Drag Force Calculation with built-in Drag Coefficients
 

Drag Coefficients, Drag Force Equations, Drag Force Calculation.


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Units: cm=centimeter, cP=centipoise, cSt=centistoke, ft=feet, g=gram, hr=hour, kg=kilogram, lb=pound, m=meters, N=Newton, s=second

Introduction
The drag force on an object is produced by the velocity of a liquid or gas approaching the object. Drag force is dependent upon the drag coefficient of the object and the geometry of the object. For some objects, the drag coefficient is independent of the object's dimensions. However, for other shapes of objects, the drag coefficient is dependent on the dimensions and may be additionally dependent on the Reynolds number. Our calculation has drag coefficients for a solid hemisphere, hollow hemisphere, solid cone, ellipsoid, annular disk, solid cylinder, solid cube, and solid square rod.

Equations
The drag force equation used for the calculation on this page is (Blevins, 2003 and Munson et al., 1998 and others):

F = 0.5 C ρA V2     Re = ρVD/μ

Area (A) is defined for each shape (Blevins, 2003):
For the solid hemispheres, hollow hemispheres, solid cone, ellipsoid, and solid cylinder, A = π D2 / 4.
For the solid cube and solid square rod, A = D2.
For the thin annular disk, A = π (Do2 - D2) / 4.

The drag coefficients (C) used in our calculation are from Blevins (2003). Drag coefficients for the solid hemisphere, hollow hemisphere, and cube are independent of dimensions or Reynolds number. The drag coefficient for the solid cone, ellipsoid, thin annular disk, solid cylinder, and solid square rod have drag coefficients that are functions of the shape's dimensions. Blevins (2003) provides tables of the drag coefficient versus dimensions. LMNO Engineering has fit equations to the Blevins tabular data with the resulting drag coefficient shown in the calculation above.

Notation
Our calculation allows you to use a variety of units with all of the conversions completed internally. The units shown below are SI (international system of units).
a = Angle in solid cone, radians.
A = Reference area (see figures above), m2.
C = Drag coefficient (see figures above), unitless.
D = Dimension shown in figures in applet, m.
Do = Outer dimension of annular disk as shown in figure in applet above, m.
F = Drag force, N.
L = Dimension shown in figures in applet, m.
Re = Reynolds number, unitless.
V = Velocity, m/s.
μ = Dynamic viscosity, N-s/m2 (same as kg/m-s).
ρ = Density of fluid (liquid or gas), kg/m3.

Messages given by calculation
Messages indicating input values are out of the acceptable ranges. Results will not be computed:
"Need Density > 0", "Need Viscosity > 0", "Need C > 0", "Need D > 0", "Must have D < Do", "Need Other dimension > 0", "Must have 10<=a<=180 deg", "Must have 1<=L/D<=10", "Need Velocity > 0", "Need Force > 0".

Run-time messages. Results will not be computed:
"Need Area > 0".

Warning messages. Results will be computed:
"C based on Re=170000" means that for this shape, the value of C is valid for a Reynolds number of 170000.
"C may not be valid for Re > 2E6" means that for this shape, C is valid for a certain range of Reynolds number.

References
Blevins, Robert D. 2003. Applied Fluid Dynamics Handbook. Krieger Publishing Co.

Munson, Bruce R., Donald F. Young, and Theodore H. Okiishi. 1998. Fundamentals of Fluid Mechanics. John Wiley and Sons, Inc. 3ed.


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