Conception de ressaut hydraulique

import math
from dataclasses import dataclass

import matplotlib.patheffects as pe
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import brentq

# Physical constants used throughout.
G = 9.81  # gravitational acceleration [m/s2]

# The lecture palette, so that figures and slides read as one piece.
NAVY, BLUE, CYAN, GREEN, WARN, GREY = (
    "#0C0C48", "#00467F", "#00CAEF", "#167D61", "#C74B2A", "#4A4A4C",
)

plt.rcParams.update({
    "figure.figsize": (8.4, 4.2),
    "figure.dpi": 110,
    "axes.spines.top": False,
    "axes.spines.right": False,
    "axes.titleweight": "bold",
    "axes.labelcolor": NAVY,
    "axes.edgecolor": NAVY,
    "text.color": NAVY,
    "xtick.color": NAVY,
    "ytick.color": NAVY,
    "font.size": 9,
})

# --- the design discharge ----------------------------------------------------
Q_design = 3200.0  # m3/s   Clyde Dam spillway design flow at lake level 195.1 m
                   #        (published; the 500-year, 0.2% AEP flood)

# --- the chute toe and the stilling basin below it ---------------------------
w_chute = 40.0     # m      four 10 m gate bays, idealised as one rectangle
H0 = 50.00         # m      energy head above the un-sunk basin invert (assumed)

# --- the Clutha River below the dam (assumed) --------------------------------
n_manning = 0.045   # s/m^(1/3)  Manning roughness of the downstream reach
slope = 6.0e-4      # -          bed slope of the downstream reach
w_tw = 60.0         # m          width of the downstream reach (rectangular idealisation)
h_tw = 19.060       # m          tailwater depth of that reach in uniform flow

print(f"spillway design flow Q  = {Q_design:7.1f} m3/s")
print(f"chute and basin width w = {w_chute:7.2f} m")
print(f"head at the invert   H0 = {H0:7.2f} m")

q_unit = Q_design / w_chute
h_crit = (q_unit**2 / G)**(1 / 3)

print(f"unit discharge   q = Q / w   = {q_unit:7.3f} m2/s")
print(f"critical depth   h_c         = {h_crit:7.3f} m")
print(f"critical velocity            = {q_unit / h_crit:7.3f} m/s")

h_crit_tw = ((Q_design / w_tw)**2 / G)**(1 / 3)

print(f"tailwater depth h_tw = {h_tw:.3f} m   (given, from the reach above)")
print(f"critical depth of the reach = {h_crit_tw:.3f} m"
      f"   -> {'subcritical' if h_tw > h_crit_tw else 'SUPERCRITICAL'}")

@dataclass(frozen=True)
class DesignData:
    Q: float       # spillway design flow [m3/s]
    q: float       # discharge per unit width [m2/s]
    H0: float      # energy head above the un-sunk basin invert [m]
    h_tw: float    # tailwater depth [m]
    w: float       # width the basin has to cover [m]


DESIGN = DesignData(
    Q=Q_design,
    q=q_unit,
    H0=H0,
    h_tw=h_tw,
    w=w_chute,
)

print(f"Q      = {DESIGN.Q:8.1f} m3/s   spillway design flow")
print(f"q      = {DESIGN.q:8.3f} m2/s   unit discharge")
print(f"H0     = {DESIGN.H0:8.2f} m      energy head above the un-sunk invert")
print(f"h_tw   = {DESIGN.h_tw:8.3f} m      tailwater depth")
print(f"w      = {DESIGN.w:8.2f} m      width the basin has to cover")

def energy_head(h, q, g=G):
    '''
    Given: specific energy head of a rectangular section [m].

    Parameters
    ----------
    h : water depth [m]
    q : discharge per unit width [m2/s]

    Returns
    -------
    the energy head h + q^2 / (2 g h^2) [m]
    '''
    return h + q**2 / (2 * g * h**2)

def froude_number(v, h, g=G):
    '''
    Task 1: Froude number of a rectangular section [-].

