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Gas and oil are flowing at volumetric flow rates g Q =0.29 m3s-1 and l Q =0.015
m3s-1 respectively through a horizontal pipe with internal diameter of d = 0.15
m. Estimate the fraction of gas, the pressure gradient, and the mean velocities
of each phase. The physical properties are given in the Table Q.2. The Fanning
friction factor is f = 0.0045 for both liquid and gas phases.

H84MPS-E1 H84MPS-E1 Turn Over The University of Nottingham Malaysia Campus DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING A LEVEL 4 MODULE, SPRING SEMESTER 2008-2009 MULTIPHASE SYSTEMS Time allowed TWO Hours Candidates may complete the front cover of their answer book and sign their desk card but must NOT write anything else until the start of the examination period is announced Answer THREE questions Only silent, self contained calculators with a Single-Line Display or Dual-Line Display are permitted in this examination. Dictionaries are not allowed with one exception. Those whose first language is not English may use a standard translation dictionary to translate between that language and English provided that neither language is the subject of this examination. Subject specific translation dictionaries are not permitted. No electronic devices capable of storing and retrieving text, including electronic dictionaries, may be used. DO NOT turn examination paper over until instructed to do so ADDITIONAL MATERIAL: Formula Sheet Nomenclature Graph Paper
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H84MPS-E1 H84MPS-E1 Turn over 2 1. To cut production time, a vinegar-making company is experimenting with air injection in an aerobic fermentation tank. The tank consists of a vertical cylindrical pool of D = 1.2 m diameter, which bottom plate has thousands of d = 0.5 mm holes, through which the air is injected. The equivalent diameter of the bubbles generated at the holes is d b = 1 mm. The mass flow rate of air is g M & = 0.025 kg/s. The tank contains M = 1600 kg of vinegar. Physical properties of vinegar and air are given in Table Q.1. Table Q.1: Properties of vinegar and air. Property Value Vinegar l ρ 1000 kg/m 3 l η 0.001 Pa·s σ 0.07 N/m Air g ρ 1.2 kg/m 3 g η 1.7·10 -5 Pa·s (a) Determine the rise velocity of the air bubbles in the tank using Reynolds-Eotvos- Morton diagram (Figure Q.1). Assumption : ignore bubbles coalescence and breakup. [8] Figure Q.1: Reynolds-Eotvos-Morton diagram for bubbly flow Continue on next page
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