For the conditions of Prob. 4.56, but assuming a turbulent boundary layer, an approximate criterion for the separation point is x. = 506(}-1 ..,., where x. is in m. Calculate the location of flow separation for a turbulent boundary layer along the diffuser wall. Prob. 4.56 The diffuser of a wind tunnel or at the inlet of an air-breathing jet engine is designed to slow the flow. Consequently, from Euler’s equation, Eq. (4.8) in the text, the pressure always increases with distance along the diffuser. Hence, in terms of the discussion in Sec. 4.20, the flow in the diffuser is experiencing an adverse pressure gradient, which encourages: the boundary layer to separate from the wall of the diffuser, thus resulting in a loss of total pressure and reducing the aerodynamic efficiency of the diffuser. For the wind tunnel and flow conditions described in Probs. 4.49-4. 55, a criterion that predicts approximately the location along the wall of the diffuser where a laminar boundary will separate is given by x. = 183(/dx)-1 .,. where x. is the separation location in m and (dp/dx).,. is the average of the pressure gradients in N/m3 at the entrance and exit of the diffuser assuming no flow separation. Assuming a laminar boundary layer along the diffuser wall, calculate the location of flow separation in the diffuser.

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