midterm_soln

# midterm_soln - J Buongiorno Spring 2007 22.313J 2.59J...

This preview shows pages 1–2. Sign up to view the full content.

J. Buongiorno / Spring 2007 22.313J, 2.59J, 10.536J THERMAL-HYDRAULICS IN POWER TECHNOLOGY OPEN BOOK MID-TERM QUIZ (solutions) 1.5 HOURS Problem 1 (50%) – Bubbly flow of air in a vinegar fermentation tank i) Note that since the vinegar velocity is zero (i.e., the vinegar is stagnant), the air bubble rise velocity coincides with the bubble-liquid relative velocity, v b . For air bubbles of 1-mm equivalent diameter in vinegar we have M 3 × 10 -11 , Eö 0.1 and, thus, from the Re-Eö-M diagram, Re 10 2 . Therefore, from the definition of Re, we get a bubble rise velocity v b 0.1 m/s. ii) The volume of vinegar in the tank is V vin =1.5 m 3 . The tank cross sectional area is A tank = π /4 D 2 1.13 m 2 , where D=1.2 m is the tank diameter. Therefore, the vinegar level prior to air injection is L o =V vin /A tank 1.33 m. Upon air injection the level rises to accommodate the air volume. The total volume of the air-vinegar mixture is V tot =V air +V vin . Since V air = α V tot , one gets V tot =V vin /(1- α ), and thus the new level, L, is: L=V tot /A tank =V vin /[(1- α )A tank ] ( 1 ) where α is the void fraction. According to the drift flux model, the void fraction can be calculated as: vj o v V j C j + = α ( 2 ) where C o =1 and V vj =v b =0.1 m/s, as per the hint in the problem statement. j v and j=j v +j are the air and total superficial velocities, respectively. However, in our case

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

### Page1 / 3

midterm_soln - J Buongiorno Spring 2007 22.313J 2.59J...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online