The hydraulic radius is a measure of the flow resistance in a channel and is calculated by dividing the area of the cross-section by the wetted perimeter.

The Manning's equation is an empirical formula used to calculate the flow rate in an open channel, where Q is the flow rate, n is the Manning's roughness coefficient, A is the cross-sectional area, R is the hydraulic radius, and S is the slope of the channel.

The Froude number is a measure of the flow regime in an open channel, where V is the flow velocity, g is the acceleration due to gravity, and D is the characteristic length, which is typically the hydraulic depth.

The critical depth is a crucial parameter in open channel flow, and it occurs when the Froude number is equal to 1, indicating the transition between subcritical and supercritical flow regimes.

Specific energy is a fundamental concept in open channel flow and is calculated as the sum of the potential energy and kinetic energy per unit weight of fluid.

The Chezy equation is an empirical formula used to calculate the flow velocity in an open channel, where V is the flow velocity, C is the Chezy coefficient, R is the hydraulic radius, and S is the slope of the channel.

The hydraulic radius is a measure of the flow resistance in a channel and is calculated by dividing the area of the cross-section by the wetted perimeter, regardless of the channel shape.

The Darcy-Weisbach equation is a fundamental formula used to calculate the head loss due to friction in a pipe, where h_f is the head loss, f is the Darcy friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the flow velocity, and g is the acceleration due to gravity.

The Reynolds number is a crucial parameter in fluid mechanics and is calculated as the ratio of inertial forces to viscous forces, where V is the flow velocity, D is the characteristic length, nu is the kinematic viscosity, and h is the characteristic height.

In a circular pipe, the hydraulic radius is calculated as the diameter of the pipe divided by 4, which is a special case of the general formula for hydraulic radius.

The continuity equation is a fundamental principle in fluid mechanics and states that the flow rate remains constant along a streamline, i.e., the mass flow rate entering a section of a channel must equal the mass flow rate leaving that section.

The energy equation is a fundamental principle in fluid mechanics and states that the total energy of a fluid remains constant along a streamline, taking into account elevation, pressure, velocity, and head loss due to friction.

The momentum equation is a fundamental principle in fluid mechanics and states that the sum of forces acting on a fluid element is equal to the rate of change of momentum of the fluid element, taking into account pressure, elevation, velocity, and external forces.

Gradually varied flow (GVF) occurs when the flow depth and velocity change gradually along a channel, typically over a long distance, resulting in a smooth transition between different flow regimes.

Rapidly varied flow (RVF) occurs when the flow depth and velocity change rapidly and abruptly over a short distance, typically at hydraulic structures such as weirs, gates, and sudden expansions or contractions.