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Dimensional Analysis
Answers


Name or description of equation
Location of equation
   

Dynamic Pressure (middle term of the total pressure equation)
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.

N= Kgm/s2


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)

 

Force
(Algebraic Form)

F = m * a
pa = kg/m3 * (m/s)2
Kgm/s2 = Kgm/s2

Force
(with mass constant)

F = m (V1 - V0)/(t1 - t0)
N = [Kg (m/s - m/s)]/(s-s)
Kgm/s2 = (Kgm/s)/s
Kgm/s2 = Kgm/s2

Velocity
(if force and mass remain constant)

V = a * t + V0
m/s = m/s2 * s + m/s
m/s = m/s + m/s
m/s = m/s

Displacement
(if force and mass remain constant)

X = (a * t2)/2 + V0 * t + X0
m = (m/s2 * s2)/2 + m/s * s + m
m = m + m + m
m = m

Lift equation

L = Cl * r * V2/2 * A
N = (Kg/m3)(m/s)2 * m2
Kgm/s2 = (Kg/m3)(m2/s2) * m2
Kgm/s2 = Kgm/s2

Lift Coefficient

Cl = L/(r*V2/2*A)
Cl = N/[(Kg/m3)(m/s)2(m2)
No units = (Kgm/s2)/(Kgm/s2)
No units = No units

Velocity squared equation V2 = 2(Pt-Ps)/r
(m/s)2 = 2(Kgm/s2 - Kgm/s2)/(Kg/m3)
m2/s2 = (Kgm/s2)/(Kg/m3)
m2/s2 = m2/s2


Related Pages:
Standards
Activity
Worksheet
Lesson Index
Aerodynamics Index

 

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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, Jun 12 04:46:38 PM EDT 2014

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