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Definition: DRAG FORCE. Drag Force \(F_D\) is found to be proportional to the square of the speed of the object. Mathematically \[F_D\propto v^2 \] \[F_D = \dfrac{1}{2} C_{\rho} Av^2, \] where \(C\) is the drag coefficient \(A\) is the area of the object facing the fluid, and \(\rho\) is the density of the fluid.
Using the equation of drag force, we find [latex]\text{mg}=\frac{1}{2}{\text{ρCAv}}^{2}[/latex]. Thus the terminal velocity [latex]{v}_{t}[/latex] can be written as [latex]{v}_{\text{t}}=\sqrt{\frac{2\text{mg}}{\text{ρCA}}}.[/latex]
Express the drag force mathematically; Describe applications of the drag force; Define terminal velocity; Determine an object’s terminal velocity given its mass
Drag force FD F D is proportional to the square of the speed of the object. Mathematically, FD = 1 2CρAv2, (6.7.2) (6.7.2) F D = 1 2 C ρ A v 2, where C C is the drag coefficient, A A is the area of the object facing the fluid, and ρ ρ is the density of the fluid.
Express mathematically the drag force. Discuss the applications of drag force. Define terminal velocity. Determine the terminal velocity given mass. Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water.
Learning Objectives. By the end of the section, you will be able to: Express the drag force mathematically. Describe applications of the drag force. Define terminal velocity. Determine an object’s terminal velocity given its mass.
The drag force, F D, can be expressed in terms of a drag coefficient, C D, the effective body area, A, normal to the flow, and the dynamic pressure, (r U 2 /2): FD = CDA (rU2/2). This expression indicates that the drag on a given body increases as the square of its speed with respect to the fluid, as shown in the diagram.
