HW4_SOLUTIONS

# HW4_SOLUTIONS - ENU 4134 – Homework Assignment#4...

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Unformatted text preview: ENU 4134 – Homework Assignment #4 SOLUTIONS – Fall 2011 – D. Schubring 1 ENU 4134 – Homework Assignment #4 SOLUTIONS – Fall 2011 Properties: P = 3 . 978 MPa (1) ρ g = 19 . 98 kg m- 3 (2) ρ f = 799 kg m- 3 (3) k f = 0 . 616 W m- 1 K- 1 (4) k g = 0 . 0495 W m- 1 K- 1 (5) Pr f = 0 . 859 (6) Pr g = 1 . 39 (7) h fg = 1 . 715 × 10 6 J kg- 1 (8) μ f = 1 . 087 × 10- 4 kg m- 1 s- 1 (9) μ g = 1 . 751 × 10- 5 kg m- 1 s- 1 (10) σ = 0 . 02619 N m- 1 (11) R = 461 . 5 J kg- 1 K- 1 (12) Task 1. Liquid Superheat Required for Nucleation at Elevated Pressure – 5 points Calculate the relation between superheat and equilibrium bubble radius for water at 250 ◦ C (Equations 12-7 and 12-8 in T&K). Consider bubbles of 20 μ m radius and get concrete answers. Equation 12-7: T b- T sat = RT b T sat h fg ln 1 + 2 σ p l r (13) T sat = 523 K (14) T b- T sat = 461 . 5 × T b × 523 1 . 715 × 10 6 ln 1 + 2 × . 02619 3 . 978 × 10 6 r (15) T b- T sat = 0 . 1407 T b ln 1 + 1 . 32 × 10- 8 r (16) ψ = 0 . 1407 ln 1 + 1 . 32 × 10- 8 r (17) T b- T sat = T b ψ (18) T b- T sat = ( T b- T sat + T sat ) ψ (19) T b- T sat = ( T b- T sat ) ψ + T sat ψ (20) ( T b- T sat ) (1- ψ ) = T sat ψ (21) T b- T sat = T sat ψ 1- ψ (22) T b- T sat = 523 ψ 1- ψ (23) Equation 12-8: T b- T sat = 2 σ T sat vol fg h fg r (24) ENU 4134 – Homework Assignment #4 SOLUTIONS – Fall 2011 – D. SchubringENU 4134 – Homework Assignment #4 SOLUTIONS – Fall 2011 – D....
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HW4_SOLUTIONS - ENU 4134 – Homework Assignment#4...

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