Manning's equation calculator, made with AI

Make a Manning's equation calculator page for an engineering team that checks ditches, channels, and culverts in the field.

What it calculates:
- Q = (k / n) A R^(2/3) S^(1/2), with k = 1 in SI and 1.486 in US units; R = A / P.
- Trapezoid (a rectangle has z = 0): A = y (b + z y), P = b + 2y √(1 + z²), T = b + 2 z y.
- Circular pipe part full: θ = 2 arccos(1 − 2y / D), A = (θ − sin θ) D² / 8, P = θ D / 2, T = D sin(θ / 2). The flow is greatest at about 0.938 D; a flow above that has no normal depth, and the page says so.
- Normal depth from a flow by bisection to 1 part in 10^10, with an iteration cap, in place of Goal Seek.
- Froude number V / √(g A / T), with g = 9.81 m/s² or 32.2 ft/s², and critical depth from A³ / T = Q² / g.
- Inputs: the section (rectangle, trapezoid, circular pipe), the bottom width and side slope or the pipe's diameter (m or ft), Manning's n, the bed slope, and the flow depth or the flow (m³/s or cfs), with the choice of finding the flow or the depth

How it calculates:
- Write each formula as a plain JavaScript function, with every coefficient, constant, and lookup table written into the file. No eval, no new Function, and no library that parses formulas with them.
- Load nothing from another site and send nothing anywhere: no fetch, no XMLHttpRequest, no form posts. The page computes everything in the browser.
- An iteration or a Goal Seek becomes a loop with a stated tolerance and an iteration cap; when it doesn't settle, say so on the page.
- A lookup (VLOOKUP, XLOOKUP, INDEX/MATCH) becomes a table in the file with the same match rule (exact, or the next row down for an approximate match), interpolated where the sheet interpolates.
- Round only where the sheet rounds, as Excel does (ROUND takes halves away from zero).
- Copy every name, tag, ID, and number the request gives exactly, character for character: P-101 stays P-101.
- Convert units in one place, a table of factors, and check each shown value against its unit label: watts shown as kilowatts are off by 1,000.

What it shows:
- Every input with its label and its unit, prefilled with the example's values, in text fields that open the number keyboard (inputmode="decimal"). Offer a unit switch (SI and US) where the calculation has units.
- The result first: a compact summary of the main result, large, with its unit, right under the title and any unit or method switch and above the inputs, so it shows on a phone's first screen and changes as an input does. It is the page's one aria-live="polite" region. The values in between go below the inputs, each with its name and unit, so someone can check the result against the sheet.
- The results update as soon as an input changes. An input that can't be calculated (empty, zero where it divides, outside the formula's range) gets a short message instead of a wrong number.
- Show 0 for a zero result, never -0, and the same number of decimals for every amount of money.
- A short "How it calculates" section that lists the formulas and their ranges (folded in details and summary, it keeps an arrow that turns when it opens: a summary set to display:flex loses the browser's own), and a last line with the version ("v1", and a date only when the request gives one) and "check its results against your own standard before you rely on them".

Layout: phone first, held upright (390px): labels above fields, two fields to a row, no sideways scrolling, body text 16px, every field and button at least 44px tall (min-height: 44px on each input, select, and button itself, with box-sizing: border-box). On a wide screen, three fields to a row. No images, web fonts, or CSS frameworks: one plain style block.

Write it as one HTML file with the CSS and JavaScript inside. Don't send anything people type anywhere, and don't use image files. Make it work on a phone held upright. Keep the bottom right of the screen clear: a Support button may show there.

That is the example. Keep how it works, its screens, and its feel, and change the content to fit what I want.
What I want: ___