Fluid mechanics calculators
16 field calculations for pipes, pumps, tanks and flow measurement. Each calculator shows its formula and offers practice problems.
Pipes and pressure drop
Pipe velocity
Water, usual guides: pump suction 0.6 to 1.5 m/s, discharge 1.5 to 3 m/s. Use the real inside diameter (from wall thickness or schedule).
Reynolds number (flow regime)
Laminar below 2300, turbulent above about 4000, transition in between. Water at 20 °C: μ ≈ 1.0 mPa·s; oils: 10 to 1000 mPa·s.
Pipe pressure drop (Darcy-Weisbach)
Darcy friction factor by Swamee-Jain (within ±1 % of Colebrook for Re 5000 to 10⁸); in the transition zone (2300 to 4000) the result is approximate. New pipe: roughness grows with age.
Minor losses (total K)
Usual K values: standard 90° elbow 0.3 to 0.9; open gate valve 0.1 to 0.2; swing check valve 2; exit into a tank 1; sharp-edged entrance 0.5.
Pressure and liquid head
For water, 1 bar ≈ 10.2 m. A denser liquid gives less head for the same pressure: a pump delivers the same head, not the same pressure.
Pumps
Hydraulic and shaft power
Pick a motor at least 10 to 15 % above the shaft power at the most demanding point of the curve. Centrifugal pump efficiency: 50 to 85 %.
Affinity laws (speed or impeller diameter)
Exact for a speed change at constant efficiency; for an impeller trim, valid only for small cuts (under 10 to 15 %). The real duty point also depends on the system curve.
NPSH available and margin
z is negative when the pump lifts from below (suction lift). Aim for NPSHa ≥ 1.3 × NPSHr (or at least 1 m margin); water at 20 °C: pv = 2.34 kPa, at 60 °C: 19.9 kPa.
Pump and system operating point
Approximation: parabolic pump curve through H₀ and the rated point, system losses in Q². For accurate work, overlay the real manufacturer's curve.
Pump flow by tank level test
Vertical tank with constant cross-section. Close the inlet if you can (Qi = 0) and time at least 2 to 5 minutes to cut reading error.
Tanks
Vertical tank: level and volume
Flat bottom. For a cone or dished bottom, add the bottom volume separately. Level measured from the inside bottom.
Horizontal tank: partial volume
Flat ends (R = D ÷ 2). With dished heads the real volume is somewhat larger: use the tank's gauging table if there is one.
Tank drain time through an orifice
Torricelli: vertical tank open to air, free outlet at the bottom, no downstream pipe. An outlet pipe adds losses and lengthens the time.
Fill or empty time
Vertical tank. To empty, set h₂ below h₁ and an outflow larger than the inflow. No answer if the level does not move the right way.
Flow measurement
Orifice plate flow
Liquids only (ε = 1). Simplified from ISO 5167: C ≈ 0.60 to 0.61 for a sharp-edged orifice, β 0.2 to 0.75 and high Re; for custody transfer, use the full (Reader-Harris/Gallagher) equation.
DP flowmeter: square-root extraction
At 25 % of DP you already have 50 % of flow. Below about 10 % of flow the reading becomes unreliable: most transmitters have a low-flow cutoff.
Learning and checking tools. The ranges shown are general guidance: always follow your plant's procedures, permits and set points. Nothing is sent anywhere: the calculations run in your browser.