# Essential Formulae

Note: All symbols have their usual meanings as used in the text. These essential formulas may be made available for use on quizzes and exams with the permission of the instructor.

• Equation of state: • Hydrostatic pressure in a stagnant fluid: • Hydrostatic pressure in scalar form: • Hydrostatic equation: • Special solutions to hydrostatic equation:
• For a constant-density fluid: • Pressure change with a linear thermal gradient with temperature lapse between two heights and : • Pressure change with an isothermal temperature between two heights and : • Specific gravity SG of a liquid =  • Specific weight of a liquid =  • Temperature conversions:
• Convert temperature to Kelvin K from Centigrade or Celsius : • Convert temperature to Rankine R from Fahrenheit : • Speed of sound: • Mach number: • Reynolds number based on length : • Kinematic viscosity = • Shear stress in a Newtonian fluid: • Equations of a streamline: • Continuity equation for a fluid: • Momentum equation for a fluid: • The energy equation for a fluid: • The energy equation for the single-stream system: • Bernoulli equation: • The hydraulic diameter of a pipe: • Pressure drop for a pipe flow along a uniform diameter pipe of length : • Head loss for a pipe flow: • Pumping power for a pipe flow: • Area of a wing: • The aspect ratio of a wing: • Mean aerodynamic chord (MAC) of a wing: • Aerodynamic coefficients for an airfoil section:
• Lift coefficient, • Drag coefficient, • Moment coefficient at some point , • Aerodynamic coefficients for a finite wing:
• Lift coefficient, • Drag coefficient, • Moment coefficient about some point , • Induced drag coefficient of a finite wing: • The drag coefficient for an airplane: • General equations of motion of an airplane: • Breguet endurance and range equations for a propeller aircraft:  • Breguet endurance and range equations for a jet aircraft:  • The equivalent exit velocity of a rocket in terms of specific impulse: • Thrust equation for rocket: • Rocket equation (with gravity term): • Conversion factors:
• 1 knot = 1.68781 ft/s
• 1 knot = 0.51444 m/s
• 1 mph = 0.44704 m/s
• 1 mph = 1.46667 ft/s
• 1 ft = 0.3048 m
• 1 statute mile = 5,280 ft
• 1 nautical mile = 6,076 ft
• 1 hp = 550 ft-lb s • Table of ISA Properties at MSL:
 Property Symbol SI units USC units Pressure 1.01325 10 N m 2116.4 ft lb Density 1.225 kg m 0.002378 slugs ft Temperature 15.0 C = 288.15 K 59.0 F  = 518.67 R Dynamic viscosity 1.789 10 kg m s 3.737 10 slug ft s Speed of sound 340.3 m s 1116.47 ft s Gas constant 287.057 J kg K 1716.59 ft-lb slug R • Moody chart for the estimation of the Darcy-Weisbach friction factor: 