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Unformatted text preview: outX ³ ˙ m i ~ V i ´ in (7) Pressure Forces on Surface General form: ~ F press = Z CS p (~ n ) dA (8) Uniform pressure, p a : ~ F UP = Z CS p a (~ n ) dA (9) ~ F UP =p a Z CS ~ ndA = 0 (10) Deﬁne a gauge pressure and simplify equation for ~ F press : p gage = pp a (11) ~ F press = Z CS ( pp a ) (~ n ) dA (12) ~ F press = Z CS p gage (~ n ) dA (13) NonUniform Momentum Flux Actual outlets/inlets are ducts of various shapes, such that ~ V is not constant across their crosssection. As a result Z u ρ ~ V · ~ ndA = Z ρ u 2 dA = ρ Z u 2 dA = β ˙ mV av (14) β > 1 (15) For laminar (usually slow speed or high viscosity or very small tube) ﬂow in a round tube/pipe, β = 4 / 3. (Not necessarily negligible.) For turbulent ﬂow, β ≈ 1 . 011 . 04. (Usually negligible.) Inclass examples: 341, 349, 353, 392/393...
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 Spring '11
 Schubring
 Force, Fpress

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