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Question In flow over a flat plate, how to calculate pressure drop by knowing displacement thickness values at 2 points. Free stream velocity is known.
Displacement thickness is a term used in fluid mechanics to describe the decrease in effective cross-sectional area of a flow channel due to the presence of a boundary layer. It represents the distance by which the boundary layer would need to be displaced to maintain the same mass flow rate in the channel.
Displacement thickness is calculated by integrating the velocity profile across the boundary layer and dividing it by the free stream velocity. This integral is then subtracted from the boundary layer thickness to obtain the displacement thickness.
Displacement thickness affects the velocity and pressure distribution within the boundary layer, which in turn affects the overall pressure drop in a flow system. It is a crucial factor in accurately predicting pressure drops in various flow scenarios.
In laminar flow, the displacement thickness is typically larger than the boundary layer thickness, indicating a larger effect on the pressure drop. In turbulent flow, the displacement thickness is typically smaller than the boundary layer thickness, but it still plays a significant role in pressure drop calculations.
No, displacement thickness should not be neglected in pressure drop calculations. It is an important factor in accurately predicting pressure drops, especially in low Reynolds number flows where the effect is more significant. Neglecting displacement thickness can lead to errors in pressure drop calculations.