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For laminar flow, i.e. Reynolds number below Re0 the friction factor is independent of wall roughness and the Hagen-Poiseulle law is applicable: f = 64 (3-29) Re For Reynolds numbers above Re0 the friction factor continues to decrease, but the rate of decrease becomes smaller. At some point the friction factor reaches its minimum and starts to increase. The Reynolds number Re1 defines this point. The Samoilenko expression is used to calculate this Reynolds number: Re1 =1160 (3-30) ∆ The range of applicability is again for ∆ > 0.007 and Re1 = 2000 is used for smaller values of roughness. For departure from the Hagen-Poiseuille law range, Reynolds numbers between Re0 and Re1, the friction factor can be calculated from: 0.00275 f=4.4Re−0.595e ∆ (3-31) For the relative roughnesses below 0.007 linear interpolation between the Hagen- Poiseuille law and the Blasius law is used. The limiting Reynolds number for the rise of the friction factor Re2 can be obtained from: ⎛ 1 ⎞0.0635 Re2 =2090⎜∆⎟ (3-32) For the range of increasing friction factor within the transition regime (Re1 < Re < Re2) the friction factor is evaluated as: f=(f2 −f*)e{−[0.0017(Re2−Re)]2}+f* (3-33) 51 ⎝⎠PDF Image | Advanced Nuclear Power Technology Program A Supercritical Carbon Dioxide Cycle for Next Generation Nuclear Reactors
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