The hydraulic gradient line joins points of the piezometric head (Pressure head + Datum head) in a pipe flow while total energy line joins points of total energy (Piezometric head + Velocity head) at various points of the flow.

The line joining the points of piezometric head and velocity head at various points in a pipe flow is called the Total Energy line.

The Total Energy line represents the total energy per unit weight of fluid at different points along the pipe flow. It is an important concept in fluid mechanics and is used to analyze and understand the behavior of fluid flow in pipes.

Components of Total Energy:
1. Piezometric Head: The piezometric head represents the potential energy of the fluid due to its elevation above a reference point. It is the height to which the fluid would rise in a piezometer connected to the pipe. The piezometric head remains constant along a horizontal pipe but changes with elevation in a vertical pipe.

2. Velocity Head: The velocity head represents the kinetic energy of the fluid due to its motion. It is the height to which the fluid would rise if it was brought to rest. The velocity head increases as the fluid velocity increases and decreases as the fluid velocity decreases.

The Total Energy line:
The Total Energy line is a graphical representation of the sum of the piezometric head and the velocity head at different points in the pipe flow. It is drawn by adding the piezometric head and the velocity head at each point along the pipe.

- The piezometric head is represented by a line above the pipe flow, indicating the elevation of the fluid.
- The velocity head is represented by a line below the pipe flow, indicating the kinetic energy of the fluid.

Interpretation of the Total Energy line:
The Total Energy line provides valuable information about the behavior of fluid flow in a pipe. It helps in understanding the distribution of energy along the pipe and identifying any changes in energy levels.

- If the Total Energy line is horizontal, it indicates a constant energy level along the pipe, meaning the pipe flow is steady and uniform.
- If the Total Energy line slopes upward in the direction of flow, it indicates a decrease in energy due to friction losses. This is typically observed in pipes with rough surfaces or high flow velocities.
- If the Total Energy line slopes downward in the direction of flow, it indicates an increase in energy due to a decrease in friction losses or an increase in elevation. This is typically observed in pipes with smooth surfaces or low flow velocities.

In conclusion, the Total Energy line represents the sum of the piezometric head and the velocity head at different points in a pipe flow. It helps in understanding the distribution of energy along the pipe and analyzing the behavior of fluid flow.