Question $2$

A $70$m long, $3"$ schedule $40$ horizontal commercial steel pipe of with an inlet gauge pressure of $172$ kPa is used to transport air. The inlet velocity of the air is $60\frac{m}{s}$ and it is at $15C.$ At this pressure and temperature the viscosity is $0\mathrm{.}0174cP$ and $=1\mathrm{.}40$

Assuming isothermal flow, calculate;

a$)$ The discharge pressure

b$)$ The maximum length of the pipe needed to maintain the inlet conditions

Hint:

a$)$ Trial and error solution, First iteration assume $P=130$kPa

b$)$ Calculate $u_2=u_w=\sqrt[\phantom{2}]{P_w{V}_w}$ and find the corresponding $L$

c$)$ E balance $\frac{P_2^2-P_1^2}{2P_1{V}_1}+G^2(ln(\frac{P_1}{P_2})+\frac{2fL}{d_i})=0$

d$)$ Express the $E$ balance in terms of the ratio $\frac{u_1}{u_2}=\frac{{}_2}{{}_1}=\frac{\frac{P_{2}MM}{RT}}{\frac{P_{1}MM}{RT}}=\frac{P_2}{P_1}$