ME 330 PS7 Solutions Fall 2010

ME 330 PS7 Solutions Fall 2010 - Problem Set 7 Problem#1...

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Problem Set 7, Problem #1 Given: An incompressible, Newtonian fluid flows steadily inside a constant area pipe of radius R. Axial velocity profiles are given for the laminar condition at Station 1 and turbulent condition at Station 2. 2 * 1 1 = = R r u U u C Station 1 7 * 2 1 = = R r u U u C Station 2 Find: a.) Volumetric flow rate at Station 1 and Station 2 b.) Ratio of U C1 /U C2 c.) Friction factor at Station 1 and Station 2 d.) Ratio of friction factor for Station 1 and Station 2 e.) Implication of friction factor ratio on pressure gradient at Station 1 and Station 2 Assumptions: Steady state, incompressible, fully developed flow at Station 1 and Station 2 (the flow is not fully developed between Station 1 and Station 2 where it turns from laminar to turbulent) Analysis: This is an internal flow problem that requires mass conservation, momentum balance, and constitutive relations for the shear stress at the walls Flow rates: dr R r r U rdr R r U rdr r u udA Q R C
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