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ApproximationsIncompressible pipe flow
with constant viscosity ...
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| Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate |
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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 |
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\frac{dp}{dl} = \rho_0 \, g \cos \theta(l) - \frac{j_m^2 f_0}{2 \, \rho_0 \, d} |
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q(l) =q_0 = \rm const |
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u(l) = u_0 = \frac{q_0}{A} = \rm const |
where
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| body | --uriencoded--f_0 = f(%7B\rm Re%7D_0, \, \epsilon) |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D_0= \frac%7Bj_m \, d%7D%7B\mu_0%7D |
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Reynolds number at inlet point ()
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| body | \mu_0 = \mu(T_0, p_0) |
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Incompressible fluid
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| body | \rho(T, 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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| body | \mu(T, p) = \mu_0 = \rm const |
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Equation
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becomes:...
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| body | --uriencoded--\displaystyle \cos \theta(l) = \frac%7Bdz(l)%7D%7Bdl%7D |
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Pressure Profile in G-Proxy Pipe Flow @model
Pressure Profile in G-Proxy Pipe Flow @model
Pressure Profile in GF-Proxy Pipe Flow @model
Pressure Profile in GF-Proxy Pipe Flow @model
Pressure Profile in GFC-Proxy Pipe Flow @model
Pressure Profile in GFC-Proxy Pipe Flow @model
Pressure Profile in FC0-Proxy Pipe Flow @model
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See also
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