    Parameters
    ----------
    v : depth-averaged velocity [m/s]
    h : water depth [m]
    '''
    # >>> YOUR CODE HERE
    raise NotImplementedError("Task 1: return the Froude number")

def conjugate_depth(h1, Fr1):
    '''
    Task 2: conjugate (sequent) depth downstream of the jump [m].

    Parameters
    ----------
    h1  : supercritical depth upstream of the jump [m]
    Fr1 : Froude number at section 1 [-]
    '''
    # >>> YOUR CODE HERE
    raise NotImplementedError("Task 2: return the conjugate depth h2")

def retention_ratio(h_tw, d_b, h2):
    '''
    Task 3: retention ratio of the basin [-].

    Parameters
    ----------
    h_tw : tailwater depth in the downstream reach [m]
    d_b  : depth of the basin floor below the downstream bed [m]
    h2   : conjugate depth required by the jump [m]
    '''
    # >>> YOUR CODE HERE
    raise NotImplementedError("Task 3: return the retention ratio")

def peterka_f(Fr1):
    '''Given: basin-length multiplier after Peterka (USBR EM 25), interpolated [-].'''
    knots_Fr = [2.4, 4.0, 5.0, 6.0, 11.0, 14.0]
    knots_f = [4.8, 5.8, 6.0, 6.13, 6.13, 6.0]
    return float(np.interp(Fr1, knots_Fr, knots_f))


print(f"f_l at Fr1 = 5.0 : {peterka_f(5.0):.3f}")
print(f"f_l at Fr1 = 8.0 : {peterka_f(8.0):.3f}")

def basin_lengths(h2, Fr1):
    '''
    Given: basin length and scour-protection length [m].

    Parameters
    ----------
    h2  : conjugate depth downstream of the jump [m]
    Fr1 : Froude number at section 1, which selects the multiplier [-]

    Returns
    -------
    (l_b, l_s) : basin length and scour-protection length [m]
    '''
    l_b = peterka_f(Fr1) * h2
    return l_b, 3.5 * l_b

CHECKS = [
    ("Task 1  froude_number(31.623, 2.5298)",
     lambda: froude_number(31.623, 2.5298), (6.348,), "-"),
    ("Task 2  conjugate_depth(2.5298, 6.348)",
     lambda: conjugate_depth(2.5298, 6.348), (21.481,), "m"),
    ("Task 3  retention_ratio(19.060, 3.5, 21.481)",
     lambda: retention_ratio(19.060, 3.5, 21.481), (1.050,), "-"),
]


def check_tasks(tolerance=5e-3, verbose=True):
    '''Compare each task against the worked values from the lecture.'''
    passed = 0
    for label, call, expected, unit in CHECKS:
        try:
            value = call()
        except NotImplementedError:
            if verbose:
                print(f"[ ] {label:<46} not implemented yet")
            continue
        got = value if isinstance(value, tuple) else (value,)
        ok = (len(got) == len(expected) and
              all(abs(g - e) <= tolerance * max(1.0, abs(e))
                  for g, e in zip(got, expected)))
        passed += ok
        if verbose:
            mark = "OK" if ok else "XX"
            shown = ", ".join(f"{g:.3f}" for g in got)
            wanted = ", ".join(f"{e:.3f}" for e in expected)
            print(f"[{mark}] {label:<46} {shown:>19} {unit:<3}"
                  f" (expected {wanted})")
    if verbose:
        print("-" * 78)
        print(f"{passed} of {len(CHECKS)} tasks correct.")
    return passed == len(CHECKS)


TASKS_DONE = check_tasks()

FR_WINDOW = (4.5, 9.0)     # steady-jump range
RT_WINDOW = (1.05, 1.15)   # retention window


