📘 Mechanical Properties of Fluids
Complete Chapter Notes
1. Pressure in Fluids
Pressure is the force acting per unit area.
Pressure (P) = Force / Area
Unit = Pascal (Pa)
Unit = Pascal (Pa)
Pressure due to Fluid Column
P = hρg
- h = height of fluid
- ρ = density
- g = acceleration due to gravity
Key Points:
- Pressure increases with depth
- Independent of container shape
2. Pascal’s Law
Pressure applied at any point in a confined fluid is transmitted equally in all directions.
P₁ = P₂
Applications:
- Hydraulic Lift: Used to lift heavy loads
- Hydraulic Brakes: Used in vehicles
3. Effect of Gravity on Pressure
- Pressure increases downward due to gravity
- Liquids at same level have same pressure
4. Viscosity
Viscosity is the internal resistance offered by a fluid to flow.
F = ηA (dv/dx)
- η = coefficient of viscosity
- Unit: Pa·s
5. Stokes’ Law
F = 6πηrv
- r = radius
- v = velocity
Applicable for small spherical bodies moving in fluid.
---6. Terminal Velocity
Maximum constant velocity attained by a falling object in fluid.
v = (2r²(ρ - σ)g) / 9η
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7. Streamline and Turbulent Flow
- Streamline Flow: Smooth, orderly flow
- Turbulent Flow: Irregular flow with eddies
Critical Velocity
Velocity at which flow changes from streamline to turbulent.
---8. Bernoulli’s Theorem
P + ½ρv² + ρgh = constant
Applications:
- Airplane wings (Dynamic Lift)
- Venturimeter
- Atomizer
9. Torricelli’s Law
v = √(2gh)
Speed of liquid flowing out of a hole.
---10. Surface Tension
Surface tension is the force acting per unit length on the surface of liquid.
T = F / L
Surface Energy
Energy required to increase surface area.
---11. Angle of Contact
- Acute angle → liquid wets surface (water)
- Obtuse angle → does not wet (mercury)
12. Excess Pressure
Drop: P = 2T/r
Bubble: P = 4T/r
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Bubble: P = 4T/r
13. Capillary Rise
h = (2T cosθ) / (ρgr)
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14. Applications of Surface Tension
- Formation of drops and bubbles
- Capillary action in plants
- Detergents reduce surface tension
- Ink flow in pens
15. Important Points
- Pressure depends on depth, not shape
- Viscosity decreases with temperature (liquids)
- Bernoulli principle used in aviation
- Surface tension decreases with temperature
