Problem 2.55 - = d dr 1 16 p L d 2 4 r 2 D 2 d 2 ln d D ln...

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Problem 2.55 [Difficulty: 3] Given: Data on flow through a tube with a filament Find: Whether no-slip is satisfied; location of zero stress;stress on tube and filament Solution: The velocity profile is Vr () 1 16 μ p L d 2 4r 2 D 2 d 2 ln d D ln 2r d = Check the no-slip condition. When r D 2 = V D 2 1 16 μ p L d 2 D 2 D 2 d 2 ln d D ln D d = VD () 1 16 μ p L d 2 D 2 D 2 d 2 () + = 0 = When r d 2 = Vd () 1 16 μ p L d 2 d 2 D 2 d 2 ln d D ln d d = 0 = The no-slip condition is satisfied. The given data is d1 μ m = D2 0 m m = p 5 kPa = L1 0 m = The viscosity of SAE 10-30 oil at 100 o C is (Fig. A.2) μ 11 0 2 × Ns m 2
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The plot looks like 0 0.25 0.5 0.75 1 2 4 6 8 10 Velocity (m/s) Radial Position (mm) For each, shear stress is given by τ rx μ du dr = τ rx μ dV r () dr
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Unformatted text preview: = d dr 1 16 p L d 2 4 r 2 D 2 d 2 ln d D ln 2 r D i = rx r ( ) 1 16 p L 8 r D 2 d 2 ln d D r = For the zero-stress point 8 r D 2 d 2 ln d D r = or r d 2 D 2 8 ln d D = r 2.25 mm = 3 2 1 1 2 3 4 2.5 5 7.5 10 Stress (Pa) Using the stress formula rx D 2 2.374 Pa = rx d 2 2.524 kPa =...
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Problem 2.55 - = d dr 1 16 p L d 2 4 r 2 D 2 d 2 ln d D ln...

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