(Solved): Problem 1 ( 60 points): Air bubbles discharge from the end of a submerged tube as shown below. The ...

Problem 1 ( 60 points): Air bubbles discharge from the end of a submerged tube as shown below. The bubble diameter, \( D \), is assumed to be a function of the air flowrate, \( Q \); the tube diameter, \( d \); the acceleration of gravity, \( g \); the density of the liquid, \( \rho \); and the surface tension of the liquid, \( \sigma \). (a \( -30 \) points ) Selecting \( d, g \), and \( \rho \) as repeating variables, determine a suitable set of dimensionless variables for this problem. Present the dimensionless equation. (b - 30 points) Model tests are to be run on the Earth for a prototype that is to be operated on a planet, where the acceleration of gravity is 16 times greater than that on Earth. The model and prototype are to use the same fluid, and the prototype tube diameter is \( 0.5 \) in. Determine the tube diameter for the model and the required model flowrate if the prototype flowrate is to be \( 0.005 \mathrm{ft}^{3} / \mathrm{s} \) ? Note that: In order to get full credit, you need to - Present all intermediate steps showing how you solve the problem. - Present equations in both symbolic and numeric forms. - Present your solution in a neat and clear format. Solution:[Please print this paper out and present your solution on \( ] \)