Question

Oxygen enters an insulated 12-cm-diameter pipe with a velocity of 70 m/s. At the pipe entrance, the oxygen is at 240 kPa and 20°C, and at the exit it is at 200 kPa and 18°C. Calculate the rate at which entropy is generated in the pipe.

Answer 1

Answer:

S = 0.10253 kW/k

Explanation:

Given data:

Velocity of oxygen ( V ) = 70 m/s  

Diameter of pipe = 12-cm = 0.12 m

At entrance

pressure of oxygen ( p1 ) = 240 kPa

Temperature of oxygen ( T1 ) = 20°c  = 293 k

At exit

pressure of oxygen ( p2 ) = 200 kPa

temperature of oxygen ( T2 ) = 18°c = 291 k

First calculate specific volume of oxygen at inlet

V1 = $\frac{RT1}{P1}$  -------- ( 1 )

  R = 0.2598 KJ/kgk ( property of oxygen )

  T1 = 293 k

  P1 = 240 kpa

substitute values into equation 1

V1 = 0.3172 m^3/kg

next we calculate the mass flow rate of Oxygen

m = $\frac{A1V}{v1}$ ----- ( 2 )

A1 ( area of pipe ) = 0.0113 m^2 ( calculated )

V = 70 m/s

V1 = 0.3172 m^3/kg

substitute value into equation 2

m ( mass flow rate of oxygen ) = 2.4936 kg/s

Finally calculate the rate at which entropy is generated in the pipe

S = $m( C_{p} In\frac{T2}{T1} - RIn\frac{P2}{P1} )$   --------- ( 3 )

$C_{p}$ = 0.918 kj/kgk  ( property of oxygen )

T2 = 291 k

T1 = 293 k

P2 = 200 kPa

P1 = 240 kPa

substitute values into equation 3 above

S = 0.10253 kW/k