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Dimensional Analysis Worksheet

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/Process

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

http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html
Dynamic Pressure equation: __________, 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.

 


Step #2.
Change derived units to fundamental units.

 

Step #3.
Perform the indicated binary operations.

Force
(Algebraic Form)

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

Step #1:

Step #2:

Step#3:

Force
(with mass constant)

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

Step #1:

Step #2:

Step#3:

Velocity
(if force and mass remain constant)

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

Step #1:

Step #2:

Step#3:

Displacement
(if force and mass remain constant)

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

Step #1:

Step #2:

Step#3:

Lift equation

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

Step #1:

Step #2:

Step#3:

Lift Coefficient

http://www.grc.nasa.gov/WWW/K-12/airplane/liftco.html
Lift Coefficient:

Step #1:

Step #2:

Step#3:

Velocity squared equation

http://www.grc.nasa.gov/WWW/K-12/airplane/pitot.html
Velocity Squared Equation:

Step #1:

Step #2:

Step#3:
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