Consider a scenario where water at room temperature is flowing through a smooth$-$walled,

horizontally oriented U$-$bend pipe. This pipe has unique characteristics and flow conditions which are

pivotal for understanding the complexities of fluid dynamics. Pipe Specifications $,$Length of Each

Straight Segment $($L$)$: $60\mathrm{.}0$ cm$,$ Diameter $($D$)$: $1\mathrm{.}30$ cm$,$ Flow Velocity $($V$)$: $0\mathrm{.}297$ m$/$s$,$ Kinematic

Viscosity of Water $($

u $)$: $1\mathrm{.}005\backslash$times $106$m $2/$s$,$ Reynolds Number $($Re$)$: $3840($Indicative of turbulent

flow$).$

Describe how you would set up a simulation for this U$-$bend pipe scenario. Include details on

boundary conditions, mesh requirements, and initial conditions for each of the three turbulence

models. Run simulations using each of the three turbulence models. Compare and contrast the

results in terms of: Flow patterns observed, especially in the bend of the pipe, Pressure distribution

along the pipe, Velocity profiles at different sections of the pipe, and Which turbulence model do

you think provides the most accurate and realistic prediction for this scenario? Justify your answer

with references to the simulation results? Evaluate the strengths and weaknesses of each turbulence

model in the context of this U$-$bend pipe flow. Discuss any discrepancies observed between the

models and possible reasons for these differences.