Single Phase 22 1A PWR has dimensions and operating conditions given below. Core Height 144 inches Core Mass Flux 2.62 x 106lbm/hr-ft2Number of Fuel Rods 56,876 Rod Diameter 0.374 inches Rod Pitch 0.496 inches Core Inlet Loss Coefficient 1.5 Core Exit Loss Coefficient 1.5 Grid Loss Coefficient 0.5 Number of Grids 8 Pressure 2250 psia Core Inlet Temperature 560 F Maximum Channel Heat Flux 265,700 Btu/hr-ft2Extrapolation Distance 0.866 ft You may assume an axial heat flux profile of the form ′′=′′+⎛⎝⎜⎞⎠⎟qzqzHe( )sin()0πλDetermine the acceleration, friction, forms, elevation and total pressure loss. Compare to that which would be obtained from a simple Bernoulli’s Equation approach where the density is approximated by the average channel density 2/)(inletexitρρ+and the density is evaluated at the average coolant temperature. Assume the same treatment holds for viscosity also. SolutionIntegrate the conservative form of the steady-state Momentum Equation over the channel length ()11gAzvvAPzPAggcxxwwxc∂∂ρ∂∂τρθ= −−−sin(1) or 122222gzGPzfDGgKzzGgggcecjjcjc∂∂ρ∂∂ρδρρθ⎛⎝⎜⎞⎠⎟ = −−+−⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪−∑()sin(2) where we have assumed a uniform flow area and a vertical flow channel. For convenience the momentum equation has been written in terms of the mass flux. 1222121221221212gzGdzPzdzfDGgdzKzzGgdzggdzcecjjcjc∂∂ρ∂∂ρδρρ⎛⎝⎜⎞⎠⎟= −−+−⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪−∫∫∫∑∫∫()(3) ()()1222121222211HHgggGKgGDLfPPgGccjjjjiciieiici−−−−−−=⎭⎬⎫⎩⎨⎧−∑∑ρρρρρ(4) Rearranging gives for the core pressure drop
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