Averaging_Example_StudentWork_solution

# Averaging_Example_StudentWork_solution - An Example of...

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An Example of Averaging Parameters 1 Air and water flow at high pressure (about 80 atmospheres) in a round tube. A slug flow forms. The geometry – cylindrical slugs of gas along the centerline, liquid everywhere else – is shown below. Assume upflow as shown. Assume a single gas velocity and a single liquid velocity apply everywhere. Diameter: 0.01 m Diameter: 0.0071 m 0.02 m 0.08 m Given the following (take phase densities as constants and mass flow rates as time averages). ρ g = 100 kg m - 3 (1) ρ f = 1000 kg m - 3 (2) ˙ m g = 0 . 005 kg s - 1 (3) ˙ m f = 0 . 05 kg s - 1 (4) Assume the gas slugs are coherent, periodic structures – they all travel at the same speed and keep constant distance between one another. Compute the following: 1. Compute the time-averaged flow quality, x . x = ˙ m g ˙ m f + ˙ m g (5) x = 0 . 005 0 . 05 + 0 . 005 (6) x = 0 . 0909 (7) 2. Compute the time-average superficial velocities, { j f } and { j g } . Liquid { j f } = ˙ m f ρ f A (8) { j f } = 4 ˙ m f ρ f πD 2 (9)

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An Example of Averaging Parameters 2 { j f } = 4 × 0 . 05 1000 π × 0 . 01 2 (10) { j f } = 0 . 637 m s - 1 (11) Gas { j g } = ˙ m g ρ g A (12) { j g } = 4 ˙ m g
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