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Units: cm=centimeter,
ft=feet, g=gram, hr=hour, kg=kilogram, lb=pound, m=meter, 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 ρ A V^{2} 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 D^{2} / 4.
For the solid cube and solid square rod, A = D^{2}.
For the thin annular disk, A = π (D_{o}^{2}  D^{2}) / 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 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), m^{2}.
C = Drag coefficient (see figures above), unitless.
D = Dimension shown in figures above, m.
D_{o} = Outer dimension of annular disk as shown in figure above, m.
F = Drag force, N.
L = Dimension shown in figures above, m.
Re = Reynolds number, unitless.
V = Velocity, m/s.
μ = Dynamic viscosity, Ns/m^{2} (same as kg/ms).
ρ = Density of fluid (liquid or gas), kg/m^{3}.
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", "Need D < D_{o}", "Need Other
dimension > 0", "Need 10^{o} ≤ a ≤ 180^{o}", "Need
1 ≤ L/D ≤ 10", "Need Velocity > 0", "Need Force > 0".
Runtime 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.
© 20082015 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or other questions.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone and
fax: (740) 5921890
LMNO@LMNOeng.com http://www.LMNOeng.com

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