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Article by Harlan Bengtson (12,538 pts )

Edited & published by Lamar Stonecypher (77,628 pts ) on Jun 1, 2010

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Home > Engineering > Civil Engineering > Hydraulics

DRAG FORCE FOR FLUID FLOW PAST ANIMMERSED OBJECT

The drag force due to fluid flow past an immersed object is the air resistance or water resistance due to the

fluid. The Reynolds number helps to determine the drag coefficient, which is needed, along with the object

size & shape and flow velocity, in the drag equation to calculate the drag force.

Introduction

When there is fluid flow past a solid object, the resulting air resistance or water resistance causes a dragforce. This drag force is of concern for a variety of applications, such as wind force on structures and drag

force of air or water on moving vehicles. This article includes the drag force equation, brief discussion of the

parameters in the equation, example drag coefficient values and an example drag force calculation.

The Drag Force Equation

The general equation for the drag force of a fluid flowing past an immersed solid

is: FD = CD(1/2)ρV2A

where: FD is the drag force in lb, ρ is the fluid density in slugs/ft3,

A is a reference area as defined for the particular solid in ft2. For many types of

immersed objects, the reference area is the frontal

area of the object normal to the direction of fluid flow.

CD is the drag coefficient, a dimensionless number, which depends upon the

shape of the solid object and perhaps upon the Reynolds Number for the fluid

flow. The diagram at the left shows the parameters for drag force due to flow

past an immersed body. At the right is a f igure showing air flow and drag force

due to air resistance for a moving car.

Drag Coefficient Values

Empirical values for drag coefficient for various shaped objects are given in the diagram at the right and the

table below. Note that a value for Reynolds Number is given for some of the

shapes. The drag coefficient, in general, depends upon the Reynold's Number as

well as the shape of the object. The effect of Reynolds Number is more important

in some cases than others. Reynolds Number for flow past an immersed body is

defined as Re = LVρ/μ, where

L is a characteristic dimension for the object in ft

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COMMENTS 3

V is the approach velocity of the fuid in ft/sec

ρ is the fluid density in slugs/ft3

and μ is the fluid viscosity in lb-sec/ft2.

Object --- (CD)

A typical bicycle plus cyclist --- (0.9)

Rough sphere (Re = 1,000,000) --- (0.4)

smooth sphere (Re = 1,000,000) --- (0.1)

Turbulent flow parallel to a flat plate (Re = 1,000,000) --- (0.005)

Laminar flow parallel to a flat plate (Re = 1,000,000) --- (0.001)

Hummer H2 (2003) --- (0.57)

Ford Mustang Fastback (1979) --- (0.44)

Chevrolet Camaro (1995) -- - (0.338)

Toyota Prius (2004 - 2009) --- (0.26)

Bullet at subsonic velocity --- (0.295)

Man in upright position --- (1.0 - 1.3)

Flow perpendicular to a long flat plate --- (1.98 - 2.0)

Skier --- (1.0 - 1.1)

Wires and cables --- (1.0 - 1.3)

Empire State Building --- (1.3 - 1.5)

Eiffel Tower --- (1.8 - 2.0)

Example Calculation

Problem: Calculate the drag force due to air resistance on a 3" diameter rough sphere moving through the air

at 90 miles per hour, with an air temperature of 50oF and air pressure of 14.7 psi.

Solution: The density of air at the specified conditions can be calculated using the ideal gas law: ρ =

(MW)(P/RT) = (29)(14.7/([345.23(50 + 459.67)] = 0.002423 slugs/ft3. (See the article: Use the ideal gas law

to find the Density of Air at Different Pressures and Temperatures for more details.)

The velocity needs to be converted to ft/sec: V = (90 mi/hr)(5280 ft/mi)/(3600 sec/hr) = 132 ft/sec.

The frontal area of the sphere is: A = ΠD2/4 = Π(3/12)

2/4 = 0.04906 ft

2.

The value of the drag coefficient, CD, from the table above is 0.4

Finally, substitute values into the drag force equation: FD = CD(1/2)ρV2A = (0.4)(1/2)(0.002423)(132

2)

(0.04906) = 0.414 lb

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bo May 15, 2010 8:06 PM

thank's

thank you for the information, it's help me

Harlan Bengtson Apr 4, 2010 9:44 AM

Error

Al, You are absolutely correct. Fortunately the correct value was used in the final calculation. I will

get the correct value put in where you noted it in the article.

Harlan Bengtson

Al Smith Apr 3, 2010 11:50 PMError

(MW)(P/RT) = (29)(14.7/([345.23(50 + 459.67)] =

0.002423

not

0.0002423

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coefficient drag 1

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