Dimensional
Analysis Activity
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.
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 )
|
kg/ms2
|
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)
|