diff --git a/engineering/pid/symbols_vessels.py b/engineering/pid/symbols_vessels.py
index f3342c7..9ffc9e2 100644
--- a/engineering/pid/symbols_vessels.py
+++ b/engineering/pid/symbols_vessels.py
@@ -1 +1,235 @@
-"""Parametric vessels - filled in by Task 10."""
+# engineering/pid/symbols_vessels.py
+"""Parametric vessels (ISO 10628-2): size and nozzles come from the caller.
+
+Unlike the fixed-size catalogue, a vessel's block definition depends on its
+parameters, so the block name carries an 8-hex hash of the validated parameter
+set (spec 4.5): identical parameters share one definition, different ones get
+their own. Nozzles become stub lines plus named ports; the default set is
+``N1`` top, ``N2`` bottom, ``N3`` left (0.7 up the wall), ``N4`` right (0.3).
+"""
+
+from __future__ import annotations
+
+from .geometry import arc, line, polyline
+from .symbols import Port, SymbolSpec, make_spec, params_hash, register, tag_attdefs
+
+VESSELS = ("vertical_vessel", "horizontal_vessel", "tank", "column", "reactor", "hopper")
+SIDES = ("top", "bottom", "left", "right")
+DEFAULT_NOZZLES = [
+    {"name": "N1", "side": "top", "fraction": 0.5},
+    {"name": "N2", "side": "bottom", "fraction": 0.5},
+    {"name": "N3", "side": "left", "fraction": 0.7},
+    {"name": "N4", "side": "right", "fraction": 0.3},
+]
+_DEFAULTS: dict[str, dict] = {
+    "vertical_vessel": {"width": 20.0, "height": 40.0},
+    "horizontal_vessel": {"width": 40.0, "height": 20.0},
+    "tank": {"width": 24.0, "height": 24.0, "roof": "flat"},
+    "column": {"width": 16.0, "height": 60.0, "trays": 0},
+    "reactor": {"width": 24.0, "height": 36.0, "jacketed": False},
+    "hopper": {"width": 24.0, "height": 24.0},
+}
+PARAMS_SCHEMA = {
+    "width": "float > 0 (mm)",
+    "height": "float > 0 (mm)",
+    "nozzles": "[{name, side: top|bottom|left|right, fraction: 0..1}]",
+    "roof": "tank only: flat | cone",
+    "trays": "column only: int >= 0",
+    "jacketed": "reactor only: bool",
+}
+#: Nozzle stub length beyond the vessel wall (symbol-local mm).
+STUB = 3.0
+#: Gap between a jacketed reactor's wall and its jacket line.
+JACKET = 2.0
+
+
+def _is_number(value) -> bool:
+    return isinstance(value, (int, float)) and not isinstance(value, bool)
+
+
+def validate_vessel_params(symbol: str, params: dict | None) -> dict:
+    """Merge ``params`` over the vessel's defaults and validate every key.
+
+    Raises ``ValueError`` naming the offending key (and nozzle index) before
+    anything is built; the returned dict is the canonical parameter set the
+    block name is hashed from.
+    """
+    if symbol not in VESSELS:
+        raise ValueError(f"unknown vessel {symbol!r}; valid: {', '.join(VESSELS)}")
+    merged = dict(_DEFAULTS[symbol])
+    merged["nozzles"] = [dict(n) for n in DEFAULT_NOZZLES]
+    if symbol == "hopper":
+        merged["nozzles"] = [dict(n) for n in DEFAULT_NOZZLES[:2]]
+    if params is not None and not isinstance(params, dict):
+        raise ValueError(f"{symbol}: params must be a dict")
+    for key, value in (params or {}).items():
+        if key not in merged:
+            raise ValueError(
+                f"{symbol}: unknown parameter {key!r}; valid: {', '.join(sorted(merged))}"
+            )
+        merged[key] = value
+    for key in ("width", "height"):
+        v = merged[key]
+        if not _is_number(v) or v <= 0:
+            raise ValueError(f"{symbol}: {key} must be a number > 0")
+        merged[key] = float(v)
+    if "roof" in merged and merged["roof"] not in ("flat", "cone"):
+        raise ValueError(f"{symbol}: roof must be 'flat' or 'cone'")
+    if "trays" in merged:
+        trays = merged["trays"]
+        if isinstance(trays, bool) or not isinstance(trays, int) or trays < 0:
+            raise ValueError(f"{symbol}: trays must be an int >= 0")
+    if "jacketed" in merged and not isinstance(merged["jacketed"], bool):
+        raise ValueError(f"{symbol}: jacketed must be a bool")
+    nozzles = merged["nozzles"]
+    if not isinstance(nozzles, list):
+        raise ValueError(f"{symbol}: nozzles must be a list")
+    names: set[str] = set()
+    clean = []
+    for i, n in enumerate(nozzles):
+        if not isinstance(n, dict) or not isinstance(n.get("name"), str) or not n["name"]:
+            raise ValueError(f"{symbol}: nozzles[{i}].name must be a non-empty string")
+        if n["name"] in names:
+            raise ValueError(f"{symbol}: nozzles[{i}].name {n['name']!r} is repeated")
+        names.add(n["name"])
+        if n.get("side") not in SIDES:
+            raise ValueError(f"{symbol}: nozzles[{i}].side must be one of {', '.join(SIDES)}")
+        f = n.get("fraction", 0.5)
+        if not _is_number(f) or not 0.0 <= f <= 1.0:
+            raise ValueError(f"{symbol}: nozzles[{i}].fraction must be within 0..1")
+        clean.append({"name": n["name"], "side": n["side"], "fraction": float(f)})
+    merged["nozzles"] = clean
+    return merged
+
+
+def _nozzles(
+    params: dict, half_w: float, half_h: float, extra: float = 0.0
+) -> tuple[list[dict], list[Port]]:
+    """Nozzle stub primitives and ports on a box of ±half_w × ±half_h.