@dataclass(frozen=True)
class BasinState:
    d_b: float     # trial basin depth [m]
    H: float       # energy head above the basin floor [m]
    h1: float      # supercritical entry depth [m]
    v1: float      # entry velocity [m/s]
    Fr1: float     # entry Froude number [-]
    h2: float      # conjugate depth [m]
    Rt: float      # retention ratio [-]

    @property
    def fr_ok(self):
        return FR_WINDOW[0] <= self.Fr1 < FR_WINDOW[1]

    @property
    def rt_ok(self):
        return RT_WINDOW[0] <= self.Rt <= RT_WINDOW[1]


def critical_depth(q, g=G):
    '''Critical depth of a rectangular section [m]; the bracket for the entry depth.'''
    return (q**2 / g)**(1 / 3)


def entry_depth(H, q):
    '''
    The shallow, supercritical root of energy_head(h, q) = H [m].

    Both roots satisfy the energy equation. The supercritical one lies below the
    critical depth, and it is the branch the spillway delivers, so the bracket is
    closed at the critical depth.
    '''
    return brentq(lambda h: energy_head(h, q) - H, 1e-4, critical_depth(q))


def basin_state(d_b, design=None):
    '''The workflow evaluated for one trial basin depth d_b.'''
    design = design or DESIGN
    H = design.H0 + d_b                          # head above the basin floor
    h1 = entry_depth(H, design.q)                # supercritical root
    v1 = design.q / h1                           # continuity
    Fr1 = froude_number(v1, h1)                  # Task 1
    h2 = conjugate_depth(h1, Fr1)                # Task 2
    Rt = retention_ratio(design.h_tw, d_b, h2)   # Task 3
    return BasinState(d_b=d_b, H=H, h1=h1, v1=v1, Fr1=Fr1, h2=h2, Rt=Rt)

def search_basin_depth(db_start=1.0, db_min=0.0, db_max=20.0, max_iter=25,
                       tol=0.005, grid=0.25, verbose=True):
    '''
    Bisection on the basin depth d_b for the SHALLOWEST depth at which both
    engineering objectives are met, rounded up to the next `grid` metres.

    Returns the accepted BasinState and the full iteration history.
    '''
    d_b = db_start
    history = []
    if verbose:
        print(f"{'iter':>4}{'d_b [m]':>9}{'Fr1':>8}{'h1 [m]':>9}{'h2 [m]':>9}"
              f"{'Rt':>8}   verdict")
        print("-" * 66)

    for i in range(1, max_iter + 1):
        state = basin_state(d_b)
        history.append(state)
        if verbose:
            flags = []
            if not state.fr_ok:
                flags.append("Fr1 low" if state.Fr1 < FR_WINDOW[0] else "Fr1 high")
            if not state.rt_ok:
                flags.append("swept out" if state.Rt < RT_WINDOW[0] else "drowned")
            print(f"{i:>4}{state.d_b:>9.3f}{state.Fr1:>8.2f}{state.h1:>9.4f}"
                  f"{state.h2:>9.4f}{state.Rt:>8.3f}   "
                  f"{'accepted' if not flags else ', '.join(flags)}")

        # A deeper basin raises H, so the entry flow is shallower and faster: Fr1 and Rt increase monotonically with d_b. One bracket therefore serves both criteria, and each verdict says which way to move: a jump that is too gentle or swept out wants a deeper basin, one that is too fierce or drowned wants a shallower one. An acceptable trial is not the end of the search either, because a deeper basin than necessary costs excavation for no benefit, so it too narrows the bracket from above.
        if not state.fr_ok:
            if state.Fr1 < FR_WINDOW[0]:
                db_min = d_b  # jump too gentle: deepen the basin
            else:
                db_max = d_b  # jump too fierce: raise the floor
        elif state.Rt < RT_WINDOW[0]:
            db_min = d_b      # swept out: deeper basin
        else:
            db_max = d_b      # accepted or drowned: try a shallower one

        if db_max - db_min < tol:
            break
        d_b = 0.5 * (db_min + db_max)
    else:
        raise RuntimeError("no acceptable basin depth found in the search range")

