Flow Analysis in a Pipe Network

Detailed Explanation:

Scenario: Analyze water flow in a network consisting of three pipes connected in series.

System Parameters:

Pipe lengths: $10m,20m,$ and $15m.$

Diameters: $5cm,4cm,$ and $6cm.$

Initial water pressure: $120$kPa.

Calculation Method: Use the Darcy$-$Weisbach equation to calculate pressure drop and flow rate, applying an iterative solution method like the Newton$-$Raphson technique.

Key Equations:

Darcy$-$Weisbach Equation for Pressure Drop: $P=f\frac{L}{D}\frac{V^2}{2}$ Where $P$ is the pressure drop, $f$ is the friction factor, $L$ is the pipe length, $D$ is the pipe diameter, $$ is the fluid density, and $v$ is the flow velocity.

Newton$-$Raphson Method for Iterative Solution $($applied to find flow rates and pressure drops$).$

Questions:

What is the flow rate in each pipe section?

How does changing the diameter of the pipes affect the overall pressure drop?

Calculate the Reynolds number for flow in each pipe. Is the flow laminar or turbulent?

What would be the effect of adding a fourth pipe in parallel to one of the existing pipes?

Calculate the pressure drop across the first pipe manually using the Darcy$-$Weisbach equation for a guessed flow rate. Then, compare this result with the pressure drop calculated using your iterative solver in MATLAB. Discuss any discrepancies and their possible causes$\mathrm{.}0$

The liquid is kerosene Viscosity is $0\mathrm{.}00164$ pa$.$s Density is $775k\frac{g}{m}3$ Roughness of the pipe is $0\mathrm{.}0001mG$ is $9\mathrm{.}81\frac{m}{s}2$

Flow Analysis in a Pipe Network

Detailed Explanation:

Scenario: Analyze water flow in a network consisting of three pipes connected in series.

System Parameters:

Pipe lengths: $10m,20m,$ and $15m.$

Diameters: $5cm,4cm,$ and $6cm.$

Initial water pressure: $120$kPa.

Calculation Method: Use the Darcy$-$Weisbach equation to calculate pressure drop and flow rate, applying an iterative solution method like the Newton$-$Raphson technique.

Key Equations:

Darcy$-$Weisbach Equation for Pressure Drop: $P=f\frac{L}{D}\frac{V^2}{2}$ Where $P$ is the pressure drop, $f$ is the friction factor, $L$ is the pipe length, $D$ is the pipe diameter, $$ is the fluid density, and $v$ is the flow velocity.

Newton$-$Raphson Method for Iterative Solution $($applied to find flow rates and pressure drops$).$

Questions:

What is the flow rate in each pipe section?

How does changing the diameter of the pipes affect the overall pressure drop?

Calculate the Reynolds number for flow in each pipe. Is the flow laminar or turbulent?

What would be the effect of adding a fourth pipe in parallel to one of the existing pipes?

Calculate the pressure drop across the first pipe manually using the Darcy$-$Weisbach equation for a guessed flow rate. Then, compare this result with the pressure drop calculated using your iterative solver in MATLAB. Discuss any discrepancies and their possible causes.