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/s^{2}


Area

A

m^{2}


Displacement

X, or X_{0}

m


Density

r

kg/m^{3}


Force

F

n (newton)

kgm/s^{2}

Lift

L

n (newton)

kgm/s^{2}

Lift Coefficient

Cl

no units


Mass

m

kg


Pressure

P, P_{t},
or P_{s}

pa
(pascals
n / A )

kg/ms^{2}

Time

t, t_{1},
or t_{0}

s


Velocity

V, V_{0},
or V_{1}

m/s


Table 2: Unit
Data Chart
Sample problem:
Dynamic Pressure equation:
P = r * V^{2}/2, where P stands for pressure and is measured in
pa (pascals), r stands for density and is measured in kg/m^{3},
and V stands for velocity and is measured in m/s.
Step #1.
Replace the variables with the correct unit; ignore constants.
pa = kg/m^{3}
* (m/s)^{2 }
^{
}Step #2.
Change derived units to fundamental units.
n/A = kg/m^{3}
* (m/s)^{2 }  (pa = n/A)
(kg * m/s^{2})/m^{2
= }kg/m^{3} * ( m/s)^{2 } (n = kg *
m/s^{2 } and A = m^{2})
Step #3.
Perform the indicated binary operations.
kg/(m * s^{2})
= kg/(m * s^{2})
