Inlet Manifold Equations
Unknown macro: {latex}
(eq-1)
\large
$$
\Delta H_
Unknown macro: {exp ansion}
= {{\left( {V_
Unknown macro: {in}
- V_
Unknown macro: {out} } \right)V_
} \over g}
$$
$$
\sum\limits_
Unknown macro: {i = 1}
^
Unknown macro: {n - 1}
{\Delta H_
= V_M ^2 } \over g}{{n - 1} \over {2n \to {\rm{Approaches}}\;} V_M ^2 } \over g}\;{\rm{for\;{\rm{large}}\;{\rm{n}}
$$
$$
{\rm{where }}V_M = {\rm{velocity}}\;{\rm{in}}\;{\rm{the}}\;{\rm{manifold}}
$$
$$
V_
Unknown macro: {in}
\;{\rm{and}}\;V_
Unknown macro: {out}
\;{\rm{are}}\;{\rm{the}}\;{\rm{velocities}}\;{\rm{before}}\;{\rm{and}}\;{\rm{after}}\;{\rm{the}}\;{\rm{expansion}}
$$
$$
f = 0.25} \over {\left[ {\log \left( {{\varepsilon \over {3.7D + {{5.74} \over {{\mathop
Unknown macro: {rm Re}
\nolimits} ^
Unknown macro: {0.9}
}}} \right)} \right]^2 }}
$$
$$
C_
Unknown macro: {long}
= \left[ {f{{L_M } \over {D_M }}2n - 1} \over {6n + n - 1} \over n \right]
$$
$$
K_
Unknown macro: {control}
= K_
Unknown macro: {e_P }
\left( {{
Unknown macro: {D_M^2 }
\over {nK_
Unknown macro: {vc}
D_P^2 }}} \right)^2
$$
$$
\Pi Q = \sqrt {{{C{p_
Unknown macro: {short}
} + K_
} \over {C_{p_
} + K_
Unknown macro: {control}
}}}
$$
$$
D_M = \left( {{
Unknown macro: {8Q_M ^2 }
\over {g\pi ^2 h_l }}{{C_
Unknown macro: {long}
} \over
Unknown macro: {1 - Pi _Q^2 }
}} \right)
$$
Energy Dissipation Constraint on Port Velocity
Unknown macro: {latex}
(eq-2)
\large
$$
D_
Unknown macro: {Port}
\cong \left[ {{1 \over {20\varepsilon _
Unknown macro: {Max}
}}\left( {{{4Q_
} \over {\pi K_
Unknown macro: {vc}
}}} \right)3 } \right]1 \over 7
$$
$$
V_
Unknown macro: {Port} = {{4Q_
^1 \over 7 } \over {\pi \left[ {{1 \over {20\varepsilon _
Unknown macro: {Max}
}}\left( {{4 \over {\pi K_
}}} \right)3 } \right]2 \over 7 }}
$$
Scour velocity
Design manifolds to have a flow velocity not less than 0.15 m/s nor greater than 0.45 m/s.
The minimum scour velocity is:
Unknown macro: {latex}
\large
$$
\tau {o
Unknown macro: {Min}
} =
Unknown macro: {2 over 3}
d_
Unknown macro: {Floc} \left( {\rho _
- \rho _
Unknown macro: {H2O}
} \right)g\tan \theta
$$
$$
V_
Unknown macro: {Scour}
= \sqrt {{{\tau {o
} } \over {\rho _
Unknown macro: {H_2 O}
}}{{\sqrt
Unknown macro: {500000}
} \over
Unknown macro: {0.332}
}}
$$
(eq-3)
$$
\varepsilon _
Unknown macro: {Max}
= {1 \over {20D_
Unknown macro: {Port}
}}\left( {{{V_
Unknown macro: {Scour}
} \over {K_
Unknown macro: {vc}
}}} \right)^3
$$