A ship of length 80 m with 0.8 m wide side strip as flat plat along the entire length of the s

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A ship of length 80 m with 0.8 m wide side strip as flat...

A ship of length $80 \mathrm{~m}$ with $0.8 \mathrm{~m}$ wide side strip as flat plat along the entire length of the ship is traveling forward at $12 \mathrm{~m} / \mathrm{s}$ on a lake. The water is still and has a temperature of $20^{\circ} \mathrm{C}$. Determine the drag force on the strip of the ship. Assume the boundary layer is completely turbulent.

Key Concepts

Drag Force

Drag force in fluid dynamics is the resistance encountered by an object moving through a fluid. It is influenced by factors such as the object's shape, size, surface roughness, fluid properties, and the velocity of the object relative to the fluid. The drag force is a combination of frictional effects caused by the fluid's viscosity acting on the surface and pressure differences created by the flow around the object.

Boundary Layer

The boundary layer is the thin region adjacent to the surface of an object where the effects of viscosity are significant and the fluid velocity changes from zero (due to the no-slip condition) to the free stream velocity. The state of the boundary layer—whether laminar or turbulent—affects the drag on the object, with turbulent boundary layers typically exhibiting higher frictional drag due to increased mixing.

Turbulent Flow

Turbulent flow is characterized by chaotic and irregular fluid motion, where eddies and fluctuations play a significant role. In the context of boundary layers, a completely turbulent boundary layer exhibits increased momentum transfer and mixing, resulting in a higher skin friction coefficient compared to a laminar flow, which directly influences the frictional drag experienced by the surface.

Skin Friction Coefficient

The skin friction coefficient is a non-dimensional parameter that quantifies the drag due to shear stress at the surface of an object moving through a fluid. It depends on factors such as the Reynolds number and the nature of the boundary layer (laminar or turbulent). For turbulent flow over a flat plate, empirical correlations are commonly used to estimate this coefficient and, thereby, the friction drag.

Reynolds Number

The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined by the ratio of inertial forces to viscous forces. In determining the drag force, the Reynolds number helps identify whether the flow is laminar or turbulent, which in turn affects parameters like the skin friction coefficient and the overall drag.

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