Explanation:
In fluid mechanics, the total energy line and hydraulic gradient line are two important concepts used to understand the behavior of fluids in pipes and channels.

Total Energy Line:
The total energy line (TEL) represents the total energy of the fluid at any point along the pipeline or channel. It is the sum of three energy components:

- Potential energy (P.E): due to the elevation of the fluid above a reference plane.
- Kinetic energy (K.E): due to the velocity of the fluid.
- Pressure energy (P.E): due to the pressure of the fluid.

Mathematically, the total energy line is given by the equation:

TEL = P.E + K.E + P.E

Hydraulic Gradient Line:
The hydraulic gradient line (HGL) represents the sum of pressure head and elevation head at any point along the pipeline or channel. It is the line connecting the points of equal pressure head.

Mathematically, the hydraulic gradient line is given by the equation:

HGL = Elevation head + Pressure head

Relation between TEL and HGL:
The total energy line and hydraulic gradient line are related to each other by the Bernoulli's equation, which states that the total energy of the fluid remains constant along a streamline.

If we assume that the fluid is incompressible and there is no energy loss due to friction, then the Bernoulli's equation can be written as:

TEL = HGL + Velocity head

where Velocity head = (V^2/2g)

Thus, the total energy line lies over the hydraulic gradient line by an amount equal to the velocity head. This is because the velocity head represents the energy that is converted from pressure energy to kinetic energy as the fluid flows through the pipe or channel. Therefore, the difference between the TEL and HGL at any point represents the velocity head at that point.

Conclusion:
In conclusion, the correct option is (B) velocity head, which represents the energy component that causes the total energy line to lie over the hydraulic gradient line.

Total head is equal to pressure head+ velocity Head+ datum head