Question 4.P.5: A vacuum distillation plant operating at 7 kN/m² pressure at...
A vacuum distillation plant operating at 7 kN/m² pressure at the top has a boil-up rate of 0.125 kg/s of xylene. Calculate the pressure drop along a 150 mm bore vapour pipe used to connect the column to the condenser. The pipe length may be taken as equivalent to 6 m, e/d = 0.002 and \mu=0.01 mN s/m².
From vapour pressure data, the vapour temperature = 338 K and the molecular weight of xylene = 106 kg/kmol.
In equation 4.55:
(G / A)^2 \ln \left(P_1 / P_2\right)+\left(P_2^2-P_1^2\right) / 2 P_1 v_1+4\left(R / \rho u^2\right)(l / d)(G / A)^2=0
Cross-sectional area of pipe, A=(\pi / 4)(0.15)^2=1.76 \times 10^{-2} m ^2
G / A=\left(0.125 / 1.76 \times 10^{-2}\right)=7.07 kg / m ^2 s
The Reynolds number, is \rho u d / \mu=d(G / A) / \mu
=\left(0.15 \times 7.07 /\left(0.01 \times 10^{-3}\right)=1.06 \times 10^5\right.
From Fig. 3.7, with e/d = 0.002 and R e=1.06 \times 10^5,\left(R / \rho u^2\right)=0.003.
Specific volume, v_1=(22.4 / 106)(338 / 273)(101.3 / 7.0)=3.79 m ^3 / kg.
Substituting in equation 4.55:
(7.0)^2 \ln \left(7 / P_2\right)+\left(P_2^2-7^2\right) \times 10^6 / 2 \times 7 \times 10^3 \times 3.79+4 \times 0.003(6 / 0.15)(7.07)^2=0where P_2 is the pressure at the condenser kN/m².
Solving by trial and error:
P_2=6.91 kN / m ^2
∴ \left(P_1-P_2\right)=(7.0-6.91)=0.09 kN / m ^2 or \underline{\underline{90 N / m ^2}}