In open channel hydraulics, specific energy is defined as the energy per unit weight of fluid relative to the channel bottom. For a given discharge, the specific energy curve shows that the specific energy is at its minimum value when the flow is at the critical depth, which corresponds to a Froude number of one.

The Hydraulic Gradient Line (HGL) is defined as the line representing the sum of the pressure head and the elevation (datum) head. It indicates the total piezometric head at any point along a pipe or channel. It does not include the velocity head, which is instead represented by the Energy Grade Line (EGL).

Specific weight is defined as weight per unit volume. For water, the density is approximately 1000 kg/m3 at 4 degrees Celsius. While technically specific weight involves gravity, in common agricultural engineering contexts, the value of 1000 kg/m3 is used for water density calculations.

One-dimensional flow is a simplification in fluid mechanics where the flow parameters, such as velocity and pressure, are assumed to vary only along one coordinate direction. In this model, the streamlines are represented as straight lines, and the flow properties are considered uniform across any cross-section perpendicular to the direction of flow, which simplifies complex hydraulic calculations.

A Pitot-static tube is a flow measurement device used to determine the velocity of a fluid. It measures both the total pressure (stagnation pressure) and the static pressure of the fluid. By calculating the difference between these two values, the device allows for the determination of the dynamic pressure, which is directly related to the fluid velocity.

In open-channel flow, the critical depth is the depth at which the specific energy is at a minimum for a given discharge. When the actual depth of flow is greater than the critical depth, the flow is termed sub-critical. In this state, the Froude number is less than one, and the flow is typically characterized by lower velocities and higher depths.

The center of gravity is the point at which the entire weight of a body may be considered to act. If a body is supported at this point, it will remain in equilibrium regardless of its orientation in a uniform gravitational field.

The Reynolds number (Re) is defined as (rho * v * D) / mu. If the flow rate (Q) is constant, velocity v is inversely proportional to the area (D^2). Thus, v is proportional to 1/D^2. Substituting this into the Re formula, Re becomes proportional to (1/D^2) * D, which simplifies to 1/D. Therefore, halving the diameter doubles the Reynolds number.

The hydraulic mean depth, or hydraulic radius (R), is defined as the ratio of the cross-sectional area (A) to the wetted perimeter (P). For a circular pipe flowing full, the area is πd²/4 and the perimeter is πd. Dividing the area by the perimeter results in (πd²/4) / (πd), which simplifies to d/4. This value is essential for calculating flow resistance in pipes.

The discharge (Q) over a rectangular notch is derived from the integration of velocity over the area of the notch opening. The standard formula is Q = (2/3) * Cd * B * sqrt(2g) * H^(3/2), where Cd is the coefficient of discharge, B is the width of the notch, g is gravity, and H is the head of water above the notch sill.