Question $2$: Pressure drop of Two$-$Phase Flow

Student ID : $21621107$

$x,$ : Sum of your student ID $=20$

Example: For ID $12345678,x=(1+2+3+4+5+6+7+8)=36$

A two$-$phase mixture of oil and steam at a pressure of $1$MPa and a temperature of $300C$ is flowing through a horizontal pipe with a diameter of $0\mathrm{.}1$ meters and a length of $100$ meters. The mass flow rate of the mixture is $(2+0\mathrm{.}02x)k\frac{g}{s},$ and the liquid to gas mass flow rate ratio is $0\mathrm{.}4.$ Assume that the flow is separated and that the pipe is smooth.

Using the Chisholm equation, determine the pressure drop across the pipe by applying entrance pressure condition method. The physical properties of oil and steam at the specified conditions are as follows:

Density of liquid oil :$681k\frac{g}{m^3}$

Viscosity of liquid oil :$0\mathrm{.}003$ Pa$.$s

Viscosity of steam :$22\mathrm{.}8{10}^{-6}Pa.S$

Solve the question for $100m,$ and then divide the pipe to two $50m$ sections, and use the downstream pressure of the first $50m$ as the upstream pressure of the next $50m.$ Compare the results and provide a comment.