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🔧 Pipe Flow & Pressure Drop Calculator

Darcy-Weisbach pressure drop with Colebrook-White friction factor, minor losses, and Moody chart visualization.

Velocity V Length L Diameter D Roughness ε Inlet P_1 Outlet P_2 Loss: ΔP = P_1 - P_2

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

Fluid Properties

Flow Rate

Minor Losses (ΣK)

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

📐 Pipe Flow Profile & Velocity Distribution

📈 Operating Point on Moody Chart

📊 Calculation Results
Verified 📥 Download

Total Pressure Drop 0.01 kPa $\Delta P_{total}$
Friction Drop 0.00 kPa $\Delta P_{friction}$
Minor Drop 0.00 kPa $\Delta P_{minor}$
Mean Velocity 2.829 m/s $V$
Reynolds Number 28,294 $Re$
Friction Factor 0.02384 $f$ (Darcy)
Head Loss 0.00 m $h_f$ (fluid column)
Pump Power (Hyd) 0.0 W $\dot{W}_{pump}$ (100% eff)

🖨️ Raw Fortran Output

============================================================
   PIPE FLOW CALCULATOR — DARCY-WEISBACH METHOD
============================================================

--- PIPE GEOMETRY ---
  Inner Diameter (D)      =       150.00 mm
  Pipe Length (L)         =      15.0000 m
  Surface Roughness (eps)   =   1.5000E-06 m
  Relative Roughness eps/D  =   1.0000E-05
  Cross-Section Area      =   1.7671E-02 m2

--- FLUID PROPERTIES ---
  Density (rho)             =         1.20 kg/m3
  Dynamic Viscosity (mu)   =   1.8000E-05 Pa.s
  Kinematic Viscosity (nu) =   1.5000E-05 m2/s

--- FLOW CONDITIONS ---
  Volume Flow Rate (Q)    =   5.0000E-02 m3/s
  Volume Flow Rate        =    3000.0000 L/min
  Mean Velocity (U)       =       2.8294 m/s
  Reynolds Number (Re)    =   2.8294E+04
  Flow Regime             = Turbulent

--- FRICTION FACTOR ---
  f (Darcy)               = 2.383558E-02
  f_laminar (64/Re)       = 2.261947E-03
  f_smooth (Petukhov)     = 2.397879E-02
  f_rough (Colebrook)     = 2.383558E-02
  Colebrook iterations    =    8 (converged)

--- MAJOR LOSSES (friction) ---
  Pressure Drop (deltaP)     =        11.45 Pa
  Pressure Drop           =       0.0114 kPa
  Head Loss (h_f)         =       0.9726 m

--- MINOR LOSSES (fittings) ---
  Total K coefficient     =       0.0000
  Minor Pressure Drop     =         0.00 Pa
  Minor Head Loss         =       0.0000 m

--- TOTAL RESULTS ---
  Total Pressure Drop     =        11.45 Pa
  Total Pressure Drop     =       0.0114 kPa
  Total Head Loss         =       0.9726 m
  Required Pump Power     =       0.5725 W

--- FRICTION FACTOR vs Re (for Moody chart) ---
  Re            f_smooth      f_rough       f_laminar
  ---
  5.0119E+02    0.09343917    0.08117170    0.12769679
  7.0514E+02    0.07974717    0.07114297    0.09076201
  9.9209E+02    0.06885815    0.06277290    0.06451018
  1.3958E+03    0.06005614    0.05572796    0.04585138
  1.9638E+03    0.05283999    0.04975215    0.03258941
  2.7630E+03    0.04685041    0.04464679      ---
  3.8874E+03    0.04182438    0.04025617      ---
  5.4693E+03    0.03756578    0.03645707      ---
  7.6950E+03    0.03392598    0.03315115      ---
  1.0826E+04    0.03079064    0.03025925      ---
  1.5232E+04    0.02807068    0.02771722      ---
  2.1431E+04    0.02569583    0.02547266      ---
  3.0152E+04    0.02361009    0.02348253      ---
  4.2422E+04    0.02176836    0.02171125      ---
  5.9685E+04    0.02013402    0.02012930      ---
  8.3973E+04    0.01867705    0.01871204      ---
  1.1814E+05    0.01737270    0.01743887      ---
  1.6622E+05    0.01620036    0.01629253      ---
  2.3387E+05    0.01514280    0.01525856      ---
  3.2903E+05    0.01418552    0.01432488      ---
  4.6293E+05    0.01331623    0.01348144      ---
  6.5132E+05    0.01252446    0.01271995      ---
  9.1637E+05    0.01180126    0.01203369      ---
  1.2893E+06    0.01113894    0.01141728      ---
  1.8139E+06    0.01053085    0.01086650      ---
  2.5521E+06    0.00997123    0.01037804      ---
  3.5906E+06    0.00945506    0.00994923      ---
  5.0518E+06    0.00897796    0.00957769      ---
  7.1076E+06    0.00853608    0.00926087      ---
  1.0000E+07    0.00812604    0.00899571      ---

--- EQUATIONS USED ---
  Darcy-Weisbach: deltaP = f(L/D)(rhoU2/2)
  Colebrook:      1/√f = -2log1₀(eps/D/3.7 + 2.51/(Re√f))
  Minor losses:   deltaP_minor = ΣK(rhoU2/2)
  Head loss:      h_f = deltaP/(rhog)

📘 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

  1. White, F. M.: Fluid Mechanics, McGraw-Hill, 8th Edition.
  2. 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.