One application of fluid resistance is air drag (or drag). It's the retarding force when an object moves through a fluid. We explore more on this concept:
Deriving the Drag Equation
Continuing from fluid resistance \(F_f\), consider a large body moving through the fluid or a relatively fast-moving object with velocity \(v\). The fluid resistance on the body is equal to:
\(F_f= kv^2\)
- \(F_f\) is the fluid resistance
- \(k\) is the constant of proportionality
- \(v\) is the velocity of the body moving through the fluid
The constant \(k\) will depend on many factors, such as the body's size and shape and the fluid's density:
\(k=\frac{1}{2} \rho A C_D\)
When we substitute this proportionality constant to \(F_f\), we have:
\(F_f=\frac{1}{2} \rho A C_D v^2\)
- \(\rho\) is the mass density of the fluid
- \(A\) is the cross-section area of the object
- \(C_D\) is the drag coefficient
- \(v\) is velocity of the object
This equation is the Drag Equation - an essential expression in many scientific fields, such as aerodynamics. From this derivation, it expands on concepts explored in fluid resistance.
Summary
Consider a large body moving through the fluid or a relatively fast-moving object with velocity \(v\). The fluid resistance \(F_f\) on the body is equal to: \(F_f= kv^2\)
The constant \(k\) will depend on many factors, such as the body's size and shape and the fluid's density: \(k=\frac{1}{2} \rho A C_D\)
The resistance force is equal to \(F_f=\frac{1}{2} \rho A C_D v^2\) where \(\rho\) is the mass density of the fluid, \(A\) is the cross-section area of the object, and \(C_D\) is the drag coefficient. This expression is the Drag Equation.