+
+    ``extra`` lengthens the stubs (a jacketed reactor's nozzles pass through
+    the jacket) so every port still sits on the symbol's outer edge.
+    """
+    prims: list[dict] = []
+    ports: list[Port] = []
+    stub = STUB + extra
+    for n in params["nozzles"]:
+        side, f = n["side"], n["fraction"]
+        if side == "top":
+            x, y0, y1 = -half_w + f * 2 * half_w, half_h, half_h + stub
+            prims.append(line(x, y0, x, y1))
+            ports.append(Port(n["name"], x, y1, 90.0))
+        elif side == "bottom":
+            x, y0, y1 = -half_w + f * 2 * half_w, -half_h, -half_h - stub
+            prims.append(line(x, y0, x, y1))
+            ports.append(Port(n["name"], x, y1, 270.0))
+        elif side == "left":
+            y, x0, x1 = -half_h + f * 2 * half_h, -half_w, -half_w - stub
+            prims.append(line(x0, y, x1, y))
+            ports.append(Port(n["name"], x1, y, 180.0))
+        else:  # right
+            y, x0, x1 = -half_h + f * 2 * half_h, half_w, half_w + stub
+            prims.append(line(x0, y, x1, y))
+            ports.append(Port(n["name"], x1, y, 0.0))
+    return prims, ports
+
+
+def _capsule_vertical(w: float, h: float) -> list[dict]:
+    """Cylinder with dished ends, axis vertical: two walls and two half-circle heads."""
+    r = w / 2
+    body = h / 2 - r
+    return [
+        line(-r, -body, -r, body),
+        line(r, -body, r, body),
+        arc(0, body, r, 0, 180),
+        arc(0, -body, r, 180, 360),
+    ]
+
+
+def _capsule_horizontal(w: float, h: float) -> list[dict]:
+    r = h / 2
+    body = w / 2 - r
+    return [
+        line(-body, -r, body, -r),
+        line(-body, r, body, r),
+        arc(body, 0, r, 270, 90),
+        arc(-body, 0, r, 90, 270),
+    ]
+
+
+def build_vessel(symbol: str = "vertical_vessel", params: dict | None = None) -> SymbolSpec:
+    p = validate_vessel_params(symbol, params)
+    w, h = p["width"], p["height"]
+    half_w, half_h = w / 2, h / 2
+    extra = 0.0
+    if symbol == "vertical_vessel":
+        prims = _capsule_vertical(w, h)
+    elif symbol == "horizontal_vessel":
+        prims = _capsule_horizontal(w, h)
+    elif symbol == "tank":
+        roof = w / 6 if p["roof"] == "cone" else 0.0
+        prims = [
+            polyline(
+                [
+                    (-half_w, -half_h),
+                    (half_w, -half_h),
+                    (half_w, half_h - roof),
+                    (-half_w, half_h - roof),
+                ]
+            )
+        ]
+        if roof:
+            prims.append(
+                polyline(
+                    [(-half_w, half_h - roof), (0, half_h), (half_w, half_h - roof)],
+                    closed=False,
+                )
+            )
+    elif symbol == "column":
+        prims = _capsule_vertical(w, h)
+        trays = p["trays"]
+        for i in range(trays):
+            y = -half_h + (i + 1) * h / (trays + 1)
+            prims.append(line(-half_w + 1, y, half_w - 1, y))
+    elif symbol == "reactor":
+        prims = _capsule_vertical(w, h)
+        if p["jacketed"]:
+            body = half_h - half_w
+            prims += [
+                line(-half_w - JACKET, -body, -half_w - JACKET, body),
+                line(half_w + JACKET, -body, half_w + JACKET, body),
+            ]
+            extra = JACKET
+    else:  # hopper: flat top, walls converging to a narrow outlet
+        prims = [
+            polyline([(-half_w, half_h), (half_w, half_h), (w / 6, -half_h), (-w / 6, -half_h)])
+        ]
+    nozzle_prims, ports = _nozzles(p, half_w, half_h, extra)
+    prims += nozzle_prims
+    xs = [-half_w - extra, half_w + extra] + [pt.x for pt in ports]
+    ys = [-half_h, half_h] + [pt.y for pt in ports]
+    box = (min(xs), min(ys), max(xs), max(ys))
+    return make_spec(
