Fluid mechanics ka ek fundamental concept hai fluid properties, jo density, specific gravity, viscosity, surface tension, compressibility jaise characteristics define karte hain. Density aur specific gravity basic yet most important properties hain, jo hydraulics, fluid flow, buoyancy, ship design, and chemical engineering me extensively use hoti hain.
1. Introduction to Fluid Properties
Fluid:
A substance that deforms continuously under the action of shear stress, no matter how small the stress is.
Fluids do types ke hote hain:
- Liquids → nearly incompressible, definite volume, indefinite shape
- Gases → compressible, indefinite volume and shape
Fluid properties determine behavior under forces, motion, and interaction with surroundings.
Density aur specific gravity are the first step in understanding fluids.
2. Density of a Fluid
2.1 Definition
Density (ρ) is defined as the mass of a substance per unit volume.
ρ=mV\rho = \frac{m}{V}ρ=Vm
Where:
- ρ\rhoρ = density (kg/m³)
- mmm = mass of fluid (kg)
- VVV = volume occupied (m³)
2.2 Units of Density
- SI unit → kg/m³
- CGS unit → g/cm³ (1 g/cm³ = 1000 kg/m³)
2.3 Variation with Temperature and Pressure
- Liquids: slight density change with pressure, decreases with temperature
- Gases: highly compressible → density changes significantly with P and T
Ideal gas relation for density: ρ=PMRT\rho = \frac{P M}{R T}ρ=RTPM
Where:
- P = pressure, Pa
- M = molar mass, kg/mol
- R = universal gas constant, 8.314 J/mol·K
- T = absolute temperature, K
2.4 Specific Weight
Specific weight (γ) = weight per unit volume
γ=WV=ρg\gamma = \frac{W}{V} = \rho gγ=VW=ρg
- g = acceleration due to gravity (9.81 m/s²)
- Units: N/m³
Applications:
- Hydrostatic pressure calculation
- Engineering structures (dams, tanks)
3. Specific Gravity
3.1 Definition
Specific Gravity (SG) is the ratio of the density of a fluid to the density of a reference substance (usually water at 4°C):
SG=ρfluidρwaterSG = \frac{\rho_{fluid}}{\rho_{water}}SG=ρwaterρfluid
- Dimensionless quantity (no units)
- Indicates whether fluid is lighter or heavier than water
3.2 Relation with Density
ρfluid=SG×ρwater\rho_{fluid} = SG \times \rho_{water}ρfluid=SG×ρwater
- SG > 1 → heavier than water
- SG < 1 → lighter than water
Examples:
- Mercury: SG ≈ 13.6 → very dense
- Oil: SG ≈ 0.8 → floats on water
3.3 Applications of Specific Gravity
- Buoyancy calculations → Archimedes principle
- Hydrometer readings → measure liquid density
- Petroleum industry → classify fuels
- Civil Engineering → soil and fluid analysis
4. Measurement of Density
4.1 Using Hydrometer
- Device floats in liquid → density determined from buoyant force
- Calibration scale → SG or ρ
4.2 Using Pycnometer
- Known volume flask filled with liquid
- Mass measured → density calculated:
ρ=mliquidVpycnometer\rho = \frac{m_{liquid}}{V_{pycnometer}}ρ=Vpycnometermliquid
4.3 Using Mass and Volume
- Measure mass using balance, volume using container
- Calculate density: ρ = m/V
5. Hydrostatic Pressure and Density
Hydrostatic pressure: Pressure due to weight of fluid column P=ρghP = \rho g hP=ρgh
- ρ = density, g = gravity, h = height of fluid
- Applications: water supply systems, dams, submarines
Example:
- Water column height h = 10 m
- ρ = 1000 kg/m³, g = 9.81 m/s²
P=1000×9.81×10=98100 Pa≈0.981 barP = 1000 \times 9.81 \times 10 = 98100 \, Pa \approx 0.981 \, barP=1000×9.81×10=98100Pa≈0.981bar
6. Buoyancy and Archimedes Principle
A body immersed in a fluid experiences an upward buoyant force equal to the weight of fluid displaced:
Fb=ρfluidgVdisplacedF_b = \rho_{fluid} g V_{displaced}Fb=ρfluidgVdisplaced
- SG determines whether object floats or sinks
- Applications: ship design, submarine buoyancy control, hydrometers
7. Density of Gas Mixtures
- For gas mixture:
ρmix=PMavgRT\rho_{mix} = \frac{P M_{avg}}{R T}ρmix=RTPMavg
- M_avg = average molar mass of mixture
- Important for combustion, air conditioning, chemical engineering
8. Temperature Dependence of Density
- Liquids:
ρT=ρ0[1−β(T−T0)]\rho_T = \rho_0 [1 – \beta (T – T_0)]ρT=ρ0[1−β(T−T0)]
- β = coefficient of volumetric expansion
- Gases (ideal):
ρ∝1T(at constant P)\rho \propto \frac{1}{T} \quad (at \, constant \, P)ρ∝T1(atconstantP)
9. Density of Mixtures and Solutions
- Liquid-Liquid mixtures
ρmix=m1+m2V1+V2\rho_{mix} = \frac{m_1 + m_2}{V_1 + V_2}ρmix=V1+V2m1+m2
- Solute in solvent
- Example: sugar solution → density increases with concentration
- SG used to express concentration
10. Practical Applications
- Hydraulic Engineering: Dam design, pressure calculation
- Petroleum Industry: SG for fuel classification
- Food Industry: Density measurement for syrups, juices
- Marine Engineering: Buoyancy, ship stability
- Medical Science: Density of blood, body fluids
11. Examples
Example 1: Density of Water at 25°C
- Mass = 250 g, Volume = 250 cm³
ρ=mV=250250=1 g/cm3=1000 kg/m3\rho = \frac{m}{V} = \frac{250}{250} = 1 \, g/cm³ = 1000 \, kg/m³ρ=Vm=250250=1g/cm3=1000kg/m3
Example 2: Specific Gravity of Oil
- Oil density = 800 kg/m³, water density = 1000 kg/m³
SG=8001000=0.8 (<1,floatsonwater)SG = \frac{800}{1000} = 0.8 \, (<1, floats on water)SG=1000800=0.8(<1,floatsonwater)
Example 3: Hydrostatic Pressure
- Tank filled with oil, ρ = 900 kg/m³, h = 5 m
P=ρgh=900×9.81×5=44,145 Pa≈0.44 barP = \rho g h = 900 \times 9.81 \times 5 = 44,145 \, Pa \approx 0.44 \, barP=ρgh=900×9.81×5=44,145Pa≈0.44bar
12. Graphical Representation
- Density vs Temperature → decreases with increasing temperature
- Specific Gravity vs Concentration → linear relation in dilute solutions
- Hydrostatic Pressure Distribution → linear with depth
P
|
| *
| *
| *
| *
|___*________ h
13. Summary Table
| Property | Symbol | Formula / Definition | Units |
|---|---|---|---|
| Density | ρ | ρ = m/V | kg/m³ |
| Specific Gravity | SG | SG = ρ_fluid / ρ_water | Dimensionless |
| Specific Weight | γ | γ = ρ g | N/m³ |
| Hydrostatic Pressure | P | P = ρ g h | Pa / N/m² |
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