Quick hydraulic calculations — pipe velocity and diameter, pressure and flow conversion, pump power, affinity laws, tank time, Cv ↔ Kv and Joukowsky

What the quick hydraulic calculations page does

The Quick hydraulic calculations page gathers eight one-line hydraulic calculations into a single screen. The calculator is live on this page, free and without sign-up: type a value and every result updates as you type. A shared density field (t/m³) feeds the cards that depend on the fluid — liquid column, mass flow, pump power and water hammer. For water, leave it at 1.

LOGOS runs these cards entirely in the browser, because they are direct formulas with no iteration and no equipment data. They deliberately give no verdict and no calculation report: they answer “how much is it?”, not “does the design pass?”. For a design check, LOGOS has dedicated calculators — for example pump sizing (system curve, operating point, NPSH) and water hammer (Korteweg wave speed, critical time, slow closure, pump trip).

Card 1 — Pipe velocity and the inverse: diameter for a target velocity

The velocity card computes v = Q/A = 4·Q/(π·D²) from the flow in m³/h and the inside diameter in mm. The inside diameter can be typed or taken from the pipe table, choosing the material (carbon steel, stainless steel or HDPE), the nominal size (DN) and the schedule or SDR/PN. The table is the same one LOGOS uses in its hydraulic calculators.

The inverse mode takes a target velocity and returns the inside diameter that gives exactly that velocity, DI = 1000·sqrt(4·(Q/3600)/(π·v)), plus the smallest pipe of the same material and schedule whose inside diameter is at least the required one. At 60 m³/h and 2.5 m/s the required ID is 92.13 mm and the suggested pipe is 4” STD/40 (ID 102.26 mm, v = 2.03 m/s).

The card shows a practical reference — up to about 1.5 m/s on suction and 1 to 2.5 m/s on discharge. It is a usual starting range, not a standard requirement: NPSH, the fluid, erosion and the project criterion decide.

Card 2 — Pressure conversion (bar, m of liquid, kPa, MPa, psi, kgf/cm²)

The pressure card converts a gauge or differential value among bar, m of liquid column, kPa, MPa, psi and kgf/cm². It uses exact unit definitions (1 psi = 6894.757 Pa, 1 kgf/cm² = 98.0665 kPa) and does not add atmospheric pressure. Only the liquid column depends on the density: 1 m of liquid = ρ·g, with g = 9.80665 m/s². That is why 10 bar is 101.97 m of water but 119.97 m of a liquid with ρ = 0.85 t/m³.

Card 3 — Flow conversion (m³/h, L/s, L/min, m³/s, gpm, t/h, kg/h)

The flow card converts volumetric and mass flows. The US gallon is 3.785411784 L, so 60 m³/h = 16.67 L/s = 1000 L/min = 264.17 US gpm. Mass flows (t/h, kg/h) use the density entered: for water at 1 t/m³, 60 m³/h is 60 t/h.

Card 4 — Pump power: hydraulic, shaft and minimum motor

The pumping power card takes the operating flow and head and returns three powers:

• Hydraulic power P_h = ρ·g·Q·H — the energy actually delivered to the fluid.
• Shaft power P_shaft = P_h/η — what the pump takes, with η from the manufacturer’s sheet at the operating point.
• Minimum motor power P_motor = P_shaft·(1 + margin) — with the margin from the project criterion or the standard adopted.

The efficiency and the margin have no built-in default: LOGOS does not guess equipment data. Without η, only the hydraulic power appears. For 60 m³/h at 45 m of water, P_h = 7.35 kW (10.0 cv); with η = 72 %, the shaft takes 10.22 kW; with a 15 % margin, the motor must be at least 11.75 kW, and the commercial motor is the first catalogue size above that.

Use the operating point — the intersection of the pump curve with the system curve — and not the desired flow. If the pump runs to the right of the design point, it delivers more flow and takes more power.

Card 5 — Affinity laws: speed change or impeller trim

The affinity card applies Q₂ = Q₁·r, H₂ = H₁·r², P₂ = P₁·r³, with r = n₂/n₁ for a speed change (VFD) or r = D₂/D₁ for an impeller trim. For speed the relations hold at homologous points of the same pump; for the impeller diameter they are an approximation, good for small trims. Reducing a pump from 1750 to 1450 rpm (r = 0.8286) takes 60 m³/h, 45 m and 10.22 kW to 49.71 m³/h, 30.89 m and 5.81 kW — the power drops with the cube, which is why speed control saves energy.

The scaled point lies on the new pump curve; the real operating point still depends on the system curve, especially when the static head is a large part of the total head.

Card 6 — Tank filling or emptying time

The tank card divides the volume by the net flow: t = V / |Q_in − Q_out|. The volume can be typed or computed for a vertical cylinder between two levels, V = (π·D²/4)·h. If the inlet exceeds the outlet, the tank fills; if the outlet is larger, it empties; if they are equal, the card says the level does not change. A cylinder 4 m in diameter and 5 m between levels (62.83 m³) fills in 1.05 h at 60 m³/h, and empties in 2.51 h with 20 m³/h in and 45 m³/h out.

Card 7 — Cv ↔ Kv

The flow coefficient card converts the US Cv (gpm of water at 1 psi) and the metric Kv (m³/h at 1 bar). LOGOS derives the factor from the unit definitions rather than from a rounded table value: Kv = 0.865·Cv and Cv = 1.156·Kv (exactly 0.86498 and 1.15610). Cv = 100 is Kv = 86.50.

Card 8 — Joukowsky surge

The water hammer card gives the maximum surge of an instantaneous closure, ΔH = a·Δv/g, and the same value as pressure, Δp = ρ·a·Δv. The wave speed a is an input because it depends on the pipe material, the wall thickness and the fluid. With a = 1200 m/s and Δv = 2 m/s, ΔH = 244.7 m and Δp = 24.0 bar. This is the upper bound for a closure within the critical time 2L/a; for wave speed, slow closures and pump trip, use the water hammer calculator.

Limits: what the quick calculations do not do

• No head loss and no system curve. The velocity card does not compute friction; head loss, the system curve and the operating point are in the pump sizing calculator.
• No verdict and no report. The cards return numbers; they do not check limits, issue warnings or produce a Word calculation report. That is the job of the dedicated calculators in the logged-in area.
• No equipment defaults. Efficiency, motor margin and wave speed must be supplied by the user.
• Simplified models. The affinity law for impeller trims is an approximation; Joukowsky is the instantaneous-closure bound.
• Engineering responsibility stays with the engineer. A result from LOGOS supports the work; it does not replace the review and the signature of the professional responsible for the design.