Rectangular Weir Calculator

At a glance:A rectangular sharp-crested weir is one of the most common 'flow-measuring structures' in open channels: a baffle plate with a sharp crest is placed across the channel, with a rectangular notch cut in the middle so water overflows above the notch. Because the overflow rate has a stable correspondence to the head H (the height from the notch crest to the upstream free surface), measuring H lets you back-calculate the flow — very convenient for field measurement. The basic formula: Q=(2/3)·Cd·b·√(2g)·H^(3/2), where Q is flow (m³/s), Cd the discharge coefficient (dimensionless), b the notch width (m), g gravitational acceleration (9.81 m/s²) and H the head (m). Term by term: the core is H^(3/2) — it comes from integrating Torricelli's exit speed (v∝√h) over the whole notch height: near the surface the head is small and the speed slow, deeper down the head is larger and the speed faster, and the integral gives a relation proportional to H^(3/2). So when the head rises, flow grows fast (H×4 → H^(3/2)×8). Cd corrects the difference between the ideal derivation and real flow (contraction, viscosity, approach velocity); a rectangular sharp-crested weir is about 0.60–0.62 (some use the Rehbock Cd≈0.611 correction). b is the crest width; if the notch is narrower than the channel, side contraction occurs and needs extra correction. Example: Cd=0.62, b=1 m, H=0.3 m → Q=(2/3)×0.62×1×√(2×9.81)×0.3^1.5=0.4133×4.429×0.16432≈0.3008 m³/s (≈301 L/s). Uses: (1) flow measurement and division metering in irrigation/drainage channels; (2) hydrology station runoff observation; (3) lab flume flow calibration; (4) small hydraulic-project flow monitoring. Notes: (1) require free overflow — the downstream level must be below the crest with adequate aeration to form a stable nappe, otherwise submerged flow is inaccurate; (2) measure H at an upstream section unaffected by the drawdown (usually ~3–4 H upstream); (3) if the notch is narrower than the channel use a side-contraction correction (e.g. Francis formula subtracts end contractions); (4) Cd varies with weir type and H/P (P crest height), calibrate for precision; (5) use consistent units (b, H in m). In short, the rectangular weir flow is Q=(2/3)Cd·b·√(2g)·H^(3/2), the classic open-channel metering formula — measure the head and you get the flow.