SCIENCE · INVESTIGATE AND EXPLAIN

Infer fluid head from an ideal jet without mixing two heights

For a large open tank with a small opening, compare the free surface and the exiting stream. Both are at atmospheric pressure, and the large surface area makes the surface speed negligible over a short interval. Bernoulli’s equation then gives exit speedv=√(2gh), whereh is the free-surface height above the opening. This is Torricelli’s result under stated ideal assumptions, not a universal discharge rate.

Learning outcome: Vary head at fixed outlet height, then vary outlet height at fixed head. Reconstruct speed and flight time separately before calculating range. Use the assigned range error to bound inferred head; identify a loss mechanism that would bias inference even if repeated ranges were precise.

Starting recap

Review density and unit conversion, perpendicular force components, static force balance, work-energy, mass conservation and projectile motion.

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Try

For head0.60 m,outlet height0.40 m andg10, exit speed√12≈3.464 m/s and flight time√0.08≈0.2828 s. Range is√0.96≈0.9798 m. An assigned range bound±0.01 m gives inferred head limits(R−0.01)²/1.6 and(R+0.01)²/1.6, approximately0.5878 to0.6123 m.

Open the experiment

Predict

Does doubling the head double range when outlet height stays fixed?

Your prediction and reason

Experiment

Vary head at fixed outlet height, then vary outlet height at fixed head. Reconstruct speed and flight time separately before calculating range. Use the assigned range error to bound inferred head; identify a loss mechanism that would bias inference even if repeated ranges were precise.

Connect an ideal efflux speed with projectile evidence

Worked teaching model · synthetic values · Large open tank and small horizontal opening, both at the same atmospheric pressure,g10. Surface speed negligible; head approximately constant during a short record. No drag or jet breakup. Assigned horizontal-range uncertainty±0.01 m; exact outlet height. No physical jet or pressurized-vessel activity.

Water-surface height above outlet: 0.6 m Horizontal outlet height above landing plane: 0.4 m

Reset keeps your prediction, captures and practice history.

Axes rescale with settings; compare numerical values, not screen angles or apparent lengths. Solid/points show the selected model relationship or observations; the dashed comparison is explained below.

Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Ideal horizontal exit speed	3.4641	m/s
Fall time	0.28284	s
Horizontal range	0.9798	m
Head inferred from range	0.6	m
Inferred head lower bound	0.58782	m
Inferred head upper bound	0.61231	m

Accessible plot coordinates

Primary plotted points
horizontal distance (m)	height above landing plane (m)
0	0.4
0.04899	0.399
0.09798	0.396
0.14697	0.391
0.19596	0.384
0.24495	0.375
0.29394	0.364
0.34293	0.351
0.39192	0.336
0.44091	0.319
0.4899	0.3
0.53889	0.279
0.58788	0.256
0.63687	0.231
0.68586	0.204
0.73485	0.175
0.78384	0.144
0.83283	0.111
0.88182	0.076
0.93081	0.039
0.9798	0

Torricelli’s speed and projectile flight combine to give range2√(head×outlet height).

v=√(2gh) follows equal surface/exit pressure and negligible surface speed. The flight time depends on outlet height, not the head. Inference h=R²/(4y) assumes these conditions; a finite reservoir speed, losses or changing head needs another model.

Torricelli’s speed and projectile flight combine to give range2√(head×outlet height).

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Frame the question

2. Build the mechanism

If the opening points horizontally at heighty above a landing plane, the flight time is√(2y/g) when air resistance is neglected. Horizontal range is thereforeR=v t=2√(hy). The headh sets speed, while the outlety sets fall time. They are different vertical distances; swapping or silently identifying them loses the geometry.

The relation can be inverted to inferh=R²/(4y) from a range observation wheny is known. If range is bounded byR±δR and stays positive, evaluate both endpoints to obtain head bounds. The resulting interval is conditional on the projectile and ideal-flow assumptions; repeated measurements do not eliminate a systematic loss or incorrect height reference.

A finite tank surface speed, changing head, viscous losses, a nonhorizontal outlet or jet breakup changes the prediction. If the outlet-to-tank area ratio is not negligible, continuity makes surface speed nonzero; some kinetic energy is already present at the surface. This lesson does not claim to simulate the draining history or instruct construction of an actual jet apparatus.

3. Work an example

4. Predict and investigate

Does doubling the head double range when outlet height stays fixed?

5. Transfer to a new case

Try a new practice case

A horizontal ideal jet has range1.2 m and outlet height0.6 m. Find the inferred head.

Your numerical result (m)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Explain the boundary

What observation could challenge the assumption that surface speed is negligible?

These bounded virtual recipes and supplied observations are not independent measurements, observed laboratory work or equipment safety calculations. No lifting, pressurizing, deep-water activity or physical jet construction is requested. Practical evidence requires an appropriate supervised setting.

Sources

Original explanations, cases and numerical models. Framework checked 30 October 2026: AP Physics 1 CED, topics 8.4; 1.5. Mechanism references: OpenStax University Physics 1, fluids overview, buoyancy, and Bernoulli energy balance. No official assessment items reproduced.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

What observation could challenge the assumption that surface speed is negligible?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Close pressure-work, kinetic and gravitational energy ledgers Next: Audit a multi-stage mechanism by changing system and law

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