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| borderColor | wheat |
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| borderWidth | 7 |
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| Incompressible fluid | LaTeX Math Inline |
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| body | \rho(p) = \rho_0 = \rm const |
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means that compressibility vanishes and fluid velocity is going to be constant along the pipeline trajectory | LaTeX Math Inline |
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| body | --uriencoded--u(l) = u_0 = \frac%7Bq_0%7D%7BA%7D = \rm const |
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.For the constant viscosity | LaTeX Math Inline |
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| body | \mu(T, p) = \mu_0 = \rm const |
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along the pipeline trajectory the Reynolds number | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7B4 \rho_0 q_0%7D%7B\pi d%7D \frac%7B1%7D%7B\mu_0%7D = \rm const |
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and Darcy friction factor | LaTeX Math Inline |
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| body | --uriencoded--f(%7B\rm Re%7D, \, \epsilon) = f_0 = \rm const |
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are going to be constant along the pipeline trajectory.Equation | LaTeX Math Block Reference |
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becomes:| LaTeX Math Block |
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| \frac{dp}{dl} = \rho_0 \, g \, \frac{dz}{dl} - \frac{\rho_0 \, q_0^2 }{2 A^2 d} f_0 |
and can be explicitly integrated leading which leads to | LaTeX Math Block Reference |
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. after substituting Substituting the | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \cos \theta(l) = \frac%7Bdz(l)%7D%7Bdl%7D |
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and can be explicitly integrated leading to | LaTeX Math Block Reference |
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The first term in the right side of
| LaTeX Math Block Reference |
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defines the hydrostatic column of static fluid while the last term defines the friction losses under fluid movement:
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