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Where represents the y-derivative and is the free stream velocity profile.
This vector is the relative wind or the free stream velocity vector.
This causes the air passing through the rotor plane to have a smaller velocity than the free stream velocity.
A shroud of suitable geometry can increase the flow velocity across the turbine by 3 to 4 times the open or free stream velocity.
This downwash alters the free stream velocity, by rotating it downward, towards the downwash.
Similarly the subsonic leading and trailing are those portions of the wing edge where the components of the free stream velocity normal to the edge are subsonic.
One can estimate the time of travel for a gas molecule from the shock wave to the stagnation point by assuming a free stream velocity of 7.8 km/s and a nose radius of 1 meter, i.e., time of travel is about 18 microseconds.
An example includes fluid motion over a flat plate (inclined or parallel to the free stream velocity) and flow over curved surfaces such as a sphere, cylinder, airfoil, or turbine blade, air flowing around an airplane and water flowing around the submarines.
For example, in the case of the Galileo Probe's entry into Jupiter's atmosphere, the shock layer was mostly in equilibrium during peak heat flux due to the very high pressures experienced (this is counterintuitive given the free stream velocity was 39 km/s during peak heat flux).