Learning Objectives
After completing this module, you should be able to:
1. Define the acceleration vector and its dependence on space, displacement, and time.
3. Differentiate between local and convective acceleration.
4. Interpret the material derivative notation for acceleration and apply the gradient operator to express convective acceleration.
Videos
Title: M4V1 – Acceleration Vector
Summary: This video lecture covers the acceleration vector, starting with a review of the velocity vector as the time rate change of the displacement vector. It explains how to derive the acceleration vector using the chain rule differentiation, considering both space and time. The lecture distinguishes between local acceleration and convective acceleration; and also introduces the material derivative notation for acceleration.
Learning Objectives: After watching this lecture, you will be able to define the acceleration vector and its dependence on space, displacement, and time, apply chain rule differentiation to derive the acceleration vector, differentiate between local and convective acceleration, and interpret material derivative notation for acceleration.
Transcript: Read the transcript
Slides With Annotations: See the slides
Title: M4V2 –Boundary Layer
Summary: This video lecture revisits concepts related to the interaction of fluid flows with solid surfaces, focusing particularity on the boundary layer phenomena. It explains the no-slip condition, where fluid velocity is zero at the surface. The lecture discusses how the boundary layer forms when fluid velocity changes with distance from the surface, and contrasts this with the free-stream region where velocity remains constant. This video lecture includes examples of velocity profiles as fluid layers interact with stationary of moving solids.
Learning Objectives: After watching this lecture, you will be able to understand the no-slip condition and how it applies at solid-fluid interfaces, define the boundary layer and explain how it develops in various flow scenarios, differentiate between the boundary layer and free-stream flow regions, and analyze velocity profiles in systems with different boundary conditions (e.g., flow between two plates, pipe flow).
Transcript: Read the transcript
Slides With Annotations: See the slides
Title: M4V3 – Newtonian Fluids
Summary: This video lecture on Newtonian fluids covers the concept of viscosity, defined as the internal resistance to flow within a fluid. The lecture explains how viscosity affects the force exerted on a body in a fluid, using examples like jogging in air versus water. The non-slip condition is revisited, and a velocity profile is drawn for a fluid between two plates, illustrating the velocity gradient. Newtonian fluids are defined as those where the rate of deformation (velocity gradient) is linearly related to the applied shear stress.
Learning Objectives: After watching this lecture, you will be able to understand viscosity and its significance as a physical property of fluids, describe how viscosity affects the force exerted on a body in a fluid, explain the no-slip condition and velocity profile, understand the relationship between shear stress and velocity gradient in Newtonian fluids, and differentiate between Newtonian and non-Newtonian fluids
Transcript: Read the transcript
Slides With Annotations: See the slides