    # db_max is the shallowest depth known to work; round it up to a buildable one.
    d_b = math.ceil(db_max / grid) * grid
    state = basin_state(d_b)
    history.append(state)
    if not (state.fr_ok and state.rt_ok):
        raise RuntimeError(f"rounding up to {d_b:.2f} m no longer meets the engineering objectives")
    if verbose:
        print(f"{'->':>4}{state.d_b:>9.3f}{state.Fr1:>8.2f}{state.h1:>9.4f}"
              f"{state.h2:>9.4f}{state.Rt:>8.3f}   shallowest, rounded up")
    return state, history


if TASKS_DONE:
    DESIGN_STATE, HISTORY = search_basin_depth()
    print(f"\naccepted basin depth d_b = {DESIGN_STATE.d_b:.3f} m")
else:
    DESIGN_STATE, HISTORY = None, []
    print("Complete Tasks 1 to 3, then re-run this cell.")

def head_loss(h1, h2):
    '''Given: head loss across the jump [m].'''
    return (h2 - h1)**3 / (4 * h1 * h2)


if TASKS_DONE:
    delta_H = head_loss(DESIGN_STATE.h1, DESIGN_STATE.h2)
    H1 = energy_head(DESIGN_STATE.h1, DESIGN.q)

    print(f"head loss           dH        = {delta_H:8.3f} m")
    print(f"energy head at 1    H1        = {H1:8.3f} m")
    print(f"relative loss       dH / H1   = {delta_H / H1:8.1%}")
else:
    delta_H = H1 = None
    print("Complete Tasks 1 to 3, then re-run this cell.")

if TASKS_DONE:
    f_peterka = peterka_f(DESIGN_STATE.Fr1)
    l_b, l_s = basin_lengths(DESIGN_STATE.h2, DESIGN_STATE.Fr1)

    print(f"Peterka multiplier  f_l  = {f_peterka:7.2f}  (at Fr1 = {DESIGN_STATE.Fr1:.2f})")
    print(f"basin length        l_b  = {l_b:7.2f} m   <- given")
    print(f"rule of thumb     6 h_2  = {6 * DESIGN_STATE.h2:7.2f} m"
          f"   ({abs(6 * DESIGN_STATE.h2 / l_b - 1):.1%} from l_b)")
    print(f"scour protection    l_s  = {l_s:7.2f} m   <- given")
else:
    f_peterka = l_b = l_s = None
    print("Complete Tasks 1 to 3, then re-run this cell.")

if TASKS_DONE:
    db_range = np.linspace(0.2, 20.0, 240)
    states = [basin_state(float(x)) for x in db_range]
    Fr_curve = np.array([s.Fr1 for s in states])
    Rt_curve = np.array([s.Rt for s in states])

    fig, axes = plt.subplots(1, 2, figsize=(9.4, 3.6), sharex=True)

    axes[0].axhspan(*FR_WINDOW, color=CYAN, alpha=0.18, lw=0)
    axes[0].plot(db_range, Fr_curve, color=BLUE, lw=2.2)
    axes[0].set_ylabel("$Fr_1$ at the basin entrance [-]")
    axes[0].set_title("Steady-jump window")
    axes[0].set_ylim(4.3, 9.3)
    axes[0].annotate("steady jump\n$4.5 \\leq Fr_1 < 9$", (0.8, 8.4),
                     color=BLUE, fontsize=8.5)

