Fluid Dynamics: Key Concepts and Principles
Fluid Energy
- Kinetic Energy
- Potential Energy
- Internal Energy
Kinematic Viscosity
Dynamic Viscosity/Density
Streamlines
Tangent to flow velocity. Velocity potential is zero when the flow is irrotational or vorticity is “0”.
Bernoulli’s Equation is Applicable When
- Along a Streamline
- Inviscid
- Steady
- Incompressible
- No work is done
- No heat transfer
Bernoulli Equation was Developed by
Daniel Bernoulli and Leonhard Euler
Apply Shear Stress
- Solids: Will stop deforming
- Fluids: Continuously deform
Gage Pressure
Positive Pressure > ATM Pressure.
Vacuum Pressure
Negative Pressure < ATM
Newtonian Fluid
Shear stress is proportional to the velocity gradient, has constant viscosity, 0 shear rate @ 0 shear stress.
Center of Gravity
Where the total weight of the body is assumed to be concentrated.
Center of Pressure
The average location of where the pressure force is applied. The total sum of pressure acts on a body. In uniform gravity, it is the same as the center of mass.
Air Incompressible
When moving slower than Mach 0.3
Air Compressible
When velocity exceeds Mach 0.3
Mass Flow Rate
Use velocity normal to the surface.
Vane Flow
Find the angle of the force applied to the flow from the horizontal angle of 90 degrees.
Kinetic Energy Correction Factor
Use when velocity is not uniform, and the 1D energy equation cannot be used. It avoids integral equations, and the 1D energy equation can be used with a small adjustment.
Solve for Fluid Properties (3 Velocity components & Pressure in incompressible flow)
Solve for Continuity Equation, & Navier Stokes equations.
Given Velocities as functions of (x,y) in 2D, find Streamlines
Find the stream function. Constant lines of the stream function represent streamlines.
Incompressible Flow
Fluid density is nearly constant in a fluid. In a gas, it is incompressible when the flow Mach number is less than 0.3.
Streamline, Pathline, and Streakline are the same when there is Steady Flow (independent of time)
Streamline
Everywhere tangent to the velocity vector.
Pathline
The actual path traversed by a fluid particle.
Streakline
The curved line of particles that earlier passed through a point.
Reynolds Number
Represents the ratio of inertial force to viscous force.
Reynolds Transport Theorem (RTT)
Converts System Analysis into Control Volume Analysis.
Wing Generates Lift via Bernoulli Principle
High flow velocity on top generates low pressure & low velocity on the bottom generates high pressure. The pressure difference between the top and bottom generates a lifting force.
Convective Acceleration becomes NON-ZERO when a Fluid Passes through a region where velocity is spatially varying (such as a NOZZLE or DIFFUSER)
Pressure Head in Manometer
P/Specific Weight
Surface Tension
Surface molecules are less dense with only 1/2 of neighbors, and the effect on the surface is tension.
Pascal’s Law
Any 2 points at the same elevation in a continuous mass of the same static fluid will be at the same pressure.
Continuum Assumption
Variation in properties is so smooth that differential calculus can be used to analyze the substance.
Viscosity
A quantitative measure of a fluid’s resistance to flow.
Capillary Tube
Water rises, but mercury reduces height because the contact angle for water is 0 & mercury is 130.
Find Center of Pressure (Hydrostatic)
The moment of elemental force about the centroid should equal the moment of resultant pressure force that acts on the center of pressure.
2nd Buoyancy Law
A floating body displaces its own weight in the fluid in which it floats.
Mercury Barometer
Measures local ATM Pressure.
Manometer
Measures pressure differences between 2 points using a static column.
Stagnation Pressure
The highest possible pressure in a flow.