Viscous Flow in Pipes.pdf
Viscous Flow in Pipes.pdf
Viscous Flow in Pipes.pdf
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8.2.2 From the Navier-Stokes Equation• Basic equationsur∇⋅ V = 0,ur∂Vur ur ∇pur ur2+ V ⋅∇ V =− + g+ v∇V∂tρ• For steady fully developed flow <strong>in</strong> a pipeur∇⋅ V = 0,r ur2∇ p+ ρgk = μ∇V• In terms of polar coord<strong>in</strong>ate∂p1 ∂ ⎛ ∂u⎞+ ρgs<strong>in</strong>θ = μ ⎜r⎟∂x r ∂r⎝∂r⎠( ) = ( )f x g r= constant,
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