Advanced Fluid Mechanics

Name: Advanced Fluid Mechanics
Rating: 4.5 (102 reviews)

Master Advanced Fluid Dynamics: In-Depth Concepts, Differential Equations, Dimensional Analysis & Practical Applications

Created byProf. Samer

Last updated 9/2020

English

What you'll learn

Understand how the differential equation of conservation of mass and the differential linear momentum equation are derived and applied
Calculate the stream function and pressure field, and plot streamlines for a known velocity field
Obtain analytical solutions of the equations of motion for simple flow fields
Understand dimensional analysis and similarity, principle of dimensional homogeneity Pi theorem, non-dimensionalization of basic equations
Understand concepts of inviscid, low Reynolds number, high Reynolds number, laminar and turbulent flow.
Identify and discuss the features of external flow
Calculate boundary layer parameters for flow past a flat plate
Calculate the lift and drag forces for various objects

Course content

6 sections • 86 lectures • 19h 3m total length

The Acceleration Field of a Fluid13:34
Example 14:01
Compute acceleration from the velocity field V = 3 t i + x j + t y^2 k by separating convective and local terms to obtain a_x, a_y, a_z.
Example 23:26
Analyze the one-dimensional velocity distribution u = V0(1 + 2x/a) and convective acceleration a_x = u du/dx, then compute entrance acceleration in g's for V0 = 10 ft/s and a = 6 inches, about 37 g.
The Differential Equation of Mass Conservation10:44
Example 31:37
Solve example three by finding the condition on the velocity field that yields an incompressible flow and satisfies the continuity equation for mass conservation in advanced fluid mechanics.
Example 41:56
Apply the continuity equation for incompressible flow to determine the form of the velocity components and their dependence on x, y, z, and time.
Linear and Shear Strain Rates20:03
Explore linear and shear strain rates in a two-dimensional incompressible flow. Derive epsilon_xx, epsilon_yy, and epsilon_xy from velocity gradients and examine volumetric dilation.
Navier-Stokes Equation23:20
Example 520:30
Example 65:37
The Stream Function11:20
Example 713:16
The Stream Function in Cylindrical Coordinates11:51
Vorticity and Irrotationality17:42
Frictionless Irrotational Flow20:34
Velocity Potential11:07
Explore the velocity potential phi for irrotational flow, relate velocity as the gradient of phi, and show streamlines orthogonal to potential lines, with spacing affecting speed.
Example 816:02
Analyze two-dimensional flow around a 90-degree corner, derive the velocity field, and show the flow is rotational with nonzero vorticity. Use Bernoulli between same-elevation points to relate pressures.
Example 94:31
Example 105:22
analyze a two-dimensional incompressible flow, verify continuity, derive velocity potential phi = 2x + 2y, and show the pressure gradient in x at x = 2 ft is zero.
Potential Flow: Uniform Flow9:51
Potential Flow: Source and Sink8:44
Potential Flow: Vortex20:19
Potential Flow: Doublet24:09
Example 113:48
Explores a draining tank that forms a vortex, deriving the surface shape from a three-vortex velocity potential and Bernoulli’s principle, linking surface elevation to the vortex circulation.
Example 123:20
Example 1310:39
Examine a tornado-like rotating flow with solid body rotation in inner and outer regions, deriving the velocity profile and pressure distribution, revealing the eye as the point of minimum pressure.
Superposition of Potential Flows: Source in a Uniform Stream—Half-Body20:30
Example 1410:09
flow over a half-body hill: a 40 mph wind accelerates to 47.4 mph above the origin, with a 100 ft elevation; Bernoulli and mass conservation show P2 < P1.
Superposition of Potential Flows: Rankine Ovals23:02
Superposition of Potential Flows: Flow Around a Cylinder35:36
Explore potential flow around a circular cylinder by superposing uniform flow and a doublet, deriving velocity and pressure, and noting drag, zero lift, and dalembert paradox.
Superposition of Potential Flows: Flow Around a Rotating Cylinder27:30
Example 155:14
Example 168:47
Apply a dimensionless length relation to determine the geometry, yielding a length of 13.1 feet. Use a bisection root-finding method on f(h/a)=0 to find a thickness of 3.3 feet.
Example 176:45

Couette Flow between a Fixed and a Moving Plate6:25
Flow Due to Pressure Gradient between Two Fixed Plates7:15
Explain how a pressure gradient between two fixed plates drives parabolic flow, yielding a velocity profile that is zero at the walls and maximum at the center.
Example 115:13
demonstrates flow between parallel plates driven by a pressure gradient, derives wall shear stress, analyzes vorticity and stream function, and relates average velocity to maximum velocity for a parabolic profile.
Fully Developed Laminar Pipe Flow26:16
Explain fully developed laminar pipe flow with a parabolic velocity profile, boundary layer concepts, and the link between pressure drop, volumetric flow, and wall shear.
Example 24:18
Flow between Long Concentric Cylinders12:21
Derives the tangential velocity profile for steady, axisymmetric flow between a rotating inner cylinder and a fixed outer cylinder, showing zero radial velocity and solving for V_theta(r) with boundary conditions.

