Question $1$

MARKS

$($a$)$ Explain what dimensional analysis is and why it is beneficial for engineers to use it over other alternatives when analysing fluid flow problems. why it is useful to engineers when analysing fluid flow problems.

$[7]$

$($b$)$ Explain and detail the process and rules an engineer should follow to utilise PI groups derived from dimensional analysis. Discuss this in the context of $($i$)$ predicting a parameter of interest by utilising existing data or $($ii$)$ designing your own downscaled experiment to characterise a problem of interest. You should identify and use a sample application of your choosing to help illustrate your answer.

$[14]$

$($c$)$ Drag Coefficient and Reynolds number are two of the most common dimensionless parameters in fluid mechanics problems. Draw an indicative plot of Drag coefficient vs$.$ Reynolds number for external flow past an object, such as a sphere or cylinder. Explain all sections of the graph in detail and use streamline illustrations to aid in describing the anticipated flow patterns for each section.

$[12]$

$[$Total $33]$