A horizontal oil-hearing stratum is (3 mathrm{~m}) high and, after hydraulic fracturing (fracking), provides a volume flow
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A horizontal oil-hearing stratum is \(3 \mathrm{~m}\) high and, after hydraulic fracturing ("fracking"), provides a volume flow rate of \(Q=1000 \mathrm{~m}^{3} / \mathrm{hr}\). The flow moves radially inward and is collected by a vertical porous pipe having an outer radius of \(1.0 \mathrm{~m}\). The Laplace equation for the potential flow model of the oil is
\[ \frac{1}{r}\left(\frac{\partial \Phi}{\partial r}\right)+\frac{\partial^{2} \Phi}{\partial r^{2}}+\frac{1}{r^{2}}\left(\frac{\partial^{2} \Phi}{\partial \theta^{2}}\right)=0 \]
Find \(\Phi\).
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Related Book For
Munson Young And Okiishi's Fundamentals Of Fluid Mechanics
ISBN: 9781119080701
8th Edition
Authors: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
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