Properties of Fluids
Density (
where:
= density (kg/m³) = mass of the fluid (kg) = volume of the fluid (m³)
Dynamic Viscosity (
where:
= shear stress (Pa) = velocity gradient (s⁻¹)
Pressure (
where:
= pressure (Pa or N/m²) = force (N) = area (m²)
Volumetric Flow Rate (Q)
The amount of fluid passing through a cross-section in a unit of time.
where:
is the volumetric flow rate (m³/s) is the cross-sectional area (m²) is the fluid velocity (m/s)
Hydrostatics
Hydrostatic Pressure (P)
The pressure in a fluid due to its depth.
where:
is the pressure (Pa) is the density of the fluid (kg/m³) is the acceleration due to gravity (9.81 m/s²) is the height or depth (m)
Absolute Pressure (Pₐ)
The sum of atmospheric pressure and hydrostatic pressure.
where:
is the absolute pressure (Pa) is the atmospheric pressure (~101,325 Pa at sea level)
Pascal’s Principle
Transmission of pressure in fluids
where:
is the force applied on piston 1 (N) is the area of piston 1 (m²) is the force applied on piston 2 (N) is the area of piston 2 (m²)
Archimedes’ Principle
The buoyant force or flotation force (E) on an object submerged in a fluid is equal to the weight of the fluid displaced.
where:
is the buoyant force (N) is the density of the fluid (kg/m³) is the volume of fluid displaced (m³) is the acceleration due to gravity (9.81 m/s²)
Conservation Principles
Continuity Equation
Conservation of Mass
where:
and = areas of the cross-sections (m²) and = fluid velocities in sections 1 and 2 (m/s)
Bernoulli’s Theorem
Bernoulli’s Equation
where:
= pressure of the fluid (Pa) = density of the fluid (kg/m³) = velocity of the fluid (m/s) = acceleration due to gravity (m/s²) = height (m)
Fluid Flow
Laminar and Turbulent Flow
Reynolds Number (
where:
= characteristic length (m) = velocity of the fluid (m/s)
Navier-Stokes Equations
- Navier-Stokes Equations (simplified form for an incompressible fluid):
Hydraulics
Flow in Pipes
Head Loss due to Friction (Darcy-Weisbach Equation)
where:
= head loss (m) = friction factor = length of the pipe (m) = diameter of the pipe (m) = acceleration due to gravity (m/s²)
Flow in Open Channels
Energy Equation for Flow in a Channel
where:
= total energy height (m) = height above the reference level (m)
Torricelli’s Theorem
Exit Velocity of a Fluid Through an Orifice
where:
= height of fluid above the orifice (m)
Non-Newtonian Fluid Flow
Bingham Model
Shear Stress
where:
= minimum shear stress (Pa)
Power Law Model
Viscosity
where:
= consistency coefficient = flow index