    axes[1].axhspan(Rt_curve.min(), RT_WINDOW[0], color=WARN, alpha=0.10, lw=0)
    axes[1].axhspan(*RT_WINDOW, color=CYAN, alpha=0.18, lw=0)
    axes[1].axhspan(RT_WINDOW[1], Rt_curve.max(), color=GREY, alpha=0.10, lw=0)
    axes[1].axhline(1.0, color=GREY, lw=0.8, ls=":")
    axes[1].plot(db_range, Rt_curve, color=BLUE, lw=2.2)
    axes[1].set_ylabel("retention ratio $r_\\mathrm{t}$ [-]")
    axes[1].set_title("Retention window")
    axes[1].set_ylim(Rt_curve.min(), Rt_curve.max())
    axes[1].annotate("jump swept out", (4.2, 0.83), color=WARN, fontsize=8.5)
    axes[1].annotate("retained", (0.8, 1.09), color=BLUE, fontsize=8.5)
    axes[1].annotate("jump drowned", (0.8, 1.42), color=GREY, fontsize=8.5)

    for ax in axes:
        ax.axvline(DESIGN_STATE.d_b, color=WARN, lw=1.4, ls="--")
        # the design variable is the one symbol set apart from the notation:
        # bold and in the warn colour, on the slides and here alike
        ax.set_xlabel("basin depth $\\mathbf{d_b}$ [m]", color=WARN)
        ax.set_xlim(0.2, 20.0)

    axes[0].plot([DESIGN_STATE.d_b], [DESIGN_STATE.Fr1], "o", color=WARN, ms=6, zorder=3)
    axes[1].plot([DESIGN_STATE.d_b], [DESIGN_STATE.Rt], "o", color=WARN, ms=6, zorder=3)
    axes[0].annotate(f"design\n$\\mathbf{{d_b}} = {DESIGN_STATE.d_b:.2f}$ m,"
                     f"  $Fr_1 = {DESIGN_STATE.Fr1:.2f}$",
                     (DESIGN_STATE.d_b, DESIGN_STATE.Fr1), textcoords="offset points",
                     xytext=(-104, 34), color=WARN, fontsize=8.5,
                     arrowprops=dict(arrowstyle="-", color=WARN, lw=0.8))
    axes[1].annotate(f"$r_\\mathrm{{t}} = {DESIGN_STATE.Rt:.3f}$",
                     (DESIGN_STATE.d_b, DESIGN_STATE.Rt), textcoords="offset points",
                     xytext=(40, -58), color=WARN, fontsize=8.5,
                     arrowprops=dict(arrowstyle="-", color=WARN, lw=0.8))

    fig.tight_layout()
    plt.show()
else:
    print("Complete Tasks 1 to 3, then re-run this cell.")

if TASKS_DONE:
    s = DESIGN_STATE
    floor = -s.d_b                       # basin floor, below the downstream riverbed
    h_avail = DESIGN.h_tw + s.d_b        # depth available over the floor
    h_need = floor + s.h2                # level the jump demands, above the datum
    top = DESIGN.H0                      # energy head above the un-sunk invert
    u = l_b / 24.8                       # one drawing unit, so the layout scales

    x_face, x_toe, x_end = -7.0 * u, 0.0, l_b
    x_tail = x_end + 0.6 * l_b
    x_j0, x_j1 = 0.26 * l_b, 0.62 * l_b

    # every label gets a white glow, so that one crossing a line stays readable
    glow = [pe.withStroke(linewidth=2.6, foreground="white")]

    fig, ax = plt.subplots(figsize=(9.4, 3.4))

    # --- structure and bed ---------------------------------------------------
    # the chute face descends from the spillway crest to the basin floor,
    # then the floor runs to the end sill and the river bed continues downstream
    ax.plot([x_face - 2.0 * u, x_face, x_face + 3.2 * u, x_toe, x_end, x_end, x_tail],
            [top, top, top, floor, floor, 0.0, 0.0],
            color=NAVY, lw=2.4, solid_joinstyle="round")

