Bernoulli_Equation_web

# Bernoulli_Equation_web - ENU 4133 Bernoulli Equation Useful...

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ENU 4133 – Bernoulli Equation January 25, 2011

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Useful for solving problems that are. .. 1. Steady-state, 2. Incompressible, 3. Frictionless, 4. Along a readily-deﬁnable streamline 5. Without heat or work The (calculus-free) equation resulting from the following derivation is termed Bernoulli’s equation are applies only when all the conditions above are met. We will also derive an equation (with two integrals) that applies without the steady-state and incompressible conditions and is sometimes called Bernoulli’s equation.
Schematics Control volume around streamline .

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Conservation of Mass d dt ±Z CV ρ d V ² + ˙ m out - ˙ m in = 0 (1) ∂ρ t d V + d ˙ m 0 (2) d V = Ads (3) d ˙ m = d ( ρ AV ) = - ∂ρ t Ads (4)
Conservation of Momentum, Streamwise Direction X dF s = d dt ±Z CV V ρ d V ² + ( ˙ mV ) out - ( ˙ mV ) in (5) ( ρ V ) t Ads + d ( ˙ mV ) (6) Assume frictionless ﬂow ( dW – diﬀerential weight, not diﬀerential work): dF s , grav = - dW sin θ = - ρ gA sin θ ds = - ρ gAdz (7) dF s , press = 1 2 dpdA - dp ( A + dA ) ≈ - Adp (8)

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## This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.

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Bernoulli_Equation_web - ENU 4133 Bernoulli Equation Useful...

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