John R. Hamilton Enterprises, Inc.
Flow Calc Software

Channel Slope: The slope of the channel represented in (ft/ft) or (m/m). In uniform flow, the slope of the energy grade line is the same as the channel bed slope and is used within the Manning's Equation.

Critical Depth: The depth of flow within a river or channel which the specific energy is a minimum for a given flow rate. At Critical Depth, the velocity of flow is also equal to the wave celerity such that the Froude Number is equal to 1. Since the Froude Number is equal to 1 at Critical Depth, Flow Calc uses the following equation by interating depth until the equation is equal.

Critical Depth Equation - Also refer to Froude Number
	Q - Flow Rate (cfs), (cms) g - Gravitational Constant, 32.174 ft/s2 for English Units g - Gravitational Constant, 9.80665 m/s2 for SI Units A - Flow Area, (ft2),(m2) T - Top Width, (ft),(m)

Critical Slope: The river or channel slope at which normal depth is equal to critical depth.

Flow Area: The cross-sectional flow area.

Froude Number: Is defined as the ratio of the actual velocity to wave celerity. The Froude Number is only defined for sections with a free surface. When the Froude Number is less than 1, the flow is said to be subcritical (i.e. flow velocity is slower than the wave celerity). When the Froude Number is greater than 1, the flow is said to be supercritical (i.e. flow velocity is faster than the wave celerity). When the Froude Number is equal to 1, the flow is said to be critical (i.e. flow velocity is equal to the wave celerity) and this condition occurs at critical depth.

Froude Number Equation
	F - Froude Number (dimensionless) V - Velocity (ft/s), (m/s) g - Gravitational Constant, 32.174 ft/s2 for English Units g - Gravitational Constant, 9.80665 m/s2 for SI Units D - Hydraulic Depth being the ratio of Flow Area (A)/Top Width (T) (ft), (m) A - Flow Area, (ft2),(m2) T - Top Width, (ft),(m)

Full Flow Discharge at Channel Slope: The computed full flow discharge within a pipe where the Normal Depth is at the top of the pipe using the specified Channel Slope.

Full Flow Slope for Specified Discharge: The computed slope of the pipe that would be required to produce full flow discharge where the Normal Depth is at the top of the pipe using the specified flow rate.

Hydraulic Depth: Is defined as the ratio of the Flow Area / Top Width.

Hydraulic Radius: Is a measure of the flow efficiency of a river or channel. It is defined as the ratio of Flow Area(A) / Wetted Perimeter(P).

Manning's Equation: It is assumed in Flow Calc that the only source of energy loss is friction between the flow and the channel wall. In general, energy can also be lost because of such factors as wind shear on the surface and eddy motion arising from abrupt changes in the channel geometry. When wall friction is the only source of energy loss, the slope of the energy grade line is equal to the friction slope. The Manning's Equation, based upon Chézy's equation, is perhaps considered the most popular engineering method for open channel flow with a free surface, such as flow in a river or in a partially full pipe. The Manning's Equation is valid for fully turbulent flow, in which the Darcy-Weisbach friction factor (f) is independent of the Reynolds number (Re). Henderson (1966) gives the following criterion for fully turbulent flow:

Manning's Equation - Velocity
	V - Velocity (ft/s), (m/s) K - Constant, 1.00 for SI Units K - Constant, 1.486 for English Units n - Manning's Roughness Coefficient R - Hydraulic Radius (ft), (m) Sf - Slope of the energy grade line

Manning's Roughness Factor and/or Friction Composite: Flow Calc provides a comprehensive table of Manning Roughness Coefficients that can be used within the Manning's Equation as obtained from the Seventh Edition, Handbook of Hydraulics by Ernest F. Brater, Horace W. King, James E. Lindell, and C.Y. Wei. Within an irregular channel, it is common that the roughness coefficient will vary across a channel section, which Flow Calc provides several commonly accepted methods to compute an equivalent Manning's Roughness Coefficient that may be selected by the user as follows:

Horton (1933) and Einstein
It is assumed that each of the subdivisions of the flow area is assumed to have the average velocity of the total section.
	ne - equivalent Mannings Roughness Coefficient P - Wetted Perimeter of the complete section N - Number of subsections

Pavlovskii, Mühlhofer, Einstein, and Banks
It is assumed that the total force resisting the flow is equal to the sum of the forces resisting the flow developed in the subdivided areas.
	ne - equivalent Mannings Roughness Coefficient P - Wetted Perimeter of the complete section N - Number of subsections

Lotter Method
It is assumed that the total discharge of the flow is equal to the sum of the discharges of the subdivided areas.
	ne - equivalent Mannings Roughness Coefficient P - Wetted Perimeter of the complete section R - Hydraulic Radius N - Number of subsections

Cox (1973) to the Los Angeles U.S. Army Corps of Engineers District
	ne - equivalent Mannings Roughness Coefficient A - Flow area N - Number of subsections

Colebatch method also described by Cox (1973)
	ne - equivalent Mannings Roughness Coefficient A - Flow area N - Number of subsections

Maximum Discharge: The computed theoretical value of discharge within either a circular or elliptical pipe where the flow discharge is a maximum.

Normal Depth: Is the depth of flow in a channel when the slope of the energy grade line, water surface, and channel bottom are the same and the water depth remains constant. Normal Depth occurs when the gravitational force of the water is equal to the friction drag along the channel and there is no acceleration of flow.

Open Channel Flow: Is channel flow with a free surface, such as flow in a river or in a partially full pipe.

Percent Full: This is the ratio of Depth/Pipe Diameter for circular pipe or Depth/Rise for elliptical pipe.

Specific Energy: The energy of the fluid as derived by the general form of the Bernoulli energy equation. The specific energy for an open channel is defined as follows.

Specific Energy Equation
The component V2/2g in the following equation is known as the Velocity Head that is represented in (ft) or (m).
	E - Specific Energy (ft), (m) y - Flow depth (ft),(m) V - Velocity (ft/s), (m/s) g - Gravitational Constant, 32.174 ft/s2 for English Units g - Gravitational Constant, 9.80665 m/s2 for SI Units

Top Width: Is a measure of the exposed free surface across the cross sectional flow area.

Uniform Flow: Steady uniform flow is the condition of flow within a river or channel where the slope of the energy grade line, water surface, and channel slope are the same and water depth remains constant along a uniform prismatic channel. A uniform prismatic channel is a channel where the channel cross section, channel bed slope, and channel boundary roughness do not change along its length.

Velocity: The flow velocity within the river or channel as computed by the Manning's Equation.

Wave Celerity: A wave is a variation in flow, such as a change in flow rate or water surface elevation, and the wave celerity is the velocity with which this variation travels along the channel. Refer to Froude Number.

Wetted Perimeter: The perimeter of the cross sectional flow area that is "wet". The greater the wetted perimeter, the more friction there is between the water and the channel bed and banks.