The free-stream velocity of the water at 50^∘ C is 0.4 m / s. Determine the boundary layer thick

step 1 The boundary layer thickness at x equals 0 .3 and 0 .5 meters in the water's at 50 degrees Celsi

The free-stream velocity of the water at 50^∘ C is 0.4 m /...

The free-stream velocity of the water at $50^{\circ} \mathrm{C}$ is 0.4 $\mathrm{m} / \mathrm{s}$. Determine the boundary layer thickness on the plate's surface at $x=0.3 \mathrm{~m}$ and at $x=0.5 \mathrm{~m}$.

Key Concepts

Boundary Layer

The boundary layer is the thin region adjacent to a solid surface where the effects of viscosity are significant and the velocity of the fluid changes from zero (due to the no?slip condition at the wall) to the free-stream velocity. This concept is central to understanding how viscous forces influence the flow behavior near surfaces, affecting drag and heat transfer characteristics.

Free-stream Velocity

Free-stream velocity refers to the constant velocity of the fluid that is unaffected by the presence of a solid boundary or any disturbances. It serves as the reference speed in boundary layer analyses, indicating the velocity at which the fluid approaches the surface from undisturbed flow regions.

Flow Over a Flat Plate

Flow over a flat plate is a canonical problem in fluid mechanics that explores the development of the boundary layer along a smooth, non-accelerating surface. This simplified scenario helps in understanding the fundamental interactions between viscous forces and the inertial flow, and it forms the basis for many theoretical and practical analyses of laminar and turbulent boundary layers.

Reynolds Number

The Reynolds number is a dimensionless parameter that describes the ratio of inertial forces to viscous forces in a fluid flow. In the context of boundary layers, it is used to characterize the flow regime (laminar or turbulent) and to predict how the thickness of the boundary layer grows with the distance downstream from the leading edge.

Boundary Layer Thickness Formula

The boundary layer thickness formula is a mathematical relation derived from the similarity solutions of the boundary layer equations, typically indicating that the thickness increases with the distance from the leading edge and is inversely related to the square root of the Reynolds number. This formula provides an estimate of the distance from the surface at which the fluid velocity reaches a significant portion of the free-stream velocity.

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