Lesson 5.1: Fluid Properties, Pressure, and Hydrostatics

Fluid Mechanics is essential for designing hydraulic machines, piping systems, and pumps. GATE and PSU exams often test fluid properties, hydrostatics, and pressure calculations.

🔹 1. Introduction

• Definition: Fluid Mechanics deals with behavior of fluids (liquids and gases) at rest and in motion.

• Applications: Hydropower, pumps, turbines, pipe networks, chemical processes

• Properties of Fluids:

  1. Density ($\rho$): Mass per unit volume

  2. Specific Weight ($\gamma =\rho g$)

  3. Viscosity ($\mu$): Resistance to flow

  4. Specific Gravity (SG): Ratio of fluid density to water

  5. Surface Tension: Cohesion at liquid surface

  6. Compressibility: Change in volume under pressure

🔹 2. Pressure in Fluids

• Definition: Force per unit area exerted by fluid

p=FAp = \frac{F}{A}p=AF​

• Units: Pa, N/m², bar, atm

• Variation with Depth:

p=p0+ρghp = p_0 + \rho g hp=p0​+ρgh

Where p0p_0p0​ = surface pressure, h = depth

• Pascal’s Law: Pressure applied at any point in fluid is transmitted equally in all directions

🔹 3. Hydrostatics

• Buoyancy: Upthrust on body immersed in fluid

FB=ρgVF_B = \rho g VFB​=ρgV

• Floating & Submerged Bodies: Archimedes’ Principle

• Manometers & Pressure Measurement: U-tube, differential manometer

🔹 4. Solved Examples (PYQ Style)

Example 1 (GATE ME 2017):
Calculate pressure at 5 m depth in water (ρ=1000kg/m3\rho = 1000 kg/m^3ρ=1000kg/m3).

$$p=\rho gh=1000\ast 9.81\ast 5\approx 49.05kPa$$

Example 2 (PSU Exam):
A body of volume 0.02 m³ floats in water. Determine buoyant force.

FB=ρgV=1000∗9.81∗0.02≈196.2NF_B = \rho g V = 1000*9.81*0.02 ≈ 196.2 NFB​=ρgV=1000∗9.81∗0.02≈196.2N

🔹 5. Practice Exercises

1. Calculate pressure at given depth in water and oil.

2. Determine buoyant force on submerged sphere.

3. Explain Pascal’s law with example.

4. Compute density of fluid from manometer reading.

5. Identify fluid properties affecting flow in pipe networks.

🔹 6. Summary

• Fluid Properties: Density, viscosity, specific gravity, compressibility

• Pressure: p = F/A, variation with depth, Pascal’s law

• Hydrostatics: Buoyancy, Archimedes’ principle, floating bodies

• Applications: Pumps, pipelines, hydraulic machines