Question

A fluid of dynamic viscosity 2 × 10^-5 kg/ms and density 1 kg/m³ flows with an average velocity of 1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is ___________

Answer 1

Concept:

The pressure drop in the duct is given as, \({\rm{\Delta }}P = \frac{{32\mu L{V_{avg}}}}{{{D^2}}}\)

Where D = 4A/P

Calculation:

Given:

μ = 2 × 10-5 kg/m-s, L = 1 m, Vavg = 1 m/s

\(D = \frac{{4 \times 25 \times 15}}{{2\left( {25 + 15} \right)}} = 18.75~mm = 0.01875~m\),

∴ ΔP =\(\frac{{32 \times \left( {2 \times {{10}^{ - 5}}} \right) \times 1 \times 1}}{{{{\left( {0.01875} \right)}^2}}} = 1.82~{\rm}\) Pa