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## Dimensional Analysis Worksheet

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.

 Name or description of equation Location of Equation/Process Dynamic Pressure (middle term of the total pressure equation) Sample problem http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html Dynamic Pressure equation: __________, 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.   Step #2. Change derived units to fundamental units.   Step #3. Perform the indicated binary operations. Force (Algebraic Form) http://www.grc.nasa.gov/WWW/K-12/airplane/newton2.html Force Equation: Step #1: Step #2: Step#3: Force (with mass constant) http://www.grc.nasa.gov/WWW/K-12/airplane/newton2.html Force Equation: Step #1: Step #2: Step#3: Velocity (if force and mass remain constant) http://www.grc.nasa.gov/WWW/K-12/airplane/motion.html Velocity Equation: Step #1: Step #2: Step#3: Displacement (if force and mass remain constant) http://www.grc.nasa.gov/WWW/K-12/airplane/motion.html Displacement Equation: Step #1: Step #2: Step#3: Lift equation http://www.grc.nasa.gov/WWW/K-12/airplane/lifteq.html Lift Equation: Step #1: Step #2: Step#3: Lift Coefficient http://www.grc.nasa.gov/WWW/K-12/airplane/liftco.html Lift Coefficient: Step #1: Step #2: Step#3: Velocity squared equation http://www.grc.nasa.gov/WWW/K-12/airplane/pitot.html Velocity Squared Equation: Step #1: Step #2: Step#3:
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 ) kgm/s2 Time t, t1, or t0 s Velocity V, V0, or V1 m/s
Table 2: Unit Data Chart