CE361 - Lecture 05

# CE361 - Lecture 05 - Water Resources Engineering - Lecture...

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1 Water Resources Engineering -Lecture±5 1 Prepared by T. Wagener & P. Reed Penn State University We’ll look at the following… 1. Momentum (Don’t try this) 2. Pressure and Pressure Forces in Static Fluids 2 Buoyancy Hydrostatic Forces Hoover Dam and Block Momentum taken from Young et al. 2005, Fluid Mech, Wiley Press.

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2 http://focus.msn.de/sport/leichtathletik/goeteborg_aid_23462.html?interface=galerie&drucken=1 Momentum 3 In order to derive the general momentum equation for fluid flow in a hydrologic or hydraulic system, we use the control volume approach along with Newton’s second law . Momentum What does the following derivative represent? () momentum t Solution: 4 2 11 1 ** * * * * * LL m mtF tF o r c e tt t t t == = =
3 Extensive Property = Momentum = m v When applying the control volume approach to fluid momentum, the extensive property is momentum, B = momentum, the extensive property is momentum, B m v (mass times velocity) and the intensive property is the momentum per unit mass, ß = d ( m v )/ dm , so that ( ) ( ) sys dB dm om e n t um v dt dt dt == 5 Newton’s 2 nd Law … states that the time rate of change of momentum is equal to the net force applied in a given direction, so ( ) ma dt momentum d F = = 6 Sum of external forces = Rate of momentum change of system (mass times acceleration)

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4 Remember the General Control Volume Equ. sys d d dd ββ ∀+ B VA [Mays Equation 3.1.13] CV CS dt dt βρ = ∫∫ 7 The total rate of change of extensive property of a flow = The rate of change of extensive property stored in the control volume The net rate of outflow of extensive property through the control surface + Integral Momentum Equation for Fluid Flow Using momentum as extensive/intensive property in the GCVE leads to the following expression, CV CS d Fv d v V d A dt ρρ =∀ + 8
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## This note was uploaded on 05/05/2009 for the course CE 361 taught by Professor Wagener during the Spring '09 term at Penn State.

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CE361 - Lecture 05 - Water Resources Engineering - Lecture...

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