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Dimensional Analysis Problems
If so instructed by your teacher, print out a worksheet page for these problems.
 

Access each location in Table 1 and note the indicated equation. (Hint: Most slides explain the variables of the equation.)

Perform a dimensional analysis on each side of the equations, reducing to fundamental units to verify validity. Table 2 is a chart of unit data and symbols to aid you in your work.

Name or description of equation
Location of equation
   

Dynamic Pressure (middle term of the total pressure equation) Sample problem

http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html

Force
(Algebraic Form)

http://www.grc.nasa.gov/WWW/K-12/airplane/newton2.html

Force
(with mass constant)

http://www.grc.nasa.gov/WWW/K-12/airplane/newton2.html

Velocity
(if force and mass remain constant)

http://www.grc.nasa.gov/WWW/K-12/airplane/motion.html

Displacement
(if force and mass remain constant)

http://www.grc.nasa.gov/WWW/K-12/airplane/motion.html

Lift equation

http://www.grc.nasa.gov/WWW/K-12/airplane/lifteq.html

Lift Coefficient

http://www.grc.nasa.gov/WWW/K-12/airplane/liftco.html
Velocity squared equation http://www.grc.nasa.gov/WWW/K-12/airplane/pitot.html

Table 1

 

Name

Symbol

Units

Fundamental units
       

Acceleration

a

m/s2

  

Area

A

m2

  

Displacement

X, or X0

m

  

Density

r

kg/m3

  

Force

F

n (newton)

kgm/s2

Lift

L

n (newton)

kgm/s2

Lift Coefficient

Cl

no units

  

Mass

m

kg

  

Pressure

P, Pt, or Ps

pa

(pascals n / A )

kgm/s2

Time

t, t1, or t0

s

  

Velocity

V, V0, or V1

m/s

  
Table 2: Unit Data Chart

Sample problem:

Dynamic Pressure equation: P = r * V2/2, where P stands for pressure and is measured in pa (pascals), r stands for density and is measured in kg/m3, and V stands for velocity and is measured in m/s.

Step #1.
Replace the variables with the correct unit; ignore constants.

pa = kg/m3 * (m/s)2


Step #2.
Change derived units to fundamental units.

n/A = kg/m3 * (m/s)2 ----------- (pa = n/A)

(kg * m/s2)/m2 = kg/m3 * ( m/s)2 ------------- (n = kg * m/s2 and A = m2)

Step #3.
Perform the indicated binary operations.

kg/(m * s2) = kg/(m * s2)
  

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Please send any comments to:
Curator: Tom.Benson@grc.nasa.gov
Responsible Official: Kathy.Zona@grc.nasa.gov