Mechanical properties of fluids (Class 11): pressure, flow and viscosity in 3D
Fluids chapter questions come from a few ideas: pressure grows with depth, the flow of a liquid must be continuous, and speed and pressure trade off along a streamline. These labs turn each idea into something you can change and measure.
NCERT Class 11 Physics, Chapter 9 (Mechanical Properties of Fluids). Every lab below runs in 3D in your browser or on a phone, in English and Hindi.
Try the labs
Barometer and U-tube manometer: measuring atmospheric and gas pressure · free · Chapter 9
To see how a liquid column measures pressure: the barometer gives the atmospheric pressure and the U-tube manometer the difference between a gas pressure and the atmosphere.
Continuity and Bernoulli in daily life: the thinning tap stream and the aeroplane wing · plan · Chapter 9
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.
Reynolds number: laminar and turbulent flow in a pipe (dye experiment) · plan · Chapter 9
To see the change from laminar to turbulent flow in a pipe, and to use the Reynolds number to predict it.
Archimedes' principle and floating bodies · plan · Chapter 9
To verify Archimedes' principle and understand why bodies float or sink.
Bernoulli's principle: venturimeter · plan · Chapter 9
To study the flow of an ideal fluid through a pipe of varying cross-section, verify the equation of continuity and Bernoulli's theorem, and use a venturimeter to measure flow rate.
Surface tension: capillary rise and contact angle · plan · Chapter 9
To study capillary rise (or fall) of liquids in narrow tubes and determine surface tension from the height.
Pressure on a dam wall and the centre of pressure · plan · Chapter 9
To study hydrostatic pressure on a dam wall: variation of pressure with depth, total force and the position of the centre of pressure.
Pascal's law and hydraulic lift · free · Chapter 9
To verify Pascal's law and understand the hydraulic lift as a force multiplier.
Poiseuille flow: viscous flow through a tube · plan · Chapter 9
To study viscous flow through a narrow tube: Poiseuille's law, the parabolic velocity profile and the laminar–turbulent limit (Reynolds number).
Excess pressure in drops and bubbles · plan · Chapter 9
To understand excess pressure inside drops and bubbles and the behaviour of two connected soap bubbles.
Stokes' law: terminal velocity and viscosity · plan · Chapter 9
To determine the coefficient of viscosity of a liquid by observing the terminal velocity of a small sphere falling through it.
Surface energy: merging and splitting water drops · plan · Chapter 9
To understand surface energy: energy released when small drops merge into a big drop and the energy needed to split a drop.
Surface tension: temperature and detergent effect · plan · Chapter 9
To measure the surface tension of water by capillary rise and see how temperature and detergent change it.
Torricelli's law: liquid from a hole in a tank · plan · Chapter 9
To verify Torricelli's theorem — speed of efflux v = √(2gh) — and find the hole position for maximum range.
Pressure and the barometer
Pressure at depth h in a liquid of density ρ is P = P₀ + ρ g h. A mercury barometer is a tube closed at the top and upturned in a dish. The mercury column is held up by the atmosphere, so P₀ = ρ g H. At 101.3 kPa the height is 760 mm of mercury, but with water the column would be about 10.3 m, which is why mercury is used.
In an open U-tube manometer the difference of levels h gives the gauge pressure of the gas, P − P₀ = ρ g h. Change the liquid and the height changes in inverse proportion to its density.
P = P₀ + ρ g hH = P₀ / (ρ g)1 atm = 760 mm Hg = 101.3 kPa
Equation of continuity: why a tap stream thins
For a steady flow of an incompressible liquid, the volume flowing past every cross-section in a second is the same: A v = constant. Water falling from a tap speeds up under gravity, v² = v₀² + 2 g y, so its cross-section must shrink. That is why the stream gets thinner as it falls.
A₁ v₁ = A₂ v₂v = √(v₀² + 2 g y)
Bernoulli's principle and the lift on a wing
Along a streamline P + ½ ρ v² + ρ g h is constant. The air above a curved wing travels faster than the air below, so the pressure above is lower and the net upward force is the lift. The aerofoil lab shows the speeds above and below and the lift for a chosen angle of attack.
P + ½ ρ v² + ρ g h = constantlift ≈ ½ ρ (v_top² − v_bottom²) × wing area
Viscosity and Reynolds number
Whether a flow is smooth (laminar) or irregular (turbulent) depends on the Reynolds number Re = ρ v d / η. Below about 2000 the flow is laminar, above about 4000 it is turbulent, and in between it is unstable. In the dye experiment a thin thread of dye stays straight in laminar flow and breaks into eddies when the speed is raised.
Re = ρ v d / ηRe < 2000 laminar, Re > 4000 turbulent
Frequently asked questions
Why is mercury used in a barometer and not water?
Mercury is 13.6 times denser than water, so the column is only 76 cm tall. A water barometer would need a tube more than 10 m long.
What does the equation of continuity say?
For a steady flow of an incompressible fluid, A v is the same at every cross-section. A narrow section therefore has a faster flow.
Why does water from a tap become thinner as it falls?
Gravity increases its speed, and since A v must stay constant the cross-sectional area has to decrease.
What is the Reynolds number and what are its limits?
Re = ρ v d / η, a ratio of inertial to viscous effects. Flow in a pipe is laminar below about 2000 and turbulent above about 4000.
How does an aeroplane wing produce lift?
The shape and angle of the wing make air move faster above it. By Bernoulli's principle the pressure is lower there, so the pressure below pushes the wing up.
How do I find gas pressure with a manometer?
Measure the difference h between the two levels. The gauge pressure is ρ g h, and the absolute pressure is P₀ + ρ g h if the gas side is lower.