A plate is used in a separator to process the mixture of two...

A plate is used in a separator to process the mixture of two fluids oil and gas mixture. If the free-stream velocity of the fluid mixture over the plate is $0.7 \mathrm{~m} / \mathrm{s}$, determine the friction drag acting on the surface of the plate. Take $v=$ $42\left(10^{-6}\right) \mathrm{m}^{2} / \mathrm{s}$ and $\rho=910 \mathrm{~kg} / \mathrm{m}^{3}$.

Key Concepts

Friction Drag

Friction drag, also known as skin friction drag, is the resistance force due to the viscosity of the fluid acting along a surface. It arises because of the shear stress generated by the velocity gradient in the thin layer of fluid adjacent to the solid boundary. Calculating friction drag requires an understanding of the interactions at the fluid-solid interface, where viscous forces dominate.

Boundary Layer Theory

Boundary layer theory describes the thin region adjacent to a solid surface where the effects of viscosity are significant. In this region, the fluid velocity changes from zero at the surface due to the no-slip condition to nearly the free-stream value away from the surface. The behavior of the boundary layer, whether laminar or turbulent, plays a crucial role in determining the friction drag encountered by the object.

Reynolds Number

The Reynolds number is a dimensionless parameter that characterizes the nature of the flow, indicating whether it is laminar or turbulent. It is defined based on the free-stream velocity, a characteristic length, and the fluid's kinematic viscosity. In problems involving drag, the Reynolds number is important because the friction coefficient varies with the flow regime, affecting the calculation of friction drag.

Drag Coefficient

The drag coefficient is a dimensionless number that relates the drag force exerted on an object to the dynamic pressure and a reference area. For friction drag on a flat plate, specific correlations based on whether the flow is laminar or turbulent are used to derive an expression for the friction coefficient. This coefficient simplifies the quantification of drag without needing to solve the full Navier–Stokes equations directly.

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