LABORATORY 28 · CIVIL ENGINEERING

Flow Discharge Over Sharp-Crested Rectangular and 90° V-Notch Weirs (Discharge Coefficient C_d)

Determine the discharge coefficient C_d and head-discharge relationships for sharp-crested rectangular and 90° triangular V-notch weirs in an open laboratory flume according to ISO 1438 / ASTM D5242. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.

STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING

Your virtual civil engineering laboratory.

FLOW DISCHARGE Q—

CIVIL INFRASTRUCTURE TELEMETRY

Ready to sample with Head Parameter = 0.13 m^(2.5).

Weir Head Parameter H^(5/2)0.13 m^(2.5)Set Head Parameter (m^(2.5))

Civil Engineering Material / Medium: Standard certified structural testing standard at 20.0 °C

Adjust Head Parameter, then execute civil engineering measurement.

Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.

Civil engineering assumptions and boundary condition limits

The civil engineering physical models apply within the specified calibrated operational window (0.05 to 0.25 m^(2.5)). Calibrated on a precision brass 90° V-notch weir plate installed across an 8-meter tilting hydraulics flume. Linearized model relates discharge Q directly to head parameter H^(5/2) with slope 1.3800 m^(0.5)/s.

Laboratory apparatus & testing equipment.

Hydraulic Tilting Flume with Recirculating Sump

8.0 m long by 0.30 m wide glass-sided open channel flume with variable speed axial centrifugal pump.

Standard Brass 90° Triangular V-Notch Weir Plate

Precision-machined beveled brass plate with sharp knife-edge crest (θ = 90° ± 0.1°).

Vernier Hook-and-Point Depth Gauge

Micrometer-driven point gauge measuring flume free-surface elevation to ±0.05 mm.

Stilling Baffle Chamber

Perforated damping baffles eliminating inlet turbulence and surface standing waves upstream of weir.

Calibrated Volumetric Measuring Tank

Sump collection tank with digital timer and sight glass for gravimetric flow rate verification.

Nappe Aeration Atmospheric Vent Pipes

Side flume ventilation ports ensuring continuous atmospheric pressure beneath the falling nappe.

FOLLOW THE METHOD

A reason behind every step.

Determine the discharge coefficient C_d and head-discharge relationships for sharp-crested rectangular and 90° triangular V-notch weirs in an open laboratory flume according to ISO 1438 / ASTM D5242. Standardized parameter settings: 0.05, 0.09, 0.13, 0.17, 0.21, 0.25 m^(2.5).

Flume Leveling & Zero Datum Establishment

Set flume bed horizontal using digital inclinometer; fill flume until water crest touches the exact vertex of the V-notch; record hook gauge zero reading H_0.

Pump Activation & Upstream Baffle Stabilization

Start recirculation pump; adjust inlet control valve to establish initial steady flow; allow 5 minutes for stilling chamber surface waves to damp out.

Upstream Head Measurement via Point Gauge

Position hook gauge at a distance 4 to 5 times maximum head upstream of weir plate; lower point until tip touches the water surface without puncturing the meniscus; log reading H_total; compute head H = H_total - H_0.

Volumetric Flow Rate Measurement

Divert flume outflow into calibrated volumetric measuring tank; record time required to collect a known volume (e.g. 200 L) with digital stopwatch to determine discharge Q.

Systematic Multi-Head Flow Acquisition

Increment control valve across six systematic head levels (H^(5/2) = 0.05, 0.09, 0.13, 0.17, 0.21, and 0.25 m^2.5); measure steady-state head and discharge for each step.

Nappe Aeration Inspection & Rating Curve Plotting

Verify continuous air envelope beneath nappe; compute transformed coordinate H^(5/2); plot Q versus H^(5/2) and determine empirical discharge multiplier.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into civil engineering insight.

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Points are your recorded observations. The solid regression line validates Weir Flow & Discharge mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b

Q = 1.3800 · H^(5/2)

#	Weir Head Parameter H^(5/2) (m^(2.5))	Flow Discharge Q (m³/s)	Weir head parameter H^(5/2) (m^2.5)	Volumetric discharge Q (m³/s)	Remove

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Calculate it yourself.

Your estimate of V-Notch Weir Discharge Coefficient Multiplier (m^(0.5)/s)

CHECK YOUR UNDERSTANDING

Explain what the civil engineering metrics mean.

The theoretical discharge over a 90° triangular V-notch weir is proportional to:

If air under a falling weir nappe is completely trapped, the measured discharge for a given head will:

A typical discharge coefficient C_d for a standard sharp-crested 90° brass V-notch weir is approximately:

The purpose of upstream stilling baffles in a weir flume is to:

THEORY AND STRUCTURAL CONTEXT

Civil engineering background & physical principles.

In open channel hydraulic engineering, sharp-crested weirs are fundamental obstruction structures utilized for precise discharge measurement, flood routing, irrigation water allotment, and storm runoff control. When water spills over an aerated sharp-crested plate, it detaches cleanly to form a free-falling jet known as a nappe. For a 90° triangular V-notch weir, the integration of elementary horizontal strips across the triangular geometry yields the theoretical discharge relation Q_th = (8/15) · tan(θ/2) · √(2g) · H^(5/2), where θ is the notch angle (90°), g is gravitational acceleration (9.81 m/s²), and H is upstream head above the vertex. Viscous boundary drag, surface tension, and contraction of streamlines reduce actual discharge relative to theoretical flow, necessitating a calibrated discharge coefficient C_d: Q = C_d · (8/15) · √(2g) · H^(5/2). For standard 90° brass notches, C_d typically ranges between 0.58 and 0.62, giving an empirical coefficient multiplier of approximately 1.38 m^(0.5)/s. Maintaining full aeration under the falling nappe is mandatory; insufficient venting creates an under-nappe partial vacuum that depresses pressure, sucks the jet downward, and induces catastrophic flow measurement errors up to 25%. In this laboratory flume experiment, water head H is accurately monitored with a vernier hook-and-point gauge at systematic discharge rates to establish the head-discharge rating curve and calibrate the weir discharge coefficient.

Q = 1.3800 · H^(5/2)

Calibrated on a precision brass 90° V-notch weir plate installed across an 8-meter tilting hydraulics flume. Linearized model relates discharge Q directly to head parameter H^(5/2) with slope 1.3800 m^(0.5)/s.