Air at 320 K flows in a duct. If a pitot tube was inserted, what would the temperature of the air be at the tip of the pitot tube (stagnation point) if the air speed was: a. 1 m/s b. 10 m/s c. 100 m/s d. 1000 m/s

Respuesta :

Answer:

320.004975 K, 320.047 K , 324.975 K ,817.5124

Explanation:

Let air is an ideal gas

The temperature at [tex]c_p[/tex] is given by [tex]T_0={T+\frac{v^2}{2c_P}}[/tex]

(a) for speed of 1 m/sec [tex]T_0={T+\frac{v^2}{2c_P}}={320+\frac{1^2}{2\times 1005}}=320.0049[/tex]

(b) for speed of 10 m/sec[tex]T_0={T+\frac{v^2}{2c_P}}={320+\frac{10^2}{2\times 1005}}=320.0497 K[/tex]

(C) For speed of 100 m/sec [tex]T_0={T+\frac{v^2}{2c_P}}={320+\frac{100^2}{2\times 1005}}=324.975 K[/tex]

(d) For speed of 1000 m/sec [tex]T_0={T+\frac{v^2}{2c_P}}={320+\frac{1000^2}{2\times 1005}}=817.5124 K[/tex]