online_wsprofiles_33: A_{2} watersurface profile
DESCRIPTION
General
 The php script [program] online_wsprofiles_33
calculates an A_{2} watersurface profile in a prismatic open channel using the directstep method (Chow, V. T.: Openchannel hydraulics, McGrawHill, 1959).
 If requested by the user, the program calculates critical depth at the downstream boundary [default value]
based on the geometric and hydraulic input data. Newton's iteration is used to solve the nonlinear equations.
 An A_{2} profile is supernormal, subcritical, and the bottom slope is adverse (to the flow; i.e., negative) (see figure).
The calculated gradually varied flow depth varies between the specified flow depth
at the downstream boundary [or, if requested, the calculated critical depth] and the specified flow depth upstream [headwater depth].
Input
 There are five required input variables: discharge Q, bottom width B, side slope z, Manning's n, and bottom slope S_{o}.
The bottom slope must be negative (Example: S_{o} = 0.001).
 For the downstream boundary condition, you can specify a suitable input flow depth.
Alternatively, if the input flow depth box is left blank,
the program will use critical depth instead.
 For the upstream boundary condition, you must specify a suitable upstream flow depth [headwater depth].
 By convention, the flow direction is assumed to be from left to right, as shown in the figure. Therefore,
the input upstream flow depth must be greater than the input [or calculated critical] downstream flow depth.
 The program echoes the input data. Internally calculated critical depth is echoed with fivedecimal (5) accuracy.
Defaults
 For the input flow depth, you can enter
any suitable subcritical supernormal flow depth.
The allowable range of input flow depth is the following: Greater than [or equal to] critical depth, and less than [input] upstream flow depth.
Leave this box blank if you want the program to use critical depth.
 You can enter the desired number of computational intervals n. The suggested range is 50200. A higher number
means higher computational accuracy.
Leave this box blank if you want the program to set the default value at 100.
 You can enter the desired number of tabular output intervals m. The suggested range is 10100. A higher number
means more detailed [longer] output.
Leave this box blank if you want the program to set the default value at 10.
Output
 A table with thirteen (13) columns: output interval index k, [flow] depth (m),
[flow] area (m^{2}), velocity (m/s), velocity head (m), specific head (m), wetted perimeter (m), hydraulic radius (m),
friction slope (m/m), average [friction] slope (m/m), specific head difference (m), length increment (m), and total [channel] length (m).
 The number of computational intervals n and the number of tabular output intervals m are printed for reference.
 The computational depth interval Δy and the tabular output depth interval (Δy)_{t} are printed for reference.
Units
 The current version is written in SI [metric] units.
Errors
 Enter only positive [nonzero] numbers for discharge.
Failure to do this will trigger an error message and halt execution (Error message No. 1).
 Enter only nonnegative [zero or greater] numbers for bottom width and side slope.
Failure to do this will trigger an error message and halt execution (Error messages No. 2: A and B, respectively).
 Bottom width and side slope cannot be zero at the same time.
Failure to do this will trigger an error message and halt execution (Error message No. 3).
 A Manning's n value outside of the range 0.0080.250
will trigger an error message and halt execution (Error message No. 4).
 A nonnegative bottom slope will trigger an error message and halt execution (Error message No. 5).
 A bottom slope smaller than 0.1 (steeper than negative 0.1) will trigger an error message and halt execution (Error message No. 6).
 An input downstream flow depth less than the calculated critical depth
will trigger an error message and halt execution (Error message No. 7).
 An input downstream flow depth greater than or equal to the input upstream flow depth [minus a tolerance of 0.001 m]
will trigger an error message and halt execution (Error message No. 8).
 An input upstream flow depth less than or equal to the input (or calculated) downstream flow depth [plus a tolerance of 0.001 m]
will trigger an error message and halt execution (Error message No. 9).
Thank you for running online_wsprofiles_33. Please call again. [Version 1.0.0, 070510]
