Chapter04

Mechanics of Fluids

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50 CHAPTER 4 The Integral Forms of the Fundamental Laws 4.1 a) No net force may act on the system: Σ v F = 0. b) The energy transferred to or from the system must be zero: Q - W = 0 . c) If 3 3 2 ˆ ˆ ˆ 10 ( ) 0 n V V n i j = = ⋅ - = v is the same for all volume elements then Σ v v F D Dt V dm = , or Σ v v F D Dt mV = ( ). Since mass is constant for a system Σ v v F m DV Dt = . Since DV Dt a F ma v v v v = = , . Σ 4.2 Extensive properties: Mass, m ; Momentum, mV v ; kinetic energy, 1 2 mV 2 ; potential energy, mgh ; enthalpy, H . Associated intensive properties (divide by the mass): unity, 1; velocity, v V ; V 2 /2; gh ; H/m = h (specific enthalpy). Intensive properties: Temperature, T ; time, t ; pressure, p ; density, r ; viscosity, m . 4.3 ( B ) 4.4 System ( ) t V = 1 c.v.( ) t V = 1 System ( ) t t V + ∆ = 1 V + 2 c.v.( ) t t V + ∆ = 1 4.5 System ( ) t V = 1 V + 2 c.v.( ) t V = 1 V + 2 System ( ) t t V + ∆ = 2 V + 3 c.v.( ) t t V + ∆ = 1 V + 2 1 2 1 2 3 pump
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