Lecture Notes: Properties of Fluid

Introduction

• Topic: Calculating specific weight, density, and specific gravity of a liquid.
• Example problem: Calculate these properties for 1 liter of a liquid weighing 7 Newtons.

Key Concepts and Definitions

• Specific Weight (Weight Density)

  • Denoted by: ( W )
  • Formula: ( W = \frac{\text{Weight}}{\text{Volume}} )
  • Units: Newton per cubic meter (N/m³)

• Density (Mass Density)

  • Denoted by: ( \rho )
  • Formula: ( \rho = \frac{\text{Weight Density}}{g} )
  • Units: Kilograms per cubic meter (kg/m³)

• Specific Gravity

  • Denoted by: ( s )
  • Formula: ( s = \frac{\text{Weight Density of Liquid}}{\text{Weight Density of Water}} )
  • Dimensionless quantity

Given Data

• Volume (( V )): 1 liter = ( 10^{-3} ) m³
• Weight (( W )): 7 Newtons

Problem Solution

Calculate Specific Weight

1. Formula: ( W = \frac{\text{Weight}}{\text{Volume}} )
2. Calculation: ( W = \frac{7}{10^{-3}} = 7000 ) N/m³
3. Specific Weight Answer: 7000 N/m³

Calculate Density

1. Formula: ( \rho = \frac{W}{g} )
2. Calculation: ( \rho = \frac{7000}{9.81} = 713.5 ) kg/m³
3. Density Answer: 713.5 kg/m³

Calculate Specific Gravity

1. Formula: ( s = \frac{\text{Weight Density of Liquid}}{\text{Weight Density of Water}} )
2. Water's weight density: 9810 N/m³
3. Calculation: ( s = \frac{7000}{9810} = 0.7135 )
4. Specific Gravity Answer: 0.7135

Conclusion

• The specific gravity of the liquid (0.7135) indicates it is lighter than water, as it is less than 1.
  • If specific gravity = 1, it's water.
  • If specific gravity > 1, the liquid is heavier than water.

Summary

• We calculated specific weight, density, and specific gravity using the given weight and volume.
• Specific gravity helps determine whether the liquid is lighter or heavier compared to water.