Question

Air enters a 16-cm-diameter pipe steadily at 200 kPa and 20โC with a velocity of 5 m/s. Air is heated as it flows, and it leaves the pipe at 180 kPa and 40โC. Determine

(a) the volume flow rate of air at the inlet,
(b) the mass flow rate of air, and
(c) the velocity and volume flow rate at the exit.

Answer 1

m = 0.239kg/s

V₂ = 0.119m^3/s

v² = 5.92m/s

Step-by-step explanation:

Given that,

Diameter = 16 cm

Enter pressure= 200 kPa

Enter temperature = 20°C

Velocity = 5 m/s

Exit pressure = 180 kPa

Exit temperature = 40°C

Mass flow rate is determine by the properties of the air at the initial state fromit initial velocity and the cross sectional area of the pipe

`m = p_1V_1`

`= (P_1)/(RT_1) A_1v_1`

`= (P_1)/(RT_1) (D^2)/(4) \pi v_1\\= (200)/(0.287) * (0.16^2)/(4) * \pi * 5\\= 0.239kg/s`

The final volume rate is determine from the mass flow rate and the final properties of the air

`V_2 = (m)/(P_2) \\= (RT_2m)/(P_2) \\= (0.287 * 313 *0.239)/(180) \\= 0.119m^3/s`

Final velocity is determine from final volume flow rate and the cross sectin area

`v^2 = (V_2)/(A) \\=(4V_2)/(D^2\pi ) \\= (4 * 0.119)/(0.16^2 * \pi ) \\= 5.92m/s`