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| body | --uriencoded--f(%7B\rm Re%7D, \, \epsilon) |
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| Darcy friction factor |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bu(l) \cdot d%7D%7B\nu%7Dnu(l)%7D |
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| Reynolds number |
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| body | --uriencoded--\displaystyle d = \sqrt%7B \frac%7B4 A%7D%7B\pi%7D%7D |
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| characteristic linear dimension of the pipe (or exactly a pipe diameter in case of a circular pipe) |
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| Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate |
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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) = u_0 = \frac{q_0}{A} = \rm const |
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| q(l) =q_0 = \rm const |
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| body | \displaystyle \cos \theta(l) = \frac{dz(l)}{dl} |
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| correction factor for trajectory inclination |
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| borderColor | wheat |
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| bgColor | mintcream |
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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 fluid velocity is going to be constant along the 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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.The Reynolds number | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bu_0 \cdot d%7D%7B\nu_0%7D |
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may still be varying along the trajectory due to the influence of temperature profile on kinematic viscosity | LaTeX Math Inline |
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| body | --uriencoded--\nu(l) = \frac%7B\mu(T(l))%7D%7B\rho_0%7D |
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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:
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