Mechanical Properties of Fluids
1. Pressure in Fluids
- Fluids exert pressure in all directions.
- Pressure = Force / Area (P = F / A)
- SI Unit: Pascal (Pa)
- In a fluid at rest, pressure increases with depth.
2. Pascal’s Law
- Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.
- Used in hydraulic lifts and brakes.
3. Atmospheric Pressure and Gauge Pressure
- Atmospheric pressure is the pressure exerted by the air above the surface.
- Gauge pressure = Absolute pressure - Atmospheric pressure.
- Measured using barometers or manometers.
4. Buoyancy and Archimedes' Principle
- Buoyant force acts upward on an object submerged in a fluid.
- Archimedes' Principle: The buoyant force is equal to the weight of fluid displaced.
- Apparent weight = Actual weight - Buoyant force.
5. Fluid Dynamics
- Study of fluids in motion.
- Steady or streamline flow: velocity of fluid at a point remains constant over time.
- Turbulent flow: irregular, chaotic motion of fluid.
6. Bernoulli’s Theorem
- For incompressible, non-viscous fluids in steady flow:
- Total energy per unit volume is constant:
P + ½ρv² + ρgh = constant - Used in airplane wings, carburetors, and atomizers.
7. Viscosity
- Internal resistance to flow in fluids.
- Viscous force is proportional to velocity gradient:
F = ηA (dv/dx) - η is the coefficient of viscosity.
- SI unit: N·s/m² or Pa·s
8. Stokes' Law
- Viscous force on a sphere moving in a fluid:
F = 6πηrv - r = radius, v = velocity, η = viscosity
- Used to calculate terminal velocity of a falling object in fluid.
9. Surface Tension
- Force acting per unit length on a line in the surface of a liquid.
- Due to cohesive forces between liquid molecules.
- SI unit: N/m
10. Capillary Action
- Rise or fall of liquid in a narrow tube due to surface tension and adhesion.
- Height is given by:
h = (2T cosθ) / (ρgr)