Liquid Flow Theory
Core principles of Hydraulics (steady‑state)
1) Conservation laws and units
Continuity: Conservation of Mass
At the heart of any liquid-flow system is the Continuity Equation:
Where: M = Mass Flow Rate A = Cross-sectional area of the pipe or channel v = Average fluid velocity
ρ = Density
This principle expresses one key idea: mass flow is conserved. In FlowDesigner, this means: The flow entering a junction must equal the flow leaving it (assuming no storage). Flow splits at tees and manifolds must balance. Any mismatch triggers a warning or is corrected automatically by the solver.
FlowDesigner uses the continuity law when solving node mass balances and determining velocities in each segment of the network.
In the example below, 10 m3/hr water at 15°C is allowed to flow to two (2) destinations. The first one has a pressure of 105 kPa, and the other one is at 104 kPa.ρ = Density
This principle expresses one key idea: mass flow is conserved. In FlowDesigner, this means: The flow entering a junction must equal the flow leaving it (assuming no storage). Flow splits at tees and manifolds must balance. Any mismatch triggers a warning or is corrected automatically by the solver.
FlowDesigner uses the continuity law when solving node mass balances and determining velocities in each segment of the network.
In the example below, 10 m3/hr water at 15°C is allowed to flow to two (2) destinations. The first one has a pressure of 105 kPa, and the other one is at 104 kPa.
Example 1 – Continuity in a Junction
FlowDesigner balanced the flow rate going to each destination and ensured continuity:
Designer Note: The continuity equation is fundamentally based on mass conservation. When using volumetric flow rate instead of mass flow, the calculation implicitly depends on the fluid density. Any change in density—whether due to temperature, pressure, or fluid composition—will affect the volumetric flow balance, even though the mass flow remains conserved.
Energy: Bernoulli’s Equation (Head Conservation)
FlowDesigner uses an energy-based formulation of the Bernoulli equation to track the movement of liquid between points:
Where:
H = Total head
P/γ = Pressure head
V²/2g = Velocity head
z = Elevation head
This form is standard in hydraulics because it expresses all energy types in a single unit: head.
How FlowDesigner Applies Bernoulli
Pressure boundaries—pumps, tanks, reservoirs—are converted to equivalent head.
Friction, local (K-factor), and equipment losses are subtracted as head loss.
The solver calculates head at each node, then back-calculates pressure and velocity.
Why Head Is Central in FlowDesigner
Expressing everything in metres or feet of fluid allows:
Simple addition and subtraction of pressure, elevation, and velocity changes, independent of fluid properties
Less confusion between gauge and absolute pressure.
A single energy framework for complex systems with pumps, valves, reducers, and elevation changes.
Example 2 – Bernoulli Head Breakdown
In the example above, water flows from 2 meters above grade down to grade level via a 10-meter of 2-inch SCH40 pipe. FlowDesigner calculates the flow rate that produces a 2-meter head loss due to friction, conserving energy.
Designer Note: FlowDesigner displays several pressure terms: P is the static pressure, Pv is the velocity pressure, and Pp is the piezometric pressure—the sum of potential energy and static pressure. P° is the stagnation pressure (static plus velocity pressure). Although not shown in the Example 2 diagram, it represents the total pressure of a flowing fluid.
Unit Handling in FlowDesigner
FlowDesigner manages units in several ways:
Automatic conversion across pressure, flow, length, velocity, and head.
User-selectable unit sets (SI, US, mixed).
Clear indication of head vs. pressure values in reports and tooltips.
Optional display of intermediate values such as pressure head or velocity head.
2) Head loss in straight pipe
Head Loss in Straight Pipe
In FlowDesigner, the head loss through a straight pipe section is calculated using the Darcy–Weisbach equation, which provides a robust and broadly applicable method across laminar, transitional, and turbulent flow regimes. This formulation expresses energy loss as head, ensuring consistency with the overall energy balance used throughout the solver.
Where:
hₙ = frictional head loss
f = Darcy friction factor
L = pipe length
D = internal diameter
V²/2g = velocity head
FlowDesigner evaluates each pipe segment based on user-defined geometry, materials, operating conditions, and flow rate to compute the appropriate head loss.
Friction Factor Determination
The friction factor (f) is central to Darcy–Weisbach calculations. FlowDesigner selects it based on the flow regime:
Laminar Flow (Re < 2,000)
This relation is exact for laminar pipe flow. FlowDesigner applies it automatically whenever the Reynolds number falls below the laminar threshold.
Turbulent Flow (Re > 3500)
For turbulent flow, FlowDesigner uses standard engineering correlations Colebrook–White (implicit), as shown below:
These correlations account for:
Pipe roughness
Reynolds number
Fluid properties (density and viscosity)
Select the appropriate pipe materials from FlowDesigner's component palette for representative roughness values, or override them manually for specialized applications.
Example 3 – Friction Factor and Straight-Pipe Loss Summary
Example 4 – Sample Absolute Roughness for Steel Pipe in FlowDesigner
3) Minor (local) losses
Local losses arise from components that disturb flow direction or velocity, such as bends, tees, valves, entrances, and exits. FlowDesigner models these using the standard K-value method:
Where K is the loss coefficient specific to each fitting.
