Question

Steam enters an insulated pipe at 200 kPa and 200°C and leaves at 150 kPa and 150°C. The inlet-to-outlet diameter ratio for the pipe is D1/D2 = 1.80. Determine the inlet and exit velocities of the steam.

Answer 1

Answer:

Inlet and exit velocities are 143.71 m/sec and 465.697 m/sec

Explanation:

At inlet of the pipe

$P_1=150kPa$ and $T_1=150^{\circ}C$

At this pressure and temperature from steam table.

$h_1=2870kj/kg$ and $s_1=7.508kj/kgK$

At pressure $P_2=200kPa$ and $T_2=200^{\circ}C$

By steam table from interpolation method.

$h_2=2776.38+(2768.80-2776.38)(\frac{150-100}{200-100})$

$h_2=2772.59kj/kg$

$Q=A_1V_1=A_2V_2$

$D_1^2V_1=D_2^2V_2$

We have given $\frac{D_1}{D_2}=1.80$

$\frac{V_1}{V_2}=\frac{D_2^2}{D_1^2}$

$\frac{V_1}{V_2}=(\frac{1}{1.80})^2$

$V_1=0.3086V_2$

Now energy equation in the pipe

$h_1+\frac{V_1^2}{2}=h_2+\frac{V_2^2}{2}$

$2870.7\times 10^3+\frac{0.3086V_2^2}{2}=2772.59\times 10^3+\frac{V^2}{2}$

$V_2=465.697m/sec$

$V_1=0.3086\times 465.697=143.714m/sec$