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The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved – under some conditions – are the: speed u, fluid density ρ, kinematic viscosity ν of the fluid,
With a doubling of speeds, the drag/force quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work. At twice the speed, the work (resulting in displacement over a fixed distance) is done twice as fast.
Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow; No inertial effects (zero Reynolds number) Spherical particles; Homogeneous (uniform in composition) material
The force F required to overcome drag is calculated with the drag equation: = Therefore: = Where the drag coefficient and reference area have been collapsed into the drag area term. This allows direct estimation of the drag force at a given speed for any vehicle for which only the drag area is known and therefore easier comparison.
Traditional displacement sailboats may at times have optimum VMG courses close to downwind; for these the dominant force on sails is from drag. [43] According to Kimball, C D ≈ 4/3 for most sails with the apparent wind angle astern, so drag force on a downwind sail becomes substantially a function of area and wind speed, approximated as ...
The force vector is not straightforward, as stated earlier there are two types of aerodynamic forces, lift and drag. Accordingly, there are two non-dimensional parameters. However, both variables are non-dimensionalized in a similar way. The formula for lift is given below, the formula for drag is given after:
Jean le Rond d'Alembert (1717-1783) From experiments it is known that there is always – except in case of superfluidity – a drag force for a body placed in a steady fluid onflow. The figure shows the drag coefficient C d for a sphere as a function of Reynolds number Re , as obtained from laboratory experiments.