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Pressure Profile in Incompressible Isoviscous Stationary Quasi-Isothermal Pipe Flow @model : 

Pressure profilePressure gradient profileFluid velocityFluid rate


LaTeX Math Block
anchorPPconst
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p(l) = p_0 + \rho_0 \, g \, z(l)  
- \frac{j_m^2  f_0}{2 \, \rho_0 \, d} \cdot l



LaTeX Math Block
anchorgradP
alignmentleft
\frac{dp}{dl} = \rho_0 \, g \cos \theta(l) - \frac{j_m^2  f_0}{2 \, \rho_0 \, d}



LaTeX Math Block
anchor1
alignmentleft
q(l) =q_0 = \rm const



LaTeX Math Block
anchor1
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u(l) = u_0 = \frac{q_0}{A} = \rm const


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In many practical applications the water in water producing wells or water injecting wells can be considered as incompressible and friction factor  can be assumed constant

LaTeX Math Inline
body f(l) = f_0 = \rm const
 along-hole ( see  Darcy friction factor in water producing/injecting wells ).


Pressure Profile in GF-Proxy Pipe Flow @model

Pressure Profile in GF-Proxy Pipe Flow @model



See also

Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Quasi-Isothermal Stationary Pipe Flow @model

[ Darcy friction factor ] [ Darcy friction factor @model ] [ Reynolds number in Pipe Flow ]

[ Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model ]

[ Temperature Profile in Homogenous Pipe Flow @model ]

[ Fluid Compressibility ] [ Fluid Compressibility @model ]


References

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