Introduction17:43
The Pi Theorem17:54
Example 19:30
Learn to rewrite centrifugal pump power as a dimensionless relation using Buckingham pi theorem. Derive flow and power coefficients and a Reynolds-like parameter for rotating centrifuges.
Example 215:41
Analyze incompressible pipe flow with non-slip walls and surface roughness, linking wall shear stress to friction, velocity profile, Reynolds number, and viscosity via dimensionless groups.
Example 312:13

Reynolds Number Regimes14:18
Explore Reynolds number regimes in pipe flow, identifying laminar, transitional, and turbulent flows and the critical Reynolds number around 2300; learn how hydraulic diameter influences calculations.
The Entrance Region10:07
Explore how a boundary layer forms at pipe inlets, creating an entrance region where velocity rises from zero at the wall to center line maximum, then develops with shear stress.
Laminar Flow in Pipes8:00
Example 15:31
Turbulent Velocity Profile10:19
The Moody Chart6:34
Example 29:26
Example 39:29
Example 46:27
Minor Losses40:49
Explore minor losses in pipe flows, including sudden contractions and expansions, elbows, tees, valves, and entrance losses, and learn how loss coefficients determine head loss.
Example 519:26
Example 610:42
Piping Systems with Pumps and Turbines13:33
Series and Parallel Pipes4:42
Analyze three parallel pipes where the area-velocity product is constant. The total flow equals the sum of individual flows while head loss is the same across all pipes.
Three-Reservoir Junction6:16
Solve a three-reservoir junction using mass conservation at junction J and energy equations between reservoirs A, B, and C, accounting for major head losses and iteration.
Example 722:43
Solve for the total flow rate and branch flows in two parallel pipes pumped from a lower reservoir to a higher one, using energy equations, friction factors, Reynolds numbers, and iterative solution.
Example 818:59
Example 921:11
Pipe Flowrate Measurement12:45
Explore pipe flowrate measurement with venturi, orifice, and nozzle meters, noting gradual contractions to minimize losses and how discharge coefficients and Reynolds number affect actual versus ideal flow.
Example 1010:23

Boundary Layer on a Flat Plate7:32
Momentum Integral Estimates: Boundary Layer Thickness24:44
Momentum Integral Estimates: Drag Force and Drag Coefficient11:05
Momentum Integral Estimates: Displacement Thickness11:13
The Boundary Layer Equations24:08
Develop the boundary layer equations for a thin, two-dimensional incompressible flow under no separation. Obtain the simplified continuity and x-momentum equations, with pressure treated as constant across the boundary layer.
Blasius Solution: PDE to ODE25:29
Blasius Solution: The Numerical Shooting Method13:11
Blasius Solution: Displacement Thickness, Drag and Drag Coefficient7:04
Turbulent Boundary Layer Flow28:52
Describe the turbulent boundary layer over a flat plate, from laminar-to-turbulent transition, using the 1/7 power-law velocity profile, and connect momentum thickness to drag coefficient and wall shear stress.
Example 111:05
This lecture models a hydrofoil as a flat plate in seawater, estimating boundary layer thickness, Reynolds number, laminar–turbulent transition, and roughness effects to compute drag.
Example 211:43
Analyze a 40 cm square duct where boundary layer displacement thickness accelerates core flow; apply continuity and Bernoulli to compute exit velocity and pressure drop.
Example 310:28
solves for downstream pitot position X for laminar boundary layer over a flat plate using a pitot tube and an oil manometer to relate pressure to velocity.
Boundary Layers with Pressure Gradients25:29
Drag Coefficient Data for Various Objects17:03
Flow over an Airfoil: Generation of Lift31:52
Example 49:57
Example 53:13
Advanced fluid mechanics: analyze how drag coefficient changes with windows and roof configurations, from 0.35 to about 0.425–0.45, and determine equal power speed, about 59.78 mph.
Example 69:54
Advanced fluid mechanics compares a square flat plate in cases a and b: case a has thicker boundary layer and higher drag than case b, whose boundary layer is thinner.
Example 78:16
Example 89:54

Requirements

Physics and Calculus
Fundamentals of Fluid Mechanics Course

Description

Dive into our Advanced Fluid Mechanics course, designed as a continuation of our Fundamentals of Fluid Mechanics course. This comprehensive program covers essential topics and concepts, offering deeper insights and advanced applications in fluid dynamics.

In this course, you will explore:

Differential Relations: Gain a deeper understanding of fluid particles, fluid acceleration, the Continuity equation, Potential flows, and the Navier-Stokes equation.
Dimensional Analysis & Similarity: Learn about the principle of dimensional homogeneity, the Pi theorem, non-dimensionalization of basic equations, and the challenges of modeling.
Flow in Ducts & Boundary Layer Flows: Examine pressure drop calculations, minor losses in fittings, and the energy equation applied to pumps and turbines.
Flow Over Immersed Bodies: Delve into drag and lift calculations, essential for analyzing fluid motion and optimizing designs.
MATLAB Codes for Potential Flows: Access MATLAB codes, enhancing your computational skills in fluid dynamics and facilitating potential flow analysis.
Advanced Applications & Real-World Examples: Discover practical applications and real-world examples, enabling you to apply your knowledge to complex fluid dynamics problems.
Hands-On Learning & Problem Solving: Engage in hands-on learning and problem-solving activities to reinforce your understanding and develop your skills.
Expert Guidance & Support: Benefit from expert guidance and support throughout the course, ensuring a thorough understanding of the material and the ability to apply it effectively.

Enroll in our Advanced Fluid Mechanics course today to expand your knowledge and skills in fluid dynamics. Master the continuation of the Fundamentals of Fluid Mechanics and boost your expertise, opening up new opportunities in your academic and professional pursuits.

Who this course is for:

Engineering Students

Advanced Fluid Mechanics

What you'll learn

Explore related topics

Course content

Differential Relations for Fluid Flow34 lectures • 7hr 15min

Approximate Solutions of the Navier-Stokes Equation6 lectures • 1hr 12min

Dimensional Analysis and Similarity5 lectures • 1hr 13min

Viscous Flow in Ducts20 lectures • 4hr 22min

Flow Past Immersed Bodies20 lectures • 5hr 2min

Bonus Section: Coupons for all courses1 lecture • 1min

Requirements

Description

Who this course is for: