You have just completed the syllabus of Fluid Mechanics subject for Mechanical Engineering Branch. Here you will find all the IMPORTANT FORMULAS Of Fluid mechanics subject. Formulas of the first chapter have displayed for your illustration.
CHAPTER 1: FLUID PROPERTIES
Introduction: Fluid is a substance that deforms continuously under the application of shear (tangential) stress no matter how small the stress may be.
Mass density (ρ): It is defined as mass per unit volume.
Weight density or specific weight (w): It is defined as weight per unit volume.
Specific gravity or (relative density S): It is defined as ratio between density of fluid and density of standard fluid i.e., water
Specific gravity of Hg is 13.6.
Specific volume (ν): It is defined as volume per unit mass.
Viscosity (µ): The viscosity of a fluid is a measure of its resistance to deformation at a given rate. Viscosity can be conceptualized as quantifying the frictional force that arises between adjacent layers of fluid that are in relative motion.
Causes of viscosity
- intermolecular force of cohesion.
- molecular momentum exchange.
Kinematic viscosity (ν):
Newton’s Law of Viscosity:
µ = dynamic viscosity of fluid
Fluid Flow Behaviour:
- General Relationship between shear stress and velocity gradient is given by:
- The fluids in which the apparent viscosity increases with increases with velocity gradient(n>1) the fluid is termed as dilatant (shear thickening) fluid.
- The fluids in which the apparent viscosity decreases with increases with velocity gradient(n<1) the fluid is termed as pseudoplastic (shear thinning) fluid.
Surface Tension (σ): Surface tension is the apparent interfacial tensile stress (force per unit length of interface) that acts whenever a liquid has a density interface, such as when the liquid contacts a gas, vapour, second liquid, or a solid. Surface tension is due to intermolecular force.
Gauge pressure inside a water droplet:
Gauge pressure for soap bubble:
Gauge pressure inside a jet of water:
Capillarity: This phenomenon is due to interplay of terms of cohesion and adhesion.
For water: θ = 0°, capillary rise: h=+ve.
For Hg: θ = 130°, capillary fall: h= −ve.
Vapour pressure and Cavitation: The vapour molecules execute a partial pressure in the space above liquid, known as vapour pressure. Cavitation is the formation of vapour bubbles in the liquid flowing through any Hydraulic Turbine.
You can find the formula notes for the rest of the chapters of Fluid Mechanics from below Link
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