# Basic Two-Phase Flow

A vertical pipe 0.1 meters in diameter is instrumented with differential pressure taps at every meter along its length.  The pipe is filled with water, and air injected as bubbles in a uniform pattern across the bottom at a total rate of 9.55e-5 kg/s.  The pressure difference between the two taps closest to the surface of the bubbly mixture is 9.289e+3 Pa.  You can assume that:
• Temperature is uniform at 300K;
• Pressure at the surface of the bubbly mixture is 1.0e5 Pa;
• Water is stationary at any given location; and
• Bubbles are moving at their terminal rise velocity.
Provide the following additional information about the state of the two phase system, showing all calculations.
1. What is the mean void fraction in the volume bounded by the pressure taps?
2. What is the mean bubble rise velocity in this volume?
3. Find and document an expression for the drag force on a moving sphere.  Balancing that against the bouyancy force on an individual bubble, give an estimate for the bubble diameter.
4. Give an estimate of the mean center-to-center separation distance between bubbles.

Remember, if you use MathCad for supporting calculations, copy the results into your report, don't give me a .mcd file.