Air-only pressure loss is the pressure consumed by moving conveying gas through the empty flow path. It includes straight pipe, bends, valves, transitions, supply components and receiver equipment. This pressure is unavailable for transporting solids, so it must be known before a roots blower is selected.
The calculation is a baseline rather than a complete conveying model. Loaded material adds separate resistance that depends on product and operating regime.
Required Inputs
A defensible calculation starts with:
- Actual internal pipe diameter.
- Straight lengths by bore and orientation.
- Bend geometry and count.
- Valves, transitions, hose and fittings.
- Gas mass flow or consistently referenced volume flow.
- Local absolute pressure and temperature.
- Pipe surface condition.
- Receiver and filter pressure losses.
Nominal pipe size is not enough. Wall thickness, lining, wear inserts and deposits can change the open bore used in the calculation.
Straight-Pipe Friction
For a local section where gas properties can be represented appropriately, Darcy-Weisbach pressure loss can be written as:
Here fD is the Darcy friction factor, L is section length, d is actual bore, ρ is local gas density and C is mean local gas velocity. The friction factor depends on Reynolds number and relative roughness; it should not be copied from an unrelated pipe condition.
Because velocity appears squared, extra airflow can increase empty-line loss strongly. Increasing blower speed is therefore not always an effective response to insufficient loaded pressure margin.
Bends, Valves and Other Local Losses
Local clean-gas losses may be represented by:
Each loss coefficient K must correspond to the fitting geometry, position and selected velocity reference. A partially open valve or internal joint step may have much more resistance than the fully open component assumed in a catalogue value.
Account for Compressibility
In a positive-pressure pipeline, gas expands as pressure falls toward the receiver. Local actual volume and velocity can therefore increase along a constant-bore line. Temperature also changes after the blower and through the route.
A long line should be divided into sections or evaluated with a validated compressible-flow method. Each section uses a representative local pressure, temperature, density and velocity, and the pressure profile is solved consistