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Consider this equation. According to my understanding, the term static and stagnation means velocity is zero. So shouldn't static temperature be equal to the stagnation temperature? What am I missing here? Also, the velocity of which point are we exactly considering in this equation?

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  • $\begingroup$ Hi user29463. Welcome to Phys.SE. Linking to private clouds, dropbox, etc, is for various reasons not acceptable on SE, cf. this meta post. $\endgroup$ – Qmechanic Oct 6 '19 at 10:16
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A stagnation point is where the flow around an object comes to a rest (i.e. the local velocity is zero). But there will be a streamline leading to this point, which ends at the stagnation point (perpendicular to the surface).

The equation describes the temperature along this streamline leading to the stagnation point. The stagnation temperature is the temperature measured at the stagnation point, where the velocity is zero.

The static temperature is the temperature at some other point on this streamline, but not taking into account the kinetic energy from the flow. This is the temperature you would measure if you were to move a thermometer along with the fluid. It will typically be lower than the stagnation temperature, because the kinetic energy from the directed motion is converted to thermal energy when it is brought to a stop at the stagnation point.

The velocity will be the local velocity at the specific point along the streamline which you want to know the temperature of.

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