© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 6 Incompressible Inviscid Flow.

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Presentation transcript:

© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 6 Incompressible Inviscid Flow

© Fox, McDonald & Pritchard Main Topics Momentum Equation for Frictionless Flow: Euler’s Equation Euler’s Equation in Streamline Coordinates Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow The Bernoulli Equation Interpreted as an Energy Equation Energy Grade Line and Hydraulic Grade Line

© Fox, McDonald & Pritchard Momentum Equation for Frictionless Flow: Euler’s Equation Euler’s Equation Continuity

© Fox, McDonald & Pritchard Momentum Equation for Frictionless Flow: Euler’s Equation Rectangular Coordinates

© Fox, McDonald & Pritchard Momentum Equation for Frictionless Flow: Euler’s Equation Cylindrical Coordinates

© Fox, McDonald & Pritchard Euler’s Equation in Streamline Coordinates Along a Streamline (Steady Flow, ignoring body forces) Normal to the Streamline (Steady Flow, ignoring body forces)

© Fox, McDonald & Pritchard Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow Euler’s Equation in Streamline Coordinates (assuming Steady Flow)

© Fox, McDonald & Pritchard Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow Integration Along s Coordinate

© Fox, McDonald & Pritchard Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow Bernoulli Equation 1.Steady Flow 2.No Friction 3.Flow Along a Streamline 4.Incompressible Flow

© Fox, McDonald & Pritchard Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow Static, Stagnation, and Dynamic Pressures (Ignore Gravity) Dynamic Static Stagnation

© Fox, McDonald & Pritchard The Bernoulli Equation Interpreted as an Energy Equation

© Fox, McDonald & Pritchard The Bernoulli Equation Interpreted as an Energy Equation Basic Equation 1.No Shaft Work 2.No Shear Force Work 3.No Other Work 4.Steady Flow 5.Uniform Flow and Properties

© Fox, McDonald & Pritchard The Bernoulli Equation Interpreted as an Energy Equation Assumption 6: Incompressible Hence Assumption 7:

© Fox, McDonald & Pritchard The Bernoulli Equation Interpreted as an Energy Equation “Energy Equation” 1.No Shaft Work 2.No Shear Force Work 3.No Other Work 4.Steady Flow 5.Uniform Flow and Properties 6.Incompressible Flow 7.u 2 – u 1 –  Q/  m = 0

© Fox, McDonald & Pritchard Energy Grade Line and Hydraulic Grade Line Energy Equation

© Fox, McDonald & Pritchard Energy Grade Line and Hydraulic Grade Line Energy Grade Line (EGL) Hydraulic Grade Line (HGL)

© Fox, McDonald & Pritchard Energy Grade Line and Hydraulic Grade Line

© Fox, McDonald & Pritchard Irrotational Flow Irrotationality Condition

© Fox, McDonald & Pritchard Irrotational Flow Velocity Potential

© Fox, McDonald & Pritchard Irrotational Flow Velocity Potential automatically satisfies Irrotationality Condition

© Fox, McDonald & Pritchard Irrotational Flow 2D Incompressible, Irrotational Flow

© Fox, McDonald & Pritchard Irrotational Flow Elementary Plane Flows

© Fox, McDonald & Pritchard Irrotational Flow Superposition