing through the pump, the TEL again slopes downward until it reaches the second reservoir.
  • If a turbine is placed downstream, the TEL drops suddenly at that point.

This example clearly shows how the TEL represents total energy changes due to different components in the flow system.

Practical Applications

  1. Water Supply Networks:
    • Used to ensure consistent pressure distribution in municipal pipelines.
  2. Hydraulic Power Systems:
    • Essential for designing energy-efficient hydraulic circuits.
  3. Industrial Flow Systems:
    • Applied in chemical, oil, and gas pipelines to analyze energy usage.
  4. Pump and Turbine Design:
    • Helps in calculating input or output energy in hydraulic machinery.
  5. Flow Troubleshooting:
    • TEL diagrams are used to identify leakage or excessive energy losses.
Conclusion

The Total Energy Line (TEL) represents the total energy head of a fluid, which includes pressure head, velocity head, and elevation head. It shows how the total energy decreases due to friction and other losses as the fluid flows through a pipeline. The TEL always lies above the Hydraulic Gradient Line by a distance equal to the velocity head and slopes downward in the flow direction. Understanding the TEL helps engineers analyze energy behavior in fluid systems, design efficient pipelines, and ensure stable hydraulic performance.