Continuity and Bernoulli in daily life: the thinning tap stream and the aeroplane wing
Why does a stream from a tap get thinner as it falls, and why does a wing lift an aeroplane? Change the flow rate, the nozzle or the air speed and angle of attack and check A·v = constant and the pressure difference ½ρ(v₁² − v₂²).
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About this experiment
| Subject | Physics |
|---|---|
| Class | 11 |
| Chapter | 9. Mechanical Properties of Fluids |
| NCERT section | 9.4–9.5 |
| Level | NCERT level |
| Time | about 15 minutes |
| Access | Included in a PractiSci plan |
Aim
To use the equation of continuity and Bernoulli's principle on two everyday examples: why a stream of water from a tap becomes narrower as it falls, and how the wing of an aeroplane gets its lift.
Theory
Equation of continuity: for steady flow of an incompressible liquid the volume that crosses every cross-section per second is the same, A₁v₁ = A₂v₂. Where the stream is faster it must be narrower.
Tap stream: after leaving the nozzle each drop falls freely and speeds up: v² = v₀² + 2gy. Since A v = Q is constant, the area becomes A = Q/v, so the radius falls as r ∝ 1/√v. The stream gets thinner and, at last, breaks into drops (surface tension).
Bernoulli's principle: along a streamline P + ½ρv² + ρgh = constant. Where the speed is high the pressure is low. A wing is shaped (and tilted by the angle of attack) so that the air above it moves faster than the air below, so the pressure above is lower. The pressure difference ΔP = ½ρ(v₁² − v₂²) acting over the wing area gives the lift. This is not the full story (the wing also deflects the air downwards), but it is a good model for a school level.
Formulas used
- A₁ v₁ = A₂ v₂ (continuity)
- P + ½ρv² + ρgh = constant (Bernoulli)
- tap: v = √(v₀² + 2 g y), A = Q / v
- wing: ΔP = ½ρ (v_top² − v_bottom²), lift = ΔP × area
Procedure: what to do in the virtual lab
- Choose the tap and set Q = 80 cm³/s, nozzle 10 mm. Read v₀ and the radius of the stream 40 cm below.
- Check that A v = Q at all heights.
- Increase the nozzle diameter: why is the stream slower and thicker?
- Switch to the wing. At 70 m/s and 5° read the lift and compare it with the weight of a 1000 kg plane.
- Double the speed. By what factor does the lift change? Then increase the angle of attack.
Observations to make
- Water speeds up as it falls and so the stream thins.
- Streamlines are closer above the wing: the air is faster and the pressure is lower there.
- The lift is proportional to v²: doubling the speed gives four times the lift.
What you can change in this experiment
- Example: Stream of water from a tap (continuity) / Aeroplane wing (Bernoulli lift)
- Flow rate of the tap (20 to 200 cm³/s)
- Diameter of the nozzle (4 to 20 mm)
- Speed of the aeroplane (relative to the air) (20 to 150 m/s)
- Angle of attack of the wing (0 to 15 °)
Viva questions on Continuity and Bernoulli in daily life
Questions an examiner may ask in the Class 11 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.
- State the equation of continuity.
- Why does the stream of water from a tap become narrower as it falls?
- How does an aeroplane wing produce lift?
- Why does the lift increase when the speed is doubled?
Frequently asked questions
What is the aim of the Continuity and Bernoulli in daily life experiment?
To use the equation of continuity and Bernoulli's principle on two everyday examples: why a stream of water from a tap becomes narrower as it falls, and how the wing of an aeroplane gets its lift.
Which formulas are used in the Continuity and Bernoulli in daily life experiment?
A₁ v₁ = A₂ v₂ (continuity); P + ½ρv² + ρgh = constant (Bernoulli); tap: v = √(v₀² + 2 g y), A = Q / v; wing: ΔP = ½ρ (v_top² − v_bottom²), lift = ΔP × area
What viva questions are asked on Continuity and Bernoulli in daily life?
State the equation of continuity. Why does the stream of water from a tap become narrower as it falls? How does an aeroplane wing produce lift? Why does the lift increase when the speed is doubled?
How do I do the equation of continuity class 11 experiment for Class 11 online?
Open the Continuity and Bernoulli in daily life virtual lab on PractiSci, follow the procedure above, change the values and read the live graph. It matches the Class 11 physics practical, with the aim, theory, observations and viva questions on this page.
Why does the water stream from a tap get thinner as it falls?
Gravity increases its speed, v² = v₀² + 2 g y, and since A v is constant the cross-section has to shrink.
How does Bernoulli's principle explain lift?
Air moves faster over the curved upper side of the wing, so the pressure there is lower. The higher pressure below pushes the wing up.
What does the equation of continuity state?
For a steady flow of an incompressible fluid, A₁ v₁ = A₂ v₂: the volume flowing per second is the same at every cross-section.
Can I do the Continuity and Bernoulli in daily life experiment online?
Yes. Open it as a 3D virtual lab in your browser or on your phone, change the values and read the results from live graphs. It is part of a PractiSci plan.
Syllabus: Class XI Physics, Chapter 9 — Mechanical Properties of Fluids, §9.4 (streamline flow), §9.5 (Bernoulli's principle and its applications)
What you do in the lab
Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.
Topics: equation of continuity · Bernoulli's principle · tap water stream · aeroplane lift · dynamic lift · streamline flow · fluids
Read the full guide: Mechanical properties of fluids.
More from this chapter
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- Bernoulli's principle: venturimeter
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- Barometer and U-tube manometer: measuring atmospheric and gas pressure
- Pascal's law and hydraulic lift
- Poiseuille flow: viscous flow through a tube
- Reynolds number: laminar and turbulent flow in a pipe (dye experiment)
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