Agricultural and physical foundations of V-Notch Weir Calibration.
Sharp-crested weirs are among the oldest and most precise primary devices used to measure water flow in small agricultural irrigation canals, spring catchments, furrow runoff channels, and drainage ditches. The 90° triangular (V-notch or Thomson) weir is especially suited for low and variable flow rates because the flow cross-section expands triangularly with water depth, maintaining high sensitivity and measurable head even during minimal trickles. Flow over a sharp-crested V-notch weir is governed by integration of the Torricelli velocity profile across triangular horizontal slices: Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^(5/2). For a standard 90° notch (θ = 90°, tan(θ/2) = 1) with clean, fully aerated nappe, this simplifies to the Thomson rating formula Q = C_w·H^2.5, where C_w = (8/15)·C_d·√(2g) ≈ 1.38 m^0.5/s for an empirical discharge coefficient C_d ≈ 0.585. To ensure accurate measurement without end contractions, the weir plate must be chamfered with a sharp bevel facing downstream, and the upstream head H must be measured at least four times the maximum head upstream to avoid surface drawdown curvature.
Viva voce questions & analytical theory
Derive the theoretical discharge equation for a triangular sharp-crested weir.
Consider an elemental strip of thickness dh at depth h below water surface: width b = 2·(H - h)·tan(θ/2). Elemental discharge dQ = C_d·b·dh·√(2gh). Integrating from h = 0 to h = H yields Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^(5/2).
Why is a V-notch weir superior to a rectangular weir for measuring low agricultural discharges?
At low flow rates, a rectangular weir spreads water thinly across its crest, resulting in very small heads (H < 2 cm) that are difficult to measure accurately. In contrast, a V-notch concentrates low flows into the apex, maintaining large measurable heads and high precision.
What is 'nappe cling' and why must the nappe be aerated?
If air beneath the falling water sheet (nappe) is evacuated by flowing water, a partial vacuum develops behind the weir plate, sucking the nappe downward and clinging it to the weir face, which artificially increases discharge by up to 10%.
Where should the point gauge be located to measure true weir head H?
The point gauge must be positioned at a distance equal to 4 to 5 times the maximum expected head upstream from the weir plate to avoid the drawdown curve where the water surface dips as it accelerates toward the crest.
What is the physical meaning of the discharge coefficient C_d in a weir?
C_d accounts for two non-ideal effects: (1) contraction of the flow stream as water streamlines curve inward around the sharp edges (vena contracta), and (2) friction and energy dissipation along the weir plate.
What maintenance is required for field V-notch weirs?
Regular removal of accumulated sediment silt upstream of the weir plate, clearing floating debris and leaves caught in the notch, and inspecting the metal knife edge for nicks or algae growth.
Experimental precautions and agricultural field safety
- Verify that the weir plate knife-edge bevel faces downstream, presenting a sharp 90° square edge to the oncoming flow.
- Ensure point gauge tip is lowered smoothly to touch the water surface without puncturing the surface tension meniscus.
- Verify atmospheric air access ports beneath the nappe remain completely unobstructed during all runs.
- Allow at least 3 minutes after adjusting pump throttle for flume wave oscillations to dissipate.
Theoretical assumptions & biological limits
- The 5/2 power law applies strictly for heads H > 0.05 m; below 5 cm, water surface tension and fluid viscosity dominate.
- Assumes negligible approach velocity; in narrow channels, approach velocity kinetic head (v²/2g) must be added to H.
- Cannot tolerate downstream submergence; the downstream water level must remain below the vertex of the V-notch.
- Sediment accumulation upstream alters approach geometry and gradually degrades measurement accuracy.