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90° V-Notch Weir — Seepage Monitoring Worked Example

Rating the 90° V-notch weir at a dam's toe-drain outfall — the standard low-flow measurement structure in dam-safety monitoring, because the triangular section keeps sensitivity high when the flow is a trickle. We derive the working rating, build the head-discharge table for the inspection log, and cover the installation rules that make a staff-gage reading defensible. Sources: USBR Water Measurement Manual; Kindsvater & Carter / Kindsvater-Shen weir research (USGS); ASTM D5242.

The structure

Weir	90° V-notch, sharp-crested steel plate in the toe-drain outfall channel
Purpose	Weekly seepage reading + comparison against historical baseline
Observed head today, H	0.35 ft above the notch vertex (staff gage)
Discharge coefficient C_d	0.58 (fully contracted sharp notch; see weir C card)

Step 1 · The rating equation

From the general triangular-weir form

Q = C_d · (8/15) · √(2g) · tan(θ/2) · H^5/2

For θ = 90°: tan(45°) = 1, √(2g) = 8.025 ft^1/2/s
Q = 0.58 · 0.533 · 8.025 · H^2.5 = 2.48 · H^2.5 [Q cfs, H ft]

The precise Kindsvater-Shen treatment adds a small head correction k (≈ 0.003 ft for 90°) and lets C_d vary slightly with geometry; for monitoring purposes the constant-coefficient form above is the standard field rating.

Step 2 · Today's reading

H = 0.35 ft

H^2.5 = 0.35^2.5 = 0.0725
Q = 2.48 · 0.0725 = 0.180 cfs = 81 gpm

The number that matters is the trend, not the value. 81 gpm of toe-drain flow can be entirely healthy for one dam and alarming for another. Dam-safety practice reads seepage against the baseline at comparable reservoir levels and after comparable rainfall: a step change at constant pool — or flow that turns turbid — is the finding that triggers investigation, not any absolute gpm.

Step 3 · Head-discharge table for the log sheet

Q = 2.48·H^2.5

Head H (ft)	Q (cfs)	Q (gpm)
0.20	0.044	20
0.35	0.180	81
0.50	0.438	197
0.75	1.21	542
1.00	2.48	1,113

Note the 5/2-power leverage: a tape-measure error of 0.05 ft at H = 0.35 moves the reported flow by roughly +40% / −32%. Read the gage carefully, and keep H above about 0.2 ft for accuracy — below that, nappe clinging and surface tension degrade the rating (a reason the notch angle, not a rectangular weir, is used for trickle flows in the first place).

Step 4 · Installation rules that make the reading valid

Why some monitoring weirs lie

Measure H upstream, not at the notch. The water surface drops as it accelerates into the notch; gage at least 4×H_max upstream of the plate.
Ventilated, free-falling nappe. The jet must spring clear of the plate with air behind it; a drowned or clinging nappe reads high. Keep tailwater well below the vertex.
Full contractions. The approach pool should be wide and deep relative to the notch so flow contracts fully; C_d = 0.58 assumes it.
Sharp, clean edge. A chamfered upstream edge (≤ ~2 mm crest thickness), free of rust bloom, algae, and debris — cleaning the notch is part of the reading.
Still approach. Baffle or still the approach pool; surging makes the staff gage unreadable at exactly the low heads where the V-notch earns its keep.

Tools used in this example

Reproduce every step: V-notch weir tool with C_d from the weir coefficient card. For the seepage quantity the weir is measuring, see embankment seepage and the exit gradient check; for the broader monitoring program, the dam-safety tool set.