🔀 Pipe Network Calculator
Series and parallel pipe network analysis with Hardy-Cross iterative method, Colebrook-White friction factors, and flow distribution visualization.
📝 Configuration
Series:
$Q_1 = Q_2 = \dots = Q_n$
$\Delta P_{total} = \sum \Delta P_i$
Parallel:
$\Delta P_1 = \Delta P_2 = \dots = \Delta P_n$
$Q_{total} = \sum Q_i$
Hardy-Cross:
$\Delta Q = -\frac{\sum R Q |Q|}{\sum 2 R |Q|}$
Darcy-Weisbach:
$\Delta P = f \frac{L}{D} \frac{\rho V^2}{2}$
$Q_1 = Q_2 = \dots = Q_n$
$\Delta P_{total} = \sum \Delta P_i$
Parallel:
$\Delta P_1 = \Delta P_2 = \dots = \Delta P_n$
$Q_{total} = \sum Q_i$
Hardy-Cross:
$\Delta Q = -\frac{\sum R Q |Q|}{\sum 2 R |Q|}$
Darcy-Weisbach:
$\Delta P = f \frac{L}{D} \frac{\rho V^2}{2}$
📊 Results & Visualization
Configure the inputs and click Calculate to see results.
ℹ️ About Pipe Networks
Pipe networks are combinations of pipes arranged in series or parallel configurations.
Series pipes:
• Same flow rate through all pipes
• Total pressure drop = sum of individual drops
• Different velocities due to different diameters
Parallel pipes:
• Same pressure drop across all branches
• Total flow = sum of branch flows
• Flow distributes according to pipe resistance
• Hardy-Cross method iterates to find distribution
Pipe networks are combinations of pipes arranged in series or parallel configurations.
Series pipes:
• Same flow rate through all pipes
• Total pressure drop = sum of individual drops
• Different velocities due to different diameters
Parallel pipes:
• Same pressure drop across all branches
• Total flow = sum of branch flows
• Flow distributes according to pipe resistance
• Hardy-Cross method iterates to find distribution
📘 Calculation Methodology
Mathematical Model & Theory
Pipe networks are solved using the conservation of mass at nodes and conservation of energy in loops (sum of head losses is zero). The Hardy-Cross method iteratively computes flow rate corrections $\Delta Q$ for each loop:
$$\sum Q_{in} = \sum Q_{out} \quad \text{(nodes)}$$
$$\sum h_f = \sum r Q |Q|^n = 0 \quad \text{(loops)}$$
$$\Delta Q = -\frac{\sum r Q_0 |Q_0|^{n-1}}{\sum n r |Q_0|^{n-1}}$$
Worked Engineering Example
Problem Statement:
A parallel flow network consists of two branches. Branch 1 ($L = 100$ m, $D = 50$ mm, $f = 0.02$) and Branch 2 ($L = 150$ m, $D = 75$ mm, $f = 0.02$). Total flow rate entering is 600 L/min. Find the flow distribution.
Step-by-step Solution:
1. Calculate resistance factors $r$ ($h_f = r Q^2$):
$$r = \frac{8 f L}{\pi^2 g D^5}$$ $$r_1 = \frac{8 \times 0.02 \times 100}{\pi^2 \times 9.81 \times 0.05^5} = 52,943 \text{ s}^2\text{/m}^5$$ $$r_2 = \frac{8 \times 0.02 \times 150}{\pi^2 \times 9.81 \times 0.075^5} = 10,457 \text{ s}^2\text{/m}^5$$ 2. Set up parallel flow condition ($r_1 Q_1^2 = r_2 Q_2^2$ and $Q_1 + Q_2 = Q_{tot} = 0.01$ m³/s):
$$\frac{Q_1}{Q_2} = \sqrt{\frac{r_2}{r_1}} = \sqrt{\frac{10457}{52943}} = 0.444$$ $$0.444 Q_2 + Q_2 = 0.01 \Rightarrow Q_2 = 0.00692 \text{ m}^3\text{s} = 415.5 \text{ L/min}$$ $$Q_1 = 0.01 - 0.00692 = 0.00308 \text{ m}^3\text{s} = 184.5 \text{ L/min}$$
Final Result:
Branch 1 has 184.5 L/min and Branch 2 has 415.5 L/min.
A parallel flow network consists of two branches. Branch 1 ($L = 100$ m, $D = 50$ mm, $f = 0.02$) and Branch 2 ($L = 150$ m, $D = 75$ mm, $f = 0.02$). Total flow rate entering is 600 L/min. Find the flow distribution.
Step-by-step Solution:
1. Calculate resistance factors $r$ ($h_f = r Q^2$):
$$r = \frac{8 f L}{\pi^2 g D^5}$$ $$r_1 = \frac{8 \times 0.02 \times 100}{\pi^2 \times 9.81 \times 0.05^5} = 52,943 \text{ s}^2\text{/m}^5$$ $$r_2 = \frac{8 \times 0.02 \times 150}{\pi^2 \times 9.81 \times 0.075^5} = 10,457 \text{ s}^2\text{/m}^5$$ 2. Set up parallel flow condition ($r_1 Q_1^2 = r_2 Q_2^2$ and $Q_1 + Q_2 = Q_{tot} = 0.01$ m³/s):
$$\frac{Q_1}{Q_2} = \sqrt{\frac{r_2}{r_1}} = \sqrt{\frac{10457}{52943}} = 0.444$$ $$0.444 Q_2 + Q_2 = 0.01 \Rightarrow Q_2 = 0.00692 \text{ m}^3\text{s} = 415.5 \text{ L/min}$$ $$Q_1 = 0.01 - 0.00692 = 0.00308 \text{ m}^3\text{s} = 184.5 \text{ L/min}$$
Final Result:
Branch 1 has 184.5 L/min and Branch 2 has 415.5 L/min.