There are many different ways to calculate air velocity in aerodynamics. They vary based on the variables that are available, the nature of the flow and the compressibility of the flow. The most common method is the use of Bernoulli’s equation. This method can be used for a wide range of airflow applications, but it cannot be used for high-speed compressible flow. Bernoulli’s equation is derived using the assumption that density is constant throughout the flow, and this is not the case in compressible flow.
Determine the static pressure (p) and density (rho) of the airflow. For routine analytical calculations, the best method is to simply look these values up in the NACA Standard Atmosphere tables. Find the altitude you are operating at in the table and use the corresponding values for pressure and density. At 10,000 feet: p = 1,455.6 lb/ft^2 rho = 0.00176 slugs/ft^3
Obtain the total pressure (p0) value. This will be given if you are solving an academic problem, or you must measure the total pressure using a Pitot tube or similar instrument on the aircraft. p0 = 1,500 lb/ft^2
Enter the values into Bernoulli's equation: p0 = p + 0.5 * rho * V^2 1,500 = 1,455.6 + 0.5 * 0.00176 * V^2
Solve the equation for velocity: V^2 = 2(1,500 - 1455.6) / 0.00176 V^2 = 50,455 V = 224.6 ft/sec
You can also obtain density using the perfect gas equation: p = rho * R * T. This is useful if you have a method of measuring temperature directly. Use the measured temperature along with the pressure value from the Standard Atmosphere tables and solve for rho.
If Mach number is greater than 0.3, this method will fail. The equations for flow regimes above M = 0.3 require far more complex calculations.