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Dezi et. al (2010)
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Projectile motion
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This calculator computes the drag force and drag force coefficient. It also includes a common case study of a sphere in Stokes' flow.

Calculation

Drag Force,


Inputs



ρ
:1.00kg/m3​



U
:15.00m/s​



A
:3.00m2​



Cd
:0.50​


Output



Fd
:168.72N​


Fd=12ρU2ACdF_{d}=\frac{1}{2}\rho U^2 A C_{d}
Where:
  1. 
    
    is the density of the fluid
  2. 
    
    is the relative velocity
  3. 
    
    is the reference area
  4. 
    
    is the drag coefficient
  5. 
    
    is the drag force


Drag Force Coefficient,



Inputs



ρ_
:1.00kg/m3​



A_
:3.00m2​



U_
:15.00m/s​



Fd_
:168.72N​


Output



Cd_
:0.50​


Cd=2FdρU2AC_{d}=\frac{2F_{d}}{\rho U^2 A}
Where:
  1. 
    
    is the density of the fluid
  2. 
    
    is the relative velocity
  3. 
    
    is the reference area
  4. 
    
    is the drag coefficient
  5. 
    
    is the drag force


Drag Force for a sphere in Stokes Flow,



Inputs



r
:0.50m​



U__
:3.00m/s​



η
:1.15Pa*s​


Output



Fd__
:32.52N​


Fd=6πUrηF_{d}=6\pi Ur\eta

Where:
  1. 
    
    is the radius of a sphere
  2. 
    
    is the relative velocity
  3. 
    
    is the viscosity of the fluid
  1. 
    
    is the drag force of the sphere


Drag Coefficient for a sphere in Stokes Flow,



Input



Re
:0.05​


Output



_Cd
:480.00​


Cd=24ReC_d=\frac{24}{Re}
Where:
  1. 
    
    is the Reynolds Number, note that Stokes Flow has a
    
    
  2. 
    
    is the relative velocity
  3. 
    
    is the viscosity of the fluid
  1. 
    
    is the drag coefficient of a sphere in Stokes Flow


Explanation

Drag force,

is the resistance that an object encounters as it moves through a fluid (such as air or water). It acts in the direction opposite to the object's motion which slows it down, and depends on factors like the object's shape, size, speed and the properties of the fluid it's moving through. The drag force increases with the square of the object's velocity and can be significant in aerodynamic or hydrodynamic considerations.
Drag force on an object

The equation for drag force is given by:

Fd=12ρu2ACdF_{d}= \dfrac{1}{2} \rho u^2AC_{d}
Drag coefficient,

is a dimensionless number that quantifies an object's drag in a particular fluid flow. The drag coefficient allows for the comparison of drag efficiency between different objects, irrespective of their size or the specific fluid properties. It plays a crucial role in designing vehicles, structures, or other objects interacting with fluids, providing a standardized measure for their aerodynamic or hydrodynamic performance. The equation for the drag coefficient is given by re-arranging the drag force equation, as provided below:

Cd=2Fdρu2AC_{d} = \dfrac{2F_{d}}{\rho u^2A}
Stokes flow refers to a specific regime of fluid flow characterized by low Reynolds numbers

. Named after the physicist Sir George Gabriel Stokes, this type of flow occurs when the inertial forces within a fluid are negligible compared to the viscous forces. This typically happens in situations with very slow fluid motion, small object sizes, or fluid with high viscosity. In Stokes flow, the equations governing fluid motion simplify significantly and the resulting flow patterns are smooth and predictable. The relationship with drag force becomes particularly interesting in the context of small particles or objects moving through a fluid at low speeds. Stokes' law for flow around a sphere says

and

is given by:

Fd=6πUrηCd=24ReF_{d}=6\pi Ur\eta \\C_d=\dfrac{24}{Re}

Related Resources

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  2. Reynolds Number Calculator
  3. Total and Partial Pressure
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