Mechanical Properties of Fluids
Master pressure, Pascal's law, buoyancy, continuity, Bernoulli's principle, viscosity, surface tension and capillary action with a clear JEE Main-focused approach.
The central idea of this chapter
Fluid problems connect pressure, density, velocity and height. First identify whether the fluid is at rest or moving; then choose hydrostatics, continuity or Bernoulli's equation.
What should you understand first?
Mechanical Properties of Fluids covers both fluids at rest and fluids in motion, along with viscosity and surface effects.
Fluid at rest
- Pressure and gauge pressure High
- Pressure variation with depth High
- Pascal's law High
- Archimedes' principle High
- Buoyancy and flotation Medium
Fluid in motion
- Equation of continuity High
- Bernoulli's principle High
- Torricelli's theorem Medium
- Viscosity and Stokes' law High
- Surface tension and capillarity High
Mechanical Properties of Fluids formula sheet
Keep the assumptions in mind. Bernoulli's equation is used for steady, incompressible and non-viscous flow along a streamline.
| Topic | Formula / Relation | Meaning or use |
|---|---|---|
| Pressure | P = F/A | Normal force per unit area. SI unit is pascal. |
| Pressure at depth | P = P₀ + ρgh | Absolute pressure at depth h. |
| Continuity equation | A₁v₁ = A₂v₂ | Steady incompressible flow through a pipe. |
| Bernoulli equation | P + ½ρv² + ρgh = constant | Energy conservation per unit volume. |
| Buoyant force | Fᵦ = ρfluidVdisplacedg | Upward force equal to displaced-fluid weight. |
| Stokes' law | F = 6πηrv | Viscous drag on a small sphere. |
| Capillary rise | h = 2T cosθ / rρg | Rise or fall of liquid in a narrow tube. |
How to choose the correct equation
Most mistakes happen when a student uses a flow equation for a fluid-at-rest problem, or ignores the assumptions behind Bernoulli's equation.
Fluid at rest
- Depth or pressure asked? Use ρgh
- Enclosed fluid and pistons? Pascal
- Object immersed? Buoyancy
- Object floats? Fᵦ = mg
- Atmospheric pressure included? Absolute P
Fluid in motion
- Area and speed change? Continuity
- Pressure and speed change? Bernoulli
- Small sphere in liquid? Stokes
- Liquid jet from hole? Torricelli
- Thin tube or drop? Surface tension
How to prepare this chapter
Build the chapter in layers: pressure, buoyancy, flow, viscosity and surface effects.
What to do
- Start with pressure, density and gauge pressure
- Practise Pascal's law and hydraulic press questions
- Use continuity before applying Bernoulli's equation
- Revise terminal velocity and Stokes' law separately
- Practise surface tension, bubbles and capillary rise
Common mistakes
- Do not confuse gauge pressure with absolute pressure
- Check whether density is of fluid or object
- Bernoulli's equation has conditions
- Radius and diameter are not interchangeable
- Track the direction of buoyant and viscous forces
Ready to test fluid mechanics?
Revise the formula sheet, then solve mixed JEE Main questions on pressure, Bernoulli flow, viscosity and surface tension.
Mechanical Properties of Fluids FAQ
Short answers to common JEE Main preparation questions.
Pressure is the normal force exerted by a fluid per unit area. Its SI unit is pascal, equal to newton per square metre.
For steady, incompressible and non-viscous flow along a streamline, the sum of pressure, kinetic and potential energy per unit volume remains constant.
Pressure, Pascal's law, buoyancy, continuity, Bernoulli's principle, viscosity, Stokes' law, terminal velocity, surface tension and capillary rise are important topics.
Understand pressure and buoyancy first, practise continuity and Bernoulli questions, then study viscosity, surface tension and mixed numerical problems.