Chapter01

Mechanics of Fluids

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1 CHAPTER 1 Basic Considerations 1.1 Conservation of mass — Mass — density Newton’s second law — Momentum — velocity The first law of thermodynamics — internal energy — temperature 1.2 a) density = mass/volume = M L / 3 b) pressure = force/area = F L ML T L M LT / / / 2 2 2 2 = = c) power = force × velocity = F L T ML T L T ML T × = × = / / / / 2 2 3 d) energy = force × distance = ML T L ML T / / 2 2 2 × = e) mass flux = r AV = M/L 3 × L 2 × L/T = M/T f) flow rate = AV = L 2 × L/T = L 3 /T 1.3 a) density = M L FT L L FT L 3 2 3 2 4 / / = b) pressure = F/L 2 c) power = F × velocity = F × L/T = FL/T d) energy = F × L = FL e) mass flux = M T FT L T FT L = = 2 / / f) flow rate = AV = L 2 × L/T = L 3 /T 1.4 ( C ) m = F/a or kg = N/m/s 2 = N . s 2 /m. 1.5 ( B ) [ m ] = [ t/ du/dy ] = ( F / L 2 )/( L / T )/ L = F . T / L 2 . 1.6 a) L = [ C ] T 2 . [ C ] = L/T 2 b) F = [ C ] M. [ C ] = F/M = ML/T 2 M = L/T 2 c) L 3 /T = [ C ] L 2 L 2/3 . [ C ] = L T L L L T 3 2 2 3 1 3 / / / = Note: the slope S 0 has no dimensions. 1.7 a) m = [ C ] s 2 . [ C ] = m/s 2 b) N = [ C ] kg. [ C ] = N/kg = kg m/s 2 kg = m/s 2 c) m 3 /s = [ C ] m 2 m 2/3 . [ C ] = m 3 /s m 2 m 2/3 = m 1/3 /s 1.8 a) pressure: N/m 2 = kg m/s 2 /m 2 = kg/m s 2 b) energy: N m = kg m/s 2 × m = kg m 2 /s 2 c) power: N m/s = kg m 2 /s 3 d) viscosity: N s/m 2 = kg m s s 1 m kg / m s 2 2 =
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