Fluid Mechanics Lecture Notes

Overview

• Special session for 11th and 12th standard students.
• Lecture 1 in the Nurture series by Shreyas from Vedantu.
• Topics Covered:
  • Pressure
  • Hydrostatic Pressure
  • Variations of Pressure with Height and Depth
  • Pascal's Law
  • Barometer and Manometer
  • Force on the walls of a container
  • Homework Questions

Key Concepts

What is a Fluid?

• A fluid is any substance that flows and can take the shape of its container, includes gases and liquids but not solids.

Pressure

• Pressure is defined as the force per unit area acting perpendicular to a surface.
• Formula:
  [ P = \frac{F}{A} ]
  • Where ( P ) is pressure, ( F ) is the force, and ( A ) is the area.
  • Units: Pascal (N/m²), atm.

Hydrostatic Pressure

• Pressure in a fluid at rest.
• Important formula:
  [ P = P_0 + \rho g h ]
  • Where ( P_0 ) is atmospheric pressure, ( \rho ) is fluid density, ( g ) is acceleration due to gravity, and ( h ) is the depth in the fluid.

Pascal's Law

• Any change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid.

Barometer

• Used to measure atmospheric pressure.
• Standard atmospheric pressure: 1 atm = 76 cm of mercury.

Manometer

• Used to measure pressure differences between two points in a fluid.
• Gauge pressure:
  [ P_{gauge} = P_{inside} - P_{atm} ]_

Important Equations

• Ideal Fluid: No viscosity, incompressible; density remains constant.
• Pressure Gradient:
  [ \frac{dP}{dh} = -\rho g ]
  • Indicates that pressure decreases with height in a fluid.

Homework Questions

1. If water is used instead of mercury in a barometer, what will be the height of the water column?
2. Find the force on the bottom surface of a container due to a liquid of density ( \rho ) neglecting atmospheric pressure.
3. What is the ratio of the densities of two immiscible liquids in a U-tube, given certain heights?

Important Points to Remember

• Fluids exert pressure in all directions.
• In a fluid at rest, pressure increases with depth due to the weight of the fluid above.
• Gauge pressure can be zero or negative depending on the scenario.
• A manometer measures pressure difference based on different heights of immiscible liquids.

Additional Notes

• Be prepared for upcoming lectures on fluid dynamics.
• Engage with homework and practice problems to enhance understanding.