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HW1_SOLUTIONS

HW1_SOLUTIONS - ENU 4134 Homework Assignment#1 SOLUTIONS...

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ENU 4134 – Homework Assignment #1 SOLUTIONS – Fall 2011 – D. Schubring 1 ENU 4134 – Homework Assignment #1 SOLUTIONS – Fall 2011 Task 1. Average Parameters (10 points) Compute the following (1 point for ﬁrst 8 items, 2 for last): a. Compute the time-averaged ﬂow quality, x . x = ˙ m g ˙ m f + ˙ m g (1) x = 0 . 15 0 . 15 + 0 . 45 (2) x = 0 . 250 (3) b. Compute the time-average superﬁcial velocities, { j f } and { j g } . Liquid { j f } = ˙ m f ρ f A (4) { j f } = 4 ˙ m f ρ f πD 2 (5) { j f } = 4 × 0 . 45 1000 π × 0 . 03 2 (6) { j f } = 0 . 637 m s - 1 (7) Gas { j g } = ˙ m g ρ g A (8) { j g } = 4 ˙ m g ρ g πD 2 (9) { j g } = 4 × 0 . 15 150 π × 0 . 03 2 (10) { j g } = 1 . 41 m s - 1 (11) Need both, with units, for the point. c. Compute the volume-averaged void fraction, < α > . The volume-averaged void fraction over the entire tube is the same as that over an arbitrary 16 cm axial section. There are two types of coherent structure moving, but they travel at one speed. Therefore, h α i = { e α } = g { α } < α > = V g V (12) V g = πD 2 slug L slug 4 + 9 × πD 3 bubble 6 (13)

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ENU 4134 – Homework Assignment #1 SOLUTIONS – Fall 2011 – D. Schubring 2 V g = π 0 . 025 2 × 0 . 07 4 + 9 × π × 0 . 01 3 6 (14) V g = 4 . 71 × 10 - 6 + 3 . 43 × 10 - 5 (15) V g = 3 . 90 × 10 - 5 m (16) V = πD 2 L 4 (17) V = π 0 . 01 2 × 0 . 16 4 (18) V = 1 . 13 × 10 - 4
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HW1_SOLUTIONS - ENU 4134 Homework Assignment#1 SOLUTIONS...

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