Scenario 2:Water flows through a 2cm diameter pipe at 1.6m/s with kinematic viscosity of 1.31 × 10-6 m2/s and densityof 1000 kg/m3. Using the Buckingham Pi Theorem:f) Calculate the Reynolds number.g) Find the velocity required to give the same Reynolds number when the same pipe is transportingair.h) Obtain the ratio of pressure drops in the same length of pipe for both cases.i) Reflect on the case studies provided—Food Processing Industry, Chemical Manufacturing, and WaterTreatment Facilities. Evaluate how the dimensional analysis using the Buckingham PiTheorem applies to these scenarios and discuss the specific challenges encountered, suchas variable fluid properties and complex fluid dynamics which are not always captured by thetheorem. Offer practical recommendations for engineers to tailor dimensional analysistechniques to the unique requirements of each case study scenario, optimizing design andoperational efficiency.For air, the kinematic viscosity is 15.1 × 10-6 m2/s and the density is 1.19 kg/m3

Scenario 2:
Water flows through a 2cm diameter pipe at 1.6m/s with kinematic viscosity of 1.31 × 10-6 m2
/s and density
of 1000 kg/m3
. Using the Buckingham Pi Theorem:
f) Calculate the Reynolds number.
g) Find the velocity required to give the same Reynolds number when the same pipe is transporting
air.
h) Obtain the ratio of pressure drops in the same length of pipe for both cases.
i) Reflect on the case studies provided—Food Processing Industry, Chemical Manufacturing, and Water
Treatment Facilities. Evaluate how the dimensional analysis using the Buckingham Pi
Theorem applies to these scenarios and discuss the specific challenges encountered, such
as variable fluid properties and complex fluid dynamics which are not always captured by the
theorem. Offer practical recommendations for engineers to tailor dimensional analysis
techniques to the unique requirements of each case study scenario, optimizing design and
operational efficiency.
For air, the kinematic viscosity is 15.1 × 10-6 m2
/s and the density is 1.19 kg/m3