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Pipeline flow simulator is addressing this problem. It should account for the varying pipeline trajectory, gravity effects, fluid friction with pipeline walls and varying heat exchange with surroundings.
Definition
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| Inputs |
| Ouputs |
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| along-pipe distribution of stabilised pressure |
Pipeline cross-section area |
| along-pipe distribution of stabilised flow rate |
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Given
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| LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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| LaTeX Math Inline |
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| body | \{ x_w(l), \, y_w(l), \, z_w(l) \} |
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| LaTeX Math Inline |
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| body | l = \int_0^l \sqrt{dx^2 + dy^2 + dz^2} = \int_0^l \sqrt{\dot x^2 + \dot y^2 + \dot z^2} dl |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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| LaTeX Math Inline |
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| body | {\bf g} = (0, \, 0, \, g) |
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Simulate
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along-pipe distribution of stabilised average flow velocity |
| LaTeX Math Block |
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\bigg( 1 - \frac{c(p) \, \rho_s^2 \, q_s^2}{A^2} \bigg ) \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl} - \frac{\rho_s^2 \, q_s^2 }{2 A^2 d} \frac{f(p)}{\rho(p)} |
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