online_wsprofiles_23:   M3 water-surface profile DESCRIPTION
General

• The php script [program]   online_wsprofiles_23   calculates an M3 water-surface profile in a prismatic open channel using the direct-step method (Chow, V. T.: Open-channel hydraulics, McGraw-Hill, 1959).

• The program calculates normal depths upstream and downstream based on the geometric and hydraulic input data. Newton's iteration is used to solve the nonlinear equations.

• An M3 profile is supernormal, supercritical, and mild (see figure). The calculated gradually varied flow depth varies between the specified flow depth at the upstream boundary [or, if requested, the calculated normal depth for the upstream channel] and the critical depth upstream of the hydraulic jump.

Input

• There are five required input variables:   discharge Q, bottom width B, side slope z, Manning's n, and bottom slope So,

• For the upstream boundary condition, you can specify a suitable input flow depth. Alternatively, if the input flow depth box is left blank, the program will use normal depth [in the steeper upstream channel] instead.

• The program echoes the input data. Internally calculated normal depth upstream is echoed with five-decimal (5) accuracy.

Defaults

• For the input flow depth, you can enter any suitable supercritical supernormal flow depth. The allowable range of input flow depth is the following: Greater than [or equal to] normal depth [upstream], and less than the calculated critical depth downstream. Leave this box blank if you want the program to use normal depth upstream.

• You can enter the desired number of computational intervals n. The suggested range is 50-200. 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 10-100. 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 fourteen (14) columns: output interval index k, [flow] depth (m), [flow] area (m2), 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), depth gradient (m/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 calculated normal depth and normal-depth Froude number are printed for reference. If the normal-depth Froude number is greater than 0.98, execution is halted (See Error message No. 8 below).

• The Froude number of the upstream flow is printed for reference.

• The critical depth and critical slope in the downstream channel are printed for reference.

Units

• The current version is written in SI [metric] units.

Errors

• Enter only positive [nonzero] numbers for discharge, Manning's n, and bottom slope (for suitable practical ranges, see error messages Nos. 4 and 5). Failure to do this will trigger an error message and halt execution (Error messages No. 1: A, B, and C, respectively).

• 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 0.008-0.250 will trigger an error message and halt execution (Error message No. 4).

• A bottom slope outside of the range 0.000001-0.005 will trigger an error message and halt execution (Error message No. 5; however, see error message No. 6).

• An upstream normal-depth Froude number less than 1.02 will trigger an error message and halt execution (Error message No. 6).

• A downstream normal-depth Froude number greater than 0.98 will trigger an error message and halt execution (Error message No. 7).

• Enter only nonnegative numbers [zero or greater] for discharge, bottom width, side slope, bottom slope, and Manning's n in the upstream channel. Failure to do this will trigger an error message and halt execution (Error messages No. 8: A, B, C, D, and E, respectively).

Caution: Do not specify an [actual] zero upstream bottom width Bu/s (a triangular cross section) when the downstream channel bottom width B is other than zero. Likewise, do not specify an [actual] zero upstream size slope zu/s (a rectangular cross section) when the downstream channel side slope z is other than zero. In either case, the upstream values will be redefined as equal to the specified nonzero downstream values.

• The upstream bottom slope should not exceed 1 (a 45o slope) (Error message No. 9).

• An input flow depth less than the calculated normal depth upstream, or greater than or equal to the calculated critical depth downstream will trigger an error message and halt execution (Error messages No. 10: A and B, respectively).

• An upstream bottom slope not steeper than the bottom slope in the [downstream] channel will trigger an error message and halt execution (Error message No. 11). For a well-posed M3 water-surface profile, the bottom slope in the downstream channel should be mild.

Thank you for running online_wsprofiles_23.   Please call again.   [Version 1.0.0,   070505]
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