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Incompressible fluid with constant friction
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| p(l) = p_0 + \rho \, g \, z(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 \, l |
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| \frac{dp}{dl} = \rho \, g \cos \theta(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 |
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| u(l) = \frac{q_0}{A(l)} |
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| q(l) =q_0 = \rm const |
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where
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| body | \displaystyle \cos \theta(l) = \frac{dz(l)}{dl} |
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| correction factor for trajectory deviation |
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The first term in
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defines the hydrostatic column of static fluid while the last term defines the friction losses under fluid movement:
In most practical applications in water producing or water injecting wells the water can be considered as incompressible and friction factor can an be assumed constant
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| body | f(l) = f_s = \rm const |
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along-hole ( see
Darcy friction factor in water producing/injecting wells ).
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