NASA Logo - Web Link to NASA.gov Vertical Line

+ Text Only Site
+ Non-Flash Version
+ Contact Glenn

Go
ABOUT NASA NEWS AND EVENTS MULTIMEDIA MISSIONS MyNASA WORK FOR NASA

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

 

     First Gov Image


+ Inspector General Hotline
+ Equal Employment Opportunity Data Posted Pursuant to the No Fear Act
+ Budgets, Strategic Plans and Accountability Reports
+ Freedom of Information Act
+ The President's Management Agenda
+ NASA Privacy Statement, Disclaimer,
and Accessibility Certification

 

NASA Logo   
Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, May 13 02:38:26 PM EDT 2021

+ Contact Glenn