The difference between the total head line and the hydraulic grade line represents the velocity head.


The total head line and the hydraulic grade line are two important concepts in fluid mechanics that help in understanding the behavior of fluids in pipes or channels. The difference between these two lines is known as the velocity head.

Total head line:
The total head line represents the total energy per unit weight of fluid at any point along the flow path. It is the sum of different types of energy including the elevation head, pressure head, and velocity head.

Hydraulic grade line:
The hydraulic grade line represents the sum of the pressure head and the elevation head. It indicates the energy available to the fluid in terms of pressure and height. The hydraulic grade line is also known as the energy line.

Velocity head:
The velocity head is a component of the total head line and represents the kinetic energy of the fluid due to its velocity. It is directly related to the velocity of the fluid and is given by the equation:

Velocity head = (velocity^2) / (2g)

Where:
- Velocity head is the energy per unit weight of fluid due to velocity (in meters)
- Velocity is the velocity of the fluid (in meters per second)
- g is the acceleration due to gravity (in meters per second squared)

Difference between the total head line and the hydraulic grade line:
The difference between the total head line and the hydraulic grade line represents the velocity head. This can be explained as follows:

- If the hydraulic grade line is above the total head line, it indicates that the pressure head and elevation head are greater than the sum of the velocity head. In this case, the velocity head is negative, which means the fluid is losing energy due to its velocity.

- If the hydraulic grade line is below the total head line, it indicates that the pressure head and elevation head are less than the sum of the velocity head. In this case, the velocity head is positive, which means the fluid is gaining energy due to its velocity.

- If the hydraulic grade line and the total head line are at the same level, it indicates that the pressure head and elevation head are exactly balanced by the velocity head, and there is no gain or loss of energy due to velocity.

Therefore, the difference between the total head line and the hydraulic grade line represents the velocity head and indicates whether the fluid is gaining or losing energy due to its velocity.