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:
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- Pressure change with a linear thermal gradient with temperature lapse between two heights and :
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- 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 :
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- 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:
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- Lift coefficient,
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- Drag coefficient,
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- Moment coefficient at some point ,
- Aerodynamic coefficients for a finite wing:
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- Lift coefficient,
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- Drag coefficient,
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- 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: