# Fluid Mechanics I (ME 311)

In this course, students learn how to analyze fluids at rest (fluid statics) and fluids in motion (fluid dynamics).

**Concept/Derivation videos**

**1.1 - Definition of a fluid**

**1.2 - Pressure**

**1.3 - Absolute pressure and gage pressure**

**1.4 - Density**

**1.5 - Viscosity**

**1.6 - Continuum approximation**

**1.7 - Vapor pressure**

**Demonstration videos (links to non-CPP content)**

**Concept: Comparing the viscosity of various liquids**

Description: Liquids with higher viscosities will flow slower than fluids with lower viscosities, assuming the flow conditions of the liquids are the same. The video also presents a molecular picture of viscosity.

**Concept: Dilitant/shear-thickening fluid #1**

Description: For some non-Newtonian fluids, the viscosity increases with increasing shear stress. In the video, a small kiddie pool is filled with a shear-thickening fluid and people are able to run on its surface without sinking. Notice that the fluid almost behaves like rubber when strong shear stresses are applied, but flows readily when when weak shear stresses are applied.

**Concept: Dilitant/shear-thickening fluid #2**

Description: A larger pool is filled with a shear-thickening fluid. People are able to walk, dance, and bike over the surface, but sink when standing in place.

**Concept: Dilitant/shear-thickening fluid #3**

Description: A shear-thickening fluid allows a slow-moving ruler to easily penetrate its surface, but can resist violent blows from a sledgehammer.

**Concept: Surface tension**

Description: Although aluminum has a greater density than water, it is possible to float aluminum coins on the surface of a body of water because the surface tension of water provides a sufficiently large upward force. When liquid soap is added to water, the surface tension of the resulting water/soap mixture is lowered and it is now insufficient to prevent the aluminum coins from sinking. Materials that lower surface tension are called "surfactants."

**Concept/Derivation videos**

**2.1 - Pascal's Law**

**2.2 - Hydrostatic pressure gradient**

**2.3 - Hydrostatic pressure distribution**

**3.1 - Introduction to manometers**

**3.2 - Barometers**

**3.3 - Piezometer tube manometers**

**3.4 - U-tube manometers**

**3.5 - Inclined tube manometers**

**4.1 - Hydrostatic force on a plane surface**

**4.2 - Center of pressure on a plane surface**

**4.3 - Hydrostatic force on a curved surface**

**5 - Archimedes' principle & buoyancy**

**Demonstration videos **** (links to non-CPP content)**

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**Concept: Existence of atmospheric pressure #1**

Description: A 55 gallon drum has a saturated liquid-vapor mixture. During heating, the contents are kept near atmospheric pressure since the cap is off. After the heating is stopped, the contents are sealed near atmospheric pressure. As the drum is cooled, some of the vapor condenses to liquid which lowers the internal pressure until the drum is crushed by atmospheric pressure.

**Concept: Existence of atmospheric pressure #2**

Description: Similar to the last video, an aluminum can initially has a saturated liquid-vapor mixture. As the can is cooled, some of the vapor condenses to liquid which lowers the internal pressure until it is crushed by atmospheric pressure.

**Concept: Existence of atmospheric pressure #3**

Description: A large storage tanker was not vented properly and the pressure inside the tanker became too low. Atmospheric pressure is sufficient to crush the large tanker.

**Concept: Buoyant force of a liquid**

Description: The density of liquid mercury is so high that it exerts a buoyant force large enough for iron cannonballs to float in it.

**Concept: Buoyant force of a gas**

Description: The density of gaseous sulfur hexaflouride is so high that it exerts a buoyant force large enough for air-filled balloons to float in it. Also notice that the gas does not rapidly dissapate into the atmosphere due to its relatively high density.

