Q$1($a$)($b$)($c$)($d$)($e$)$ Fluids can be classified as compressible or incompressible depending on their response to pressure changes. Name the two classes of fluids that can be considered either compressible or$,$ to a first approximation, incompressible. $[1]$ Fluids can also be classified as Newtonian or non$-$Newtonian. i$.$ ii$.$ Define a Newtonian fluid and provide two examples. Define a non$-$Newtonian fluid and provide two examples. $[2][2]$ The Reynolds number is a dimensionless quantity used to predict the flow regime of a fluid. i$.$ ii$.$ iii. Define the Reynolds number and give its mathematical expression. $[2]$ Explain the significance of the Reynolds number in determining whether a fluid flow is laminar or turbulent. $[2]$ For a flow through a pipe, if the velocity of the fluid is doubled while all other parameters remain constant, how does the Reynolds number change? $[1]$ In the Buckingham$-$Pi method of Dimensional Analysis, what is meant by repeating and non$-$repeating variables? $[2]$ The thrust force $$ from an airplane propeller can be assumed to be a function of propeller diameter $,$ air density $,$ airplane speed $,$ and propeller angular velocity $.$ Viscous effects are assumed to be negligible. Selecting appropriate repeating variables, perform a dimensional analysis of the problem to obtain the relevant nondimensional groups. Q$1$

$($a$)$ Fluids can be classified as compressible or incompressible depending on their response to pressure changes. Name the two classes of fluids that can be considered either compressible or$,$ to a first approximation, incompressible.

$($b$)$ Fluids can also be classified as Newtonian or non$-$Newtonian.

i$.$ Define a Newtonian fluid and provide two examples.

ii$.$ Define a non$-$Newtonian fluid and provide two examples.

$($c$)$ The Reynolds number is a dimensionless quantity used to predict the flow regime of a fluid.

i$.$ Define the Reynolds number and give its mathematical expression.

ii$.$ Explain the significance of the Reynolds number in determining whether a fluid flow is laminar or turbulent.

iii. For a flow through a pipe, if the velocity of the fluid is doubled while all other parameters remain constant, how does the Reynolds number change?

$($d$)$ In the Buckingham$-$Pi method of Dimensional Analysis, what is meant by repeating and non$-$repeating variables?

$($e$)$ The thrust force $\backslash ($ T $\backslash )$ from an airplane propeller can be assumed to be a function of propeller diameter $\backslash ($ D $\backslash ),$ air density $\backslash (\backslash$rho $\backslash ),$ airplane speed $\backslash ($ V $\backslash ),$ and propeller angular velocity $\backslash ($ N $\backslash ).$ Viscous effects are assumed to be negligible. Selecting appropriate repeating variables, perform a dimensional analysis of the problem to obtain the relevant nondimensional groups.