Hydraulic Lab · Specific energy

4.30 m × 0.30 m × 0.45 m flume

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Mean measured depth y—m

Velocity head V²/(2g)—m

Specific energy E—m above bed

Froude number—Take readings

Specific-energy curve · fixed discharge

Blue: E(y) · gray dashed: E=y · gold: critical point · white: recorded depths at the current discharge · green: selected alternate-depth pair.

Explore energy E/Emin 1.50×

This slider explores the theoretical curve; it does not alter pump flow or the 3D flume. The alternate-depth pair has equal specific energy, not equal momentum. It is not a hydraulic-jump pair.

Procedure

Hold discharge constant.
Set a slope and take three depth readings.
Calculate mean depth, velocity, velocity head and specific energy.
Repeat for more than three slopes and plot E against y.

#	S	Q m³/s	y₁ m	y₂ m	y₃ m	ȳ m	A m²	V m/s	V²/2g m	E m	Fr

Constant-discharge series

Pump discharge Bed slope

Upstream gauge (m)Middle gauge (m)Downstream gauge (m)

Critical conditions

At yc, Fr=1 and E is minimum. Above Emin there are two mathematical depths: shallow/supercritical and deep/subcritical. Below Emin, no steady section depth exists for that discharge.

Equations

q=Q/b · V=Q/(by)
E=y+V²/(2g)=y+q²/(2gy²)
yc=(q²/g)⅓ · Emin=1.5yc
Fr=V/√(gy) · g=9.81 m/s²

Book sample check

Page 20 row 1 gives velocity head 0.986 m. The raw readings imply V=0.450 m/s and V²/(2g)=0.01032 m; E≈0.07699 m. Derived sample values are recalculated, not copied.

Assumptions & measurement limits

Rectangular channel, alpha=1, small slope and energy relative to the bed. The theoretical E–y curve is a section relation, not a backwater or transient-flow solution.

Virtual depths use uniform Manning flow at n=0.010. A zero bed slope has no positive-discharge uniform Manning solution: virtual sampling is disabled, but real observations can still be entered. Readings are rounded to 0.1 mm and are synthetic, not validation data.

After calculation, the 3D view shows the mean measured depth uniformly; before readings, it shows the predicted depth. Spatially varying readings do not generate a backwater profile. Values above the 0.45 m apparatus height are rejected; theoretical alternate depths outside that height remain labeled as outside the apparatus.

Changing discharge starts a different series; the plotted observations and progress filter to the current Q. All series remain in the CSV.

Experiment 2 · Specific energy & depth

Specific-energy curve · fixed discharge

Procedure

Observation sheet