Dimensional Analysis - Answers

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