Consider air flow through a relatively short circular duct, having a diameter d = 100 mm....

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Consider air flow through a relatively short circular duct, having a diameter d = 100 mm. You may assume that the boundary layer developing along the duct wall is fully turbulent from the start and has a profile that can be approximated by the 1/7 power law. Measurements show that, at a streamwise location 1, the flow velocity on the centreline is Uc = 20 m/s and the boundary layer thickness is d = 16 mm, whereas, at a downstream location 2, the boundary layer thickness is 82 = 32 mm. (a) Calculate the displacement thickness 8* at the two locations. (b) Calculate the centreline velocity Uc at location 2. (c) Calculate the static pressure difference between the two locations. Assume that the density of air is p = 1.2 kg/m. Consider air flow through a relatively short circular duct, having a diameter d = 100 mm. You may assume that the boundary layer developing along the duct wall is fully turbulent from the start and has a profile that can be approximated by the 1/7 power law. Measurements show that, at a streamwise location 1, the flow velocity on the centreline is Uc = 20 m/s and the boundary layer thickness is d = 16 mm, whereas, at a downstream location 2, the boundary layer thickness is 82 = 32 mm. (a) Calculate the displacement thickness 8* at the two locations. (b) Calculate the centreline velocity Uc at location 2. (c) Calculate the static pressure difference between the two locations. Assume that the density of air is p = 1.2 kg/m.