Unformatted text preview: pressure tap, and a deflection of 10 cm is measured. What is the velocity at station 2? p + γz + ρv s = constant 22 v p + z + s = constant γ 2g
2 Lagrangian vs. Eulerian descriptions
Lagrangian: follow particle: Bernoulli (follows streamline) Eulerian: measure local velocities, etc.: Continuity …before continuity Volume and mass flow rates and mass flow rates Volume and mass discharge
Imagine a wire ring With cross section A m2 A Vector calculusreview
Force and velocity are vectors and important quantities in fluid mechanics dot product between two vectors b a θ a ⋅ b = AB cos θ
a = ( ai, aj, ak )
2 A ≡ a = ai2 + a2 + ak j Place this ring in so that it area is normal to a fluid flow of average speed V m/s V Q = v ⋅ nA = VN cos θA = V cos θA
Fluid Volume passing through the ring per second If the ring is placed at an angle to the flow v n v Magnitude Q = VA m3/s
n Unit outward normal Vector with unit magnitude (N =1) in direction normal to a surface A Q = v ⋅ nA = VN cos θA = V cos θA
dot product Mass Rate crossing the surface is m = ρQ v ⋅ n = VN cos θ = V cos θ So dotproduct gives Magnitude of vector u in direction of outward normal 2 5.3 (8th ed) 5.7 (9th ed)
A pipe with a 2 m diameter carries water having a velocity of 4 m/s. What is the discharge in cubic meters per second and in cubic feet per second? 3...
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 Fall '08
 KimberlyHill
 Fluid Dynamics, Vector Space, Dot Product, Force, Mass flow rate, mass flow rates

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