Question

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

Answer 1

320.004975 K, 320.047 K , 324.975 K ,817.5124

Step-by-step explanation:

Let air is an ideal gas

The temperature at
`c_p` is given by
`T_0={T+(v^2)/(2c_P)}`

(a) for speed of 1 m/sec
`T_0={T+(v^2)/(2c_P)}={320+(1^2)/(2* 1005)}=320.0049`

(b) for speed of 10 m/sec
`T_0={T+(v^2)/(2c_P)}={320+(10^2)/(2* 1005)}=320.0497 K`

(C) For speed of 100 m/sec
`T_0={T+(v^2)/(2c_P)}={320+(100^2)/(2* 1005)}=324.975 K`

(d) For speed of 1000 m/sec
`T_0={T+(v^2)/(2c_P)}={320+(1000^2)/(2* 1005)}=817.5124 K`