**Concept: Rigid body rotation **Description: A tank containing water rotates at a certain angular velocity. The water's momentum attempts to carry it away toward the walls, but is kept in check by the pressure of the fluid above it. After the initial sloshing dies down, the water and tank rotate at the same rate and appear as a rigid body, with the free surface forming a paraboloid. The pressure is atmospheric over the entire free surface and the lines of constant pressure (isobars) are parabolic as well.

**Concept/Derivation videos**

**6.1 - Systems & Control Volumes**

**6.2 - Reynolds transport theorem**

**7.1 - Conservation of mass for a control volume**

**7.2 - Conservation of linear momentum for a control volume**

**7.2.1 - Analyzing pressure forces on a control volume**

**7.3 - Conservation of energy for a control volume**

**7.3.1 - Energy grade line (EGL) & Hydraulic grade line (HGL)**

**7.3.2 - The Bernoulli equation**

**7.3.3 - Definition of pump efficiency & turbine efficiency**

**Demonstration videos ****(links to non-CPP content)**

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### Concept/Derivation videos

**8.1 - General Characteristics of laminar and turbulent flows in pipes**

**8.2 - Developing and fully-developed flow in pipes**

**8.3 - Pressure drop and head loss in pipe flow**

**8.4 - Velocity profile of fully-developed laminar flow in pipes**

**8.5 - Velocity profile for fully-developed turbulent flow in pipes**

**8.6.1 - Major losses in circular pipe systems**

**8.6.2 - The Moody chart**

**8.6.3 - Major losses in non-circular ducts**

**8.7 - Minor losses in pipe systems**

**9.1 - Categories of pipe flow**

### Demonstration videos **(links to non-CPP content)**

**Concept: Transition from laminar to turbulent flow**

Description: At lower flow rates, laminar flow is observed as the dye streamline remains unchanged as it travels down the pipe. At higher flow rates, turbulent outburst are observed, followed by turbulent flow.

**Concept/Derivation videos**

**10.1 - Lagrangian vs. Eulerian descriptions of flow**

**10.2 - The material derivative**

**10.3 - Streamlines, streaklines, and pathlines**

**10.4 - Kinematics of fluid elements (translation and linear deformation)**

**10.5 - Kinematics of fluid elements (shear strain, rotation, and vorticity)**

**11.1 - The continuity equation**

**Demonstration videos ****(links to non-CPP content)**

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**Concept: Streaklines and steamlines**

Description: A colored fluid is released at locations upstream from an airfoil, producing streaklines. Since the flow is steady, the streaklines and streamlines are identical.

**Syllabus for Winter 2015 (similar to Fall 2014)**

**Lecture 1 - Fundamental Concepts, Fluid Properties**

**Lecture 2 - Pascal’s Law, Hydrostatic Pressure Variations, Manometry**

**Lecture 3 - Forces on Submerged Surfaces (Part I)**

**Lecture 4 - Forces on Submerged Surfaces (Part II)**

**Lecture 5 - Buoyancy & the Bernoulli Equation**

**Lecture 6 - Bernoulli Equation Examples**

**Lecture 7 - Fluid Statics Examples**

**Lecture 8 - Fluid Kinematics**

**Lecture 9 - Reynolds Transport Theorem, Conservation of Mass, Kinematics**

**Lecture 10 - Continuity Equation, Bernoulli Equation, & Kinematics Examples**

**Lecture 11 - Linear Momentum Equation and Bernoulli Equation Examples**

**Lecture 12 - Linear Momentum Equation Examples**

**Lecture 13 - Energy Equation and Kinematics Examples**

**Lecture 14 - Energy Equation Examples, Differential Continuity Equation**

**Lecture 15 - Navier-Stokes Equations, Conservation of Energy Examples**

**Lecture 16 - Viscous Flow in Pipes, Laminar Pipe Flow Characteristics**

**Lecture 17 - Laminar & Turbulent Pipe Flow, The Moody Diagram**

**Lecture 18 - Minor Losses in Pipe Flow**

**Interview with Dr. John Biddle**

This lecture series was filmed live during Fall 2014 at Cal Poly Pomona.