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Unformatted text preview: Fluids • P ( N / m 2 ) = F / A • P atm = 1.01e 5 Pa • P absolute = P gauge + P atm • Density ( ) = ρ m / v • Pressure at a depth: o P = P o + ( ) ρ (g)(h) • Buoyancy & archimedes principle o Floating object: o Immersed object: o Buoyant force = weight of fluid displaced by object • F B = ( ρ L )(v) (g) • Flow rate o Q (m 3 / s ) = (velocity) (area) • Bernoulli’s equation: o P 1 + (1/2) v ρ 1 2 + gh ρ 1 = P 2 + (1/2) v ρ 2 2 + gh ρ 2 o Flow rate = constant • Q 1 = Q 2 • V 1 A 1 = v 2 A 2 Harmonic motion & elasticity • Frequency = 1 /Period • Simple harmonic motion: o Y coordinate = Asin(wt) o X coordinate = Acos(wt) o W = 2 f π • Angular displacement: o = wt Ѳ o T = 2 /w π o f = w/2 π • springs: o F spring = -kx o Frequency for simple harmonic motion: • f = (1/2 ) ( π √ k/m) • simple pendulum: o f = (1/2 ) (g/l) π √ • Torsional oscillator: o Torque directly proportional to twist angle Ѳ o = -k τ Ѳ o k = torsion constant o f = (1/2 ) (k/ π √ I) • stress, strain, Hooke’s law o hooke’s law: • F = -kx o Tensile strain and stress: • Tensile stress = F/A • Tensile strain= L/L Δ o • Force perpen dicular to area • Tensile stress = young’s modulu s x tensile strain o F/ A = y ( Δ L/ L o ) • Shear stress and strain o Shear stress = F/ A o Shear strain = x/ Δ L o o force parallel to area o shear stress = shear modulus x shear strain • F/A = S ( x/L Δ o ) • Harmonic motion and energy: o Amplitude (A) = max displacemen t o P.E. spring = (1/2)kx 2 • If x=x max = A then, P.E....
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This note was uploaded on 02/14/2011 for the course ORGANIC CH 341 taught by Professor Idk during the Spring '11 term at University of Wisconsin.
- Spring '11