+        f"PID_VESSEL_{symbol.upper()}_{params_hash(p)}",
+        "vessel",
+        symbol,
+        None,
+        prims,
+        tag_attdefs(box[3]),
+        ports,
+        "ISO 10628-2:2012 vessels",
+        bbox=box,
+        parametric=True,
+        params=p,
+    )
+
+
+def _vessel_builder(symbol: str):
+    def build(params: dict | None = None) -> SymbolSpec:
+        return build_vessel(symbol, params)
+
+    return build
+
+
+for _symbol in VESSELS:
+    register(_symbol, "vessel", _vessel_builder(_symbol), params_schema=PARAMS_SCHEMA)
diff --git a/tests/test_pid_symbols.py b/tests/test_pid_symbols.py
index e2ed4ce..c923cba 100644
--- a/tests/test_pid_symbols.py
+++ b/tests/test_pid_symbols.py
@@ -348,3 +348,81 @@ def test_equipment_families_register():
     assert next(p for p in ecc.ports if p.name == "out").y == pytest.approx(-1.0)
     assert resolve("reducer").name == "PID_MISC_REDUCER_CONCENTRIC"
     assert resolve("agitator").ports[0] == Port("shaft", 0.0, 0.0, 270.0, "process")
+
+
+# ── parametric vessels (Task 10) ─────────────────────────────────────────────
+
+from engineering.pid.symbols_vessels import (  # noqa: E402
+    VESSELS,
+    build_vessel,
+    validate_vessel_params,
+)
+
+
+def test_vessels_are_parametric_and_hash_named():
+    assert len(VESSELS) == 6
+    v = build_vessel("vertical_vessel")
+    assert v.parametric is True and v.name.startswith("PID_VESSEL_VERTICAL_VESSEL_")
+    assert len(v.name.rsplit("_", 1)[1]) == 8
+    assert {p.name: p.direction_deg for p in v.ports} == {
+        "N1": 90.0,
+        "N2": 270.0,
+        "N3": 180.0,
+        "N4": 0.0,
+    }
+    same = build_vessel("vertical_vessel", {"width": 20, "height": 40})
+    assert same.name == v.name, "identical parameters share one definition"
+    other = build_vessel("vertical_vessel", {"width": 30})
+    assert other.name != v.name
+
+
+def test_vessel_nozzles_are_where_the_parameters_say():
+    v = build_vessel(
+        "vertical_vessel",
+        {
+            "width": 20,
+            "height": 40,
+            "nozzles": [{"name": "F", "side": "right", "fraction": 0.25}],
+        },
+    )
+    port = v.ports[0]
+    assert (port.name, port.x, port.y, port.direction_deg) == ("F", 13.0, -10.0, 0.0)
+    assert v.bbox == (-10.0, -20.0, 13.0, 20.0)
+
+
+def test_vessel_variants_draw_their_features():
+    column = build_vessel("column", {"trays": 5})
+    assert sum(1 for p in column.primitives if p["type"] == "line") >= 5 + 2
+    cone = build_vessel("tank", {"roof": "cone"})
+    assert any(p["type"] == "polyline" and not p["closed"] for p in cone.primitives)
+    jacketed = build_vessel("reactor", {"jacketed": True})
+    assert jacketed.bbox[2] == pytest.approx(12.0 + 5.0), "half width 12 + jacket 2 + stub 3"
+    hopper = build_vessel("hopper")
+    assert {p.direction_deg for p in hopper.ports} == {90.0, 270.0}
+
+
+@pytest.mark.parametrize(
+    "params, key",
+    [
+        ({"width": 0}, "width"),
+        ({"height": -1}, "height"),
+        ({"nozzles": [{"name": "A", "side": "up", "fraction": 0.5}]}, "side"),
+        ({"nozzles": [{"name": "A", "side": "top", "fraction": 1.5}]}, "fraction"),
+        (
+            {
+                "nozzles": [
+                    {"name": "A", "side": "top", "fraction": 0.5},
+                    {"name": "A", "side": "top", "fraction": 0.2},
+                ]
+            },
+            "name",
+        ),
+        ({"trays": -2}, "trays"),
+        ({"roof": "dome"}, "roof"),
+        ({"bogus": 1}, "bogus"),
+    ],
+)
+def test_vessel_params_are_validated(params, key):
+    symbol = "column" if "trays" in params else ("tank" if "roof" in params else "vertical_vessel")
+    with pytest.raises(ValueError, match=key):
+        validate_vessel_params(symbol, params)