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.

- What is the mean void fraction in the volume bounded by the pressure taps?
- What is the mean bubble rise velocity in this volume?
- 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.
- 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.