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Problem 1.41

# Problem 1.41 - T u p p u ρ So the uncertainty in the...

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Problem 1.41 [Difficulty: 2] Given: Air in hot air balloon Hg mm 1 759 ± = p C 1 60 ° ± = T Find: (a) Air density using ideal gas equation of state (b) Estimate of uncertainty in calculated value Solution: We will apply uncertainty concepts. Governing Equations: ρ p R T = (Ideal gas equation of state) 2 1 2 1 1 1 + ± = L x R u x R R x u (Propagation of Uncertainties) We can express density as: ρ 101 10 3 N m 2 × kg K 287 N m × 1 333 K × 1.06 kg m 3 = = ρ 1.06 kg m 3 = 2 1 2 2 + ± = T p u T
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Unformatted text preview: T u p p u ρ So the uncertainty in the density is: 1 1 = = ∂ ∂ RT RT p p Solving each term separately: u p 1 759 0.1318% ⋅ = = 1 2 − = − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ∂ ∂ RT p RT p T T T u T 1 333 0.3003% ⋅ = = ( ) ( ) [ ] ( ) ( ) [ ] 2 1 2 2 2 1 2 2 % 3003 . % 1318 . − + ± = − + ± = T p u u u Therefore: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × ± ± = − 3 3 m kg 10 47 . 3 % 328 . u...
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