✁ Flow over a Rectangular Notch
A virtual re-creation of the sharp-crested weir experiment on the hydraulics bench. Set the point-gauge datum at the crest, step the head up in increments, measure discharge with the volumetric tank, watch the nappe change character — then determine the coefficient of discharge from your Q vs Hn plot. Repeat with the V-notch and see why it wins at low flows.
Objective
To determine the characteristics of flow over a rectangular weir (and a 90° V-notch): the head–discharge relationship, the coefficient of discharge Cd, and the behaviour of the nappe.
Theory
Applying the energy equation from upstream to the weir crest — with the usual simplifying assumptions — gives:
Rectangular notch: Q = Cd·(2/3)·√(2g)·b·H3/2 • V-notch: Q = Cd·(8/15)·√(2g)·tan(θ/2)·H5/2 • H = h − h₀
Cd absorbs everything the ideal theory neglects — the approach velocity, the contraction of the nappe, viscosity and surface tension. It must be found by experiment: plot Q against H3/2 (rectangular) or H5/2 (V-notch); the slope of the straight line through the origin gives Cd.
Equipment
F1-10 hydraulics bench; F1-13 rectangular and V-notch weir plates; vernier hook & point gauge on an instrument carrier; stopwatch.
Rectangular notch: b = 30 mm V-notch: θ = 90° Gauge ≥ 3H upstream of the plate Collect ≥ 120 s per reading
Procedure — perform it here
Observations & Computations
Take ~7 readings per notch. H = h − h₀; Cd = Q / (K·Hn) where K = (2/3)√(2g)·b for the rectangular notch (n = 3/2) and K = (8/15)√(2g)·tan(θ/2) for the V-notch (n = 5/2). Note the nappe type at each head.
| No. | Notch | h₀ (mm) | h (mm) | H (mm) | Hn (mn) | Vol (L) | t (s) | Q (L/s) | Cd | Nappe |
|---|---|---|---|---|---|---|---|---|---|---|
| No readings yet — set the datum, adjust the valve, read the gauge, collect, then Record. | ||||||||||
Calibration plot — Q vs Hn
A straight line through the origin confirms the theoretical exponent; its slope gives Cd. The dashed line is the textbook value for comparison.
Report Questions & Precautions
What are the limitations of the theory?
The derivation assumes an ideal fluid (no viscosity or surface tension), negligible approach velocity, uniform upstream velocity distribution, atmospheric pressure throughout the nappe, and no contraction — none strictly true. All the neglected effects are swept into Cd, which is why it must be measured.
Why is there wider variation of Cd at lower flow rates?
At small heads, surface tension and viscosity are proportionally much stronger — the nappe may cling to the plate instead of springing clear, changing the flow pattern entirely. Measurement errors are also relatively larger: a ±0.3 mm gauge error on a 8 mm head is ~4%, and H enters the formula raised to the 1.5 or 2.5 power.
Nappe types
Springing clear: the sheet leaves the crest cleanly with air beneath — the condition the theory assumes. Depressed: partial vacuum under the nappe pulls it down, increasing discharge slightly. Clinging: at very low heads the nappe adheres to the downstream face — Cd becomes erratic and the calibration is unreliable.
Why use a V-notch at low flows?
With Q ∝ H5/2, a small discharge still produces a usefully large, accurately measurable head, and the notch keeps a proper springing nappe. A rectangular notch at the same low flow runs at a few millimetres of head, where gauge error and surface tension ruin the accuracy.
Precautions: level the bench before starting; measure the head at least 3H upstream of the plate (the surface draws down near the crest); let the level stabilise before reading; collect for at least 120 seconds; do not let water spill over the plate top beside the notch.