Recommended Practices in FlowDesigner
Use trusted K-data sources such as Crane, Idelchik, or manufacturer-specific values.
Sum all minor losses along the flow path to obtain the total local loss contribution.
Ensure fittings are properly placed and oriented (e.g., tee branch vs. run), as K-values differ significantly.
Note that expansions, contractions, and entrance/exit losses can be substantial, particularly in systems with large velocity changes or short pipe runs.
FlowDesigner automatically calculates the total minor loss in each pipe or component based on the specified K-values or built-in fitting libraries.
Example 5 – Example K component in FlowDesigner, each component is K = 5
4) Compressible vs incompressible flow
FlowDesigner distinguishes between incompressible and compressible flow regimes to ensure that head loss and energy relationships are handled correctly.
Liquids: Incompressible Assumption
Most liquid applications can be treated as incompressible for steady-state hydraulic sizing. Under this assumption:
Density remains effectively constant
Darcy–Weisbach applies directly
Head-based energy accounting remains valid across the system
This leads to stable, predictable results for water-based systems, oils, brines, refrigerants (subcooled), and other common fluids.
Currently, FlowDesigner supports the Liquid module only. Gas and other phase modules will be added in future releases.
Pump and system interaction
1) System curve
A system curve describes how much head the piping network requires at each possible flow rate. FlowDesigner computes this automatically by evaluating static and dynamic losses across all components.
For most liquid systems, the system curve takes the general form:
Where:
H_static = static head (elevation difference between suction source and discharge point)
KQ² = frictional and minor (velocity-dependent) losses
Q = volumetric flow rate
Static Head
Static head is independent of flow. It represents the gravitational lift or drop required by the system. In FlowDesigner, this is governed by the relative elevation of boundary pressures, reservoirs, or tanks.
Dynamic Head
Dynamic losses depend on the square of the flow rate (Q²). As flow increases:
Pipe friction increases rapidly
Minor losses (fittings, valves, reducers, bends) also increase
Local velocity-induced losses play a more significant role
FlowDesigner evaluates these losses at each solved flow condition, allowing you to generate a complete system curve by sweeping flow across a defined range.
Example 6 — Sample System Curve Plot
2) Pump curves and duty point
Pump performance curves describe the relationship between flow rate and pump head. FlowDesigner overlays the pump curve onto the system curve to find the operating point, also known as the duty point.
Operating Point
The duty point occurs where the head of the pump is equal to the head required by the system:
Example 7 — Duty Point shown in the different charts available for centrifugal pumps
At this intersection, the pump delivers the flow rate that satisfies both the pump’s ability to generate head and the system’s hydraulic resistance.
FlowDesigner automatically computes this intersection and reports:
Pump operating flow
Developed head
Power and efficiency
NPSH performance
Importance of BEP (Best Efficiency Point)
Pump manufacturers identify a Best Efficiency Point (BEP) at which the pump operates at optimal performance. Operating near BEP offers:
Higher efficiency and lower energy cost
Reduced vibration and noise
Lower shaft deflection
Extended mechanical seal and bearing life
FlowDesigner displays BEP markers when pump data includes efficiency curves, helping the designer verify that the duty point falls within the recommended operating range.
Affinity Laws are discussed in detail in the Help File - Components under pumps. These relationships allow quick what-if evaluations, such as increased system demand, speed changes via VFDs, or matching a new pump to an existing line.
Example 8 - Input Editor for Centrifugal Pump highlighting the field for impeller diameter and speed where affinity laws apply
3) Net Positive Suction Head (NPSH) Basics
Net Positive Suction Head ensures that the pump inlet pressure stays high enough to avoid cavitation, a destructive phenomenon caused by vapor bubble formation and collapse.
NPSHa vs. NPSHr
NPSHa (Available) = the actual suction head provided by the system
NPSHr (Required) = the minimum suction head needed by the pump as specified by the manufacturer
To prevent cavitation:
FlowDesigner calculates NPSHa based on:
Suction elevation
Fluid vapor pressure (temperature-dependent)
Suction pressure or tank level
Suction line friction and minor losses
The software then compares NPSHa with the manufacturer-provided NPSHr curve and highlights any violations.
Valves and control elements (steady‑state view)
FlowDesigner models valves and control devices by their hydraulic behavior in steady-state conditions. Each valve introduces a pressure drop that depends on its geometry, flow coefficient, and operating position. Understanding how these elements interact with the surrounding piping system is essential for predicting flow distribution, ensuring stable control, and preventing equipment-damaging conditions such as cavitation.
Control valves in FlowDesigner impose a controllable pressure drop (ΔP) that changes with valve position. This adjustable restriction allows the system to regulate flow or pressure to meet design conditions.
Valve Pressure Drop Behavior
FlowDesigner uses standard control-valve characteristics such as:
Cv/Kv curves
Equal-percentage or linear trim behaviors
Valve opening position vs. ΔP relationships
During simulation, the solver balances the valve’s ΔP with the upstream and downstream hydraulic conditions to determine the resulting flow.
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