The difference between the total head and the hydraulic grade line represents the velocity head. Let's understand each term separately to see why.

1. Total Head:
The total head in a fluid system is the sum of different energy components. It represents the energy per unit weight of fluid at a specific point. The total head consists of four main components:

a) Elevation Head: This is the potential energy due to the elevation of the fluid above a reference point. It is calculated as the product of the fluid weight, acceleration due to gravity, and the vertical distance from the reference point.

b) Pressure Head: This is the energy due to the pressure exerted by the fluid. It is calculated as the ratio of pressure to the fluid weight.

c) Velocity Head: This is the energy due to the motion of the fluid. It is calculated as the ratio of the square of the fluid velocity to twice the acceleration due to gravity.

d) Piezometric Head: This is the sum of the elevation head and the pressure head.

2. Hydraulic Grade Line (HGL):
The hydraulic grade line represents the total head of the fluid flowing in a pipe or open channel. It is a graphical representation of the energy line along the flow path. The HGL takes into account both the elevation head and the pressure head components.

Explanation:
When we subtract the hydraulic grade line from the total head, we are essentially removing the elevation head and the pressure head components. This leaves us with the remaining energy component, which is the velocity head.

The velocity head represents the energy associated with the fluid motion. It is an important parameter in fluid mechanics, especially in the analysis of flow behavior and energy transformations in pipes, channels, and other flow systems. By understanding the velocity head, engineers can determine the flow characteristics, such as the velocity and discharge, and make informed design decisions for fluid systems.

In conclusion, the difference between the total head and the hydraulic grade line represents the velocity head. This represents the energy due to the motion of the fluid and is an important component in fluid mechanics analysis.