Fluid Mechanics Formula Sheet 2 | ME 3340, Study notes of Fluid Mechanics

Download Fluid Mechanics Formula Sheet 2 | ME 3340 and more Study notes Fluid Mechanics in PDF only on Docsity! ME 3340 Fluid Mechanics Formula Sheet 2 Basic Formulas Pressure in a static fluid: g dz dp ρ−= Shear stress in a Newtonian fluid: dy duµτ = Mass balance: 0=⋅+ ∫∫ dSnvdVdt d cV ρρ Momentum balance: dSnvvdVv dt dFF cc c c SV V S sb )( ⋅+=+ ∫∫∑ ∑ ρρ Moment of momentum balance: ( ) dSnvvrdVvr dt dM cc SV )( ⋅×+×= ∫∫∑ ρρ Total energy balance: WQdSnvgzVpudVgzVu dt d cc SV && +=⋅++++++ ∫∫ )()()( 221221 ρρρ Mechanical energy balance with constant density: lSV HWdSnvgzVpdVgzV dt d cc && −=⋅++++ ∫∫ )()()( 221221 ρρρ The mechanical energy loss can be written using the head loss hl, as or using a loss coefficient K, as ll ghmH && = 2 2 1VKmHl && = , where V is the average velocity through the device. The pump head hp is defined as W . pp ghm&& = Material derivative: z w y v x u t v tDt D ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ =∇⋅+ ∂ ∂ = Bernoulli’s equation: constant221 =++∫ gzV dp ρ Basic Constants Standard atmospheric pressure: p0 = 101.33 kPa Acceleration of gravity: g = 9.807 m/s2 Material Properties Water: density, ρ = 1000 kg/m3, viscosity, µ = 1.12 x 10–3 kg/(m.s) Air: density, ρ = 1.23 kg/m3, viscosity, µ = 1.79 x 10–5 kg/(m.s)