Fluid flows past the two-dimensional bar shown in Fig. P9.2....

Fluid flows past the two-dimensional bar shown in Fig. P9.2. The pressures on the ends of the bar are as shown, and the average shear stress on the top and bottom of the bar is $\tau_{\mathrm{avg}}$. Assume that the drag due to pressure is equal to the drag due to viscous cffects. (a) Determine $\tau_{\text {ave }}$ in terms of the dynamic pressure, $\rho U^{2} / 2$ (b) Determine the drag coefficient for this object.

Fluid flows past the two-dimensional bar shown in Fig. P9.2. The pressures on the ends of the bar are as shown, and the average shear stress on the top and bottom of the bar is $\tau_{\mathrm{avg}}$. Assume that the drag due to pressure is equal to the drag due to viscous cffects.
(a) Determine $\tau_{\text {ave }}$ in terms of the dynamic pressure, $\rho U^{2} / 2$
(b) Determine the drag coefficient for this object.

Key Concepts

Shear Stress and Viscous Drag

Shear stress arises from the frictional forces exerted by a fluid as it flows over a surface, and it is responsible for viscous drag. Viscous drag is the resistive force arising from the fluid's viscosity, which manifests as a shear stress distributed over the surface of an object in a flow. Understanding the relationship between shear stress and the resulting drag is critical for analyzing and predicting the behavior of objects immersed in viscous flows.

Drag Coefficient

The drag coefficient is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment relative to the dynamic pressure and a characteristic area. It provides a standardized way to compare the drag characteristics of different objects regardless of their size and is defined by the ratio of the drag force to the product of dynamic pressure and the reference area. This coefficient encapsulates both pressure and viscous effects and is a key parameter in the design and analysis of aerodynamic and hydrodynamic bodies.

Dynamic Pressure

Dynamic pressure is a fluid mechanics concept that represents the kinetic energy per unit volume of a fluid flow. It is typically expressed as ?U²/2, where ? is the fluid density and U is the flow velocity. This parameter is fundamental in analyzing forces due to fluid motion, as it provides a measure against which pressure and drag forces can be compared.

Pressure Drag

Pressure drag, also known as form drag, is the resistance force experienced by an object due to pressure differences between its front and rear surfaces. It originates from the distribution of static pressure over the surface of the body and is influenced by the shape and orientation of the object. Analyzing pressure drag is important in fluid dynamics as it contributes significantly to the total drag force, particularly in bluff bodies or objects with sharp edges.

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