flow through an annulus

# flow through an annulus - FLOW THROUGH AN ANNULUS November...

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FLOW THROUGH AN ANNULUS November 4, 2016 1 The integration steps Equation (2.4-5) is dV z dr = - ( P 0 - P L ) R 2 μ L ( r R - λ 2 R r ) (1) Eq. (1) can be integrated using a separation of variables, that is, dV z = - ( P 0 - P L ) R 2 μ L ( r R - λ 2 R r ) dr (2) Z dV z = - ( P 0 - P L ) R 2 μ L ( Z r R dr - λ 2 Z R r dr ) (3) using Z r R dr = r 2 2 R + Constant (4) and Z R r dr = R lnr + Constant (5) then, integrating Eq. (3) and using Eqs. (4) and (5), gives us V z = - ( P 0 - P L ) R 2 μ L ( r 2 2 R - λ 2 R ln r + Constant ) (6) 1

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Equation (6) can be re-written as
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