In flow measurement practice, a stepped notch is essentially a combination of which type(s) of basic notches to extend the measurement range?

Introduction / Context:
Laboratory flumes and small channels often require a single gauge to measure wide ranges of discharge. A stepped notch is a practical device that changes effective crest length with head, enabling better sensitivity at low flows while accommodating higher flows without drowning the notch.

Given Data / Assumptions:

• Steady, free-flow conditions over a sharp crest (fully aerated nappe).
• Steps are arranged vertically so progressively higher steps engage as head increases.
• Objective is to vary effective rectangular width with stage.

Concept / Approach:

A stepped notch is constructed from a series of rectangular openings at different elevations, each “step” adding rectangular width as the head rises. This provides discrete increments in effective length b used in Q = C_d * b * √(2 g) * H^(3/2), improving resolution across a range of flows. It is different from a compound notch that deliberately mixes triangular and rectangular openings in one crest to achieve a single continuous head–discharge law.

Step-by-Step Solution:

Verification / Alternative check:

Most textbooks describe stepped notches as “multiple rectangular notches placed one above another.” Compound (or combination) notches, on the contrary, mix V and rectangular shapes in the same crest opening.

Why Other Options Are Wrong:

(b) and (e) misidentify the geometry. (c) describes a compound notch, not a stepped notch. (d) cannot be correct because all listed variants do not describe the same device.

Common Pitfalls:

Confusing “stepped” with “compound.” The former stacks similar rectangular openings; the latter blends dissimilar notch shapes.

Final Answer:

Rectangular notches of different sizes (at different steps)