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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,
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.
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.
The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation of the force acting on the particle. In Cartesian coordinates the vector-gradient is identical to the Jacobian matrix. The matrix I represents the identity-matrix.
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.
The derivation of Stokes' law, which is used to calculate the drag force on small particles, assumes a no-slip condition which is no longer correct at high Knudsen numbers. The Cunningham slip correction factor allows predicting the drag force on a particle moving a fluid with Knudsen number between the continuum regime and free molecular flow.
It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the drag on the body is small in proportion to its mass. BC can be expressed with the units kilogram-force per square meter (kgf/m 2) or pounds per square inch (lb/in 2) (where 1 lb/in 2 corresponds to 703.069 581 kgf/m 2).
This increase can cause the drag coefficient to rise to more than ten times its low-speed value. The value of the drag-divergence Mach number is typically greater than 0.6; therefore it is a transonic effect. The drag-divergence Mach number is usually close to, and always greater than, the critical Mach number.