# 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:

• Unique solutions to the 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:

• Free stream dynamic pressure:

• 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 loss term):

• Mean equivalent exhaust velocity (for multiple boosters):

• 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 1.0132510 N m 2116.4 lb ft Density 1.225 kg m 0.002378 slugs ft Temperature 15.0C = 288.15 K 59.0F  = 518.67 R Dynamic viscosity 1.78910 kg m s 3.73710slug ft s Speed of sound 340.3 m s 1116.47 ft s Gas constant 287.057 J kg K 1716.49 ft-lb slugR
• Moody chart for the estimation of the Darcy-Weisbach friction factor: