Pipe Flow & Pressure Drop Calculator

Pipe Friction & Flow Profile

Viscous friction and fitting restrictions drop flow line pressure. The Reynolds number determines whether flow remains laminar or experiences shear mixing in the turbulent regime.

• Laminar Flow (Re < 2300): Parabolic profile, friction factor is independent of roughness.
• Turbulent Flow (Re > 4000): Flatter profile, friction depends heavily on wall roughness ($\varepsilon$).
• Minor Losses ($\Sigma K$): Added local restrictions that create turbulence and extra drop.

📝 Configuration

Pipe Geometry

Inner Diameter ($D$) [mm]:

Length ($L$) [m]:

Surface Roughness ($\varepsilon$) [mm]:

Fluid Properties

Fluid:

Density ($\rho$) [kg/m³]:

Viscosity ($\mu$) [Pa·s]:

Flow Rate

Volume Flow Rate [L/min]:

Minor Losses (ΣK)

Fittings:

90° Elbows (K=0.9):

45° Elbows (K=0.4):

Tees (K=1.8):

Gate Valves (K=0.2):

Globe Valves (K=10):

Check Valves (K=2.5):

Total ΣK = 0

Darcy-Weisbach:
ΔP = f × (L/D) × (ρU²/2)

Colebrook-White:
1/√f = -2 log₁₀(ε/D/3.7 + 2.51/(Re√f))

Minor losses:
ΔP_minor = ΣK × (ρU²/2)

📊 Results & Visualization

Configure the inputs and click Calculate to see results.

ℹ️ About Pipe Flow

The Darcy-Weisbach equation is the most general equation for calculating pressure drop in fully developed pipe flow. Combined with the Colebrook-White equation, it accurately predicts friction factors for all flow regimes.

Key factors:
• Re < 2300: Laminar flow (f = 64/Re)
• Re > 4000: Turbulent flow (f from Colebrook-White)
• Surface roughness significantly affects turbulent friction
• Minor losses from fittings can dominate in short pipes

📘 Calculation Methodology

Mathematical Model & Theory

Pipe flow pressure drop is modeled using the Darcy-Weisbach equation, combined with the Colebrook-White equation for turbulent regime friction and minor loss sum coefficients ($\Sigma K$):

$$\Delta P = \left( f \frac{L}{D} + \sum K \right) \frac{\rho V^2}{2}, \quad Re = \frac{\rho V D}{\mu}$$ $$\text{Laminar: } f = \frac{64}{Re}, \quad \text{Turbulent: } \frac{1}{\sqrt{f}} = -2\log_{10}\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}}\right)$$

The implicit Colebrook-White equation is solved iteratively using the Newton-Raphson method to a tolerance of $10^{-6}$. Pump/blower hydraulic power is computed using:

$$\dot{W}_{pump} = \Delta P_{total} \times Q \quad \text{[W]}$$

Assumptions

Incompressible and steady flow conditions.
Fully developed velocity profile along the main friction length $L$.
Constant physical properties (density and viscosity) throughout the pipeline.

Academic References

White, F. M.: Fluid Mechanics, McGraw-Hill, 8th Edition.
Munson, B. R. et al.: Fundamentals of Fluid Mechanics, Wiley.

Worked Engineering Example

Problem Statement:
Water ($\rho = 1000$ kg/m³, $\mu = 1.0 \times 10^{-3}$ Pa·s) flows through a 100 m long pipe of diameter 50 mm (roughness $\varepsilon = 0.046$ mm) at a flow rate of 300 L/min. Calculate the pressure drop.

Step-by-step Solution:
1. Calculate velocity $V$ and Reynolds number:
$$Q = 300 \text{ L/min} = 0.005 \text{ m}^3/\text{s}$$ $$V = \frac{4Q}{\pi D^2} = \frac{4 \times 0.005}{\pi \times 0.05^2} = 2.546 \text{ m/s}$$ $$Re = \frac{1000 \times 2.546 \times 0.05}{1.0 \times 10^{-3}} = 127,300 \quad \text{(Turbulent flow)}$$ 2. Solve Colebrook-White equation ($\varepsilon/D = 0.00092$):
$$f \approx 0.0211$$ 3. Calculate pressure drop:
$$\Delta P = f \frac{L}{D} \frac{\rho V^2}{2} = 0.0211 \times \frac{100}{0.05} \times \frac{1000 \times 2.546^2}{2} = 136,770 \text{ Pa} = 136.8 \text{ kPa}$$
Final Result:
The friction pressure drop is 136.8 kPa.

🔧 Pipe Flow & Pressure Drop Calculator