    # --- water body ----------------------------------------------------------
    xs = np.linspace(x_toe, x_tail, 500)
    bed = np.where(xs <= x_end, floor, 0.0)
    ramp = np.clip((xs - x_j0) / (x_j1 - x_j0), 0.0, 1.0)
    surface = (floor + s.h1) + (DESIGN.h_tw - floor - s.h1) * (
        0.5 - 0.5 * np.cos(math.pi * ramp))
    # a small crest at the end of the jump, so that the roller reads as a roller
    # rather than as a smooth asymptote; it is schematic, like the ramp itself
    surface = surface + 0.04 * (DESIGN.h_tw - floor - s.h1) * np.exp(
        -((xs - x_j1) / (0.09 * l_b))**2)

    ax.fill_between(xs, surface, bed, color=CYAN, alpha=0.30, lw=0)
    ax.plot(xs, surface, color=BLUE, lw=2.0)

    # --- dimensions ----------------------------------------------------------
    def dim(x, y0, y1, label, colour=NAVY, dx=0.7 * u, ha="left", frac=0.5,
            outside=False, ext=0.4 * u):
        '''
        A dimension between two levels, with a tick at each end so that what it
        measures from and to is unambiguous. outside=True puts the two heads
        beyond the span, pointing in, for a span too short to hold them.
        '''
        for y in (y0, y1):
            ax.plot([x - 0.5 * u, x + 0.5 * u], [y, y], color=colour, lw=0.8)
        if outside:
            ax.annotate("", (x, y0), (x, y0 - ext),
                        arrowprops=dict(arrowstyle="->", color=colour, lw=1.1))
            ax.annotate("", (x, y1), (x, y1 + ext),
                        arrowprops=dict(arrowstyle="->", color=colour, lw=1.1))
        else:
            ax.annotate("", (x, y0), (x, y1),
                        arrowprops=dict(arrowstyle="<->", color=colour, lw=1.1))
        if label:
            ax.text(x + dx, y0 + frac * (y1 - y0), label, color=colour,
                    fontsize=8.2, va="center", ha=ha, path_effects=glow)

    # the level the jump demands, carried downstream so that it can be compared
    # with the water surface; it starts right of the jump arrow, never under it
    ax.plot([0.48 * x_end, x_end + 6.0 * u], [h_need] * 2,
            color=WARN, lw=1.0, ls="--")
    dim(0.50 * x_end, floor, h_need,
        f"required\n$h_2 \\approx {s.h2:.1f}$ m", colour=WARN, dx=-0.7 * u,
        ha="right", frac=0.86)
    dim(0.86 * x_end, floor, DESIGN.h_tw,
        f"available\n$h_{{tw}}+\\mathbf{{d_b}} \\approx {h_avail:.1f}$ m",
        dx=-0.7 * u, ha="right")

    # the surplus is 1.1 m on a 22 m bar, so it is named rather than left to the eye
    x_gap = x_end + 4.6 * u
    dim(x_gap, h_need, DESIGN.h_tw, "", colour=WARN, outside=True)
    ax.annotate(f"surplus $\\approx {h_avail - s.h2:.1f}$ m\n"
                f"(water above the level $h_2$ demands)",
                (x_gap, DESIGN.h_tw + 0.6 * u), textcoords="offset points",
                xytext=(0, 32), color=WARN, fontsize=8.2, ha="center",
                arrowprops=dict(arrowstyle="->", color=WARN, lw=0.9),
                path_effects=glow)

    ax.annotate(f"$h_1 \\approx {s.h1:.1f}$ m",
                (x_toe + 3.2 * u, floor + 0.5 * s.h1), textcoords="offset points",
                xytext=(2, 54), color=NAVY, fontsize=8.2,
                arrowprops=dict(arrowstyle="->", color=NAVY, lw=0.9),
                path_effects=glow)
    dim(x_end + 2.4 * u, floor, 0.0,
        f"$\\mathbf{{d_b}} \\approx {s.d_b:.1f}$ m", colour=WARN, outside=True,
        ext=0.8 * u, dx=1.2 * u)
    dim(x_end + 9.0 * u, 0.0, DESIGN.h_tw,
        f"$h_{{tw}} \\approx {DESIGN.h_tw:.1f}$ m")

    ax.annotate("", (x_toe, floor - 0.365 * s.h2), (x_end, floor - 0.365 * s.h2),
                arrowprops=dict(arrowstyle="<->", color=NAVY, lw=1.1))
    ax.text(0.5 * x_end, floor - 0.62 * s.h2,
            f"basin length $l_b \\approx {l_b:.1f}$ m",
            color=NAVY, fontsize=8.2, ha="center", path_effects=glow)

    # --- labels --------------------------------------------------------------
    ax.axhline(0.0, color=GREY, lw=0.7, ls=":")
    # the arrow points at the crest of the roller, and stays above the dashed
    # level line so that it can cross neither that line nor the "required" label
    x_jump = x_j1
    y_jump = float(np.interp(x_jump, xs, surface))
    ax.text(x_jump, y_jump + 1.75 * u, "hydraulic jump", color=NAVY, fontsize=9,
            ha="center", style="italic", path_effects=glow)
    ax.annotate("", (x_jump, y_jump + 0.25 * u), (x_jump, y_jump + 1.45 * u),
                arrowprops=dict(arrowstyle="->", color=NAVY, lw=0.9))
    ax.text(x_face - 1.6 * u, top + 0.12 * s.h2,
            f"from the spillway chute,  $H_0 \\approx {top:.1f}$ m",
            color=NAVY, fontsize=8.2, path_effects=glow)

    ax.set_xlim(x_face - 2.5 * u, x_tail + 1.0 * u)
    ax.set_ylim(floor - 0.75 * s.h2, top + 0.55 * s.h2)
    ax.set_aspect("equal")
    ax.set_xlabel("distance along the basin [m]")
    ax.set_ylabel("level above the\ndownstream bed [m]")
    ax.spines["left"].set_visible(True)
    fig.tight_layout()
    plt.show()
else:
    print("Complete Tasks 1 to 3, then re-run this cell.")

if TASKS_DONE:
    s = DESIGN_STATE
    rows = [
        ("given", "spillway design flow", "Q", DESIGN.Q, "m3/s"),
        ("given", "unit discharge", "q", DESIGN.q, "m2/s"),
        ("given", "energy head above the invert", "H0", DESIGN.H0, "m"),
        ("given", "tailwater depth", "h_tw", DESIGN.h_tw, "m"),
        ("design", "basin depth", "d_b", s.d_b, "m"),
        ("design", "energy head above the floor", "H", s.H, "m"),
        ("design", "entry depth", "h1", s.h1, "m"),
        ("design", "entry velocity", "v1", s.v1, "m/s"),
        ("design", "entry Froude number", "Fr1", s.Fr1, "-"),
        ("design", "conjugate depth", "h2", s.h2, "m"),
        ("design", "retention ratio", "Rt", s.Rt, "-"),
        ("result", "head loss", "dH", delta_H, "m"),
        ("result", "relative head loss", "dH/H1", 100 * delta_H / H1, "%"),
        ("result", "basin length", "l_b", l_b, "m"),
        ("result", "scour protection length", "l_s", l_s, "m"),
    ]

    print(f"{'':8}{'quantity':<34}{'symbol':<14}{'value':>10}  unit")
    group = None
    for kind, name, symbol, value, unit in rows:
        if kind != group:
            print("-" * 70)
            group = kind
        print(f"{kind:<8}{name:<34}{symbol:<14}{value:>10.3f}  {unit}")

    print("=" * 70)
    print(f"windows: Fr1 in [{FR_WINDOW[0]}, {FR_WINDOW[1]}) -> "
          f"{'met' if s.fr_ok else 'NOT met'};  "
          f"Rt in [{RT_WINDOW[0]}, {RT_WINDOW[1]}] -> "
          f"{'met' if s.rt_ok else 'NOT met'}")
else:
    print("Complete Tasks 1 to 3, then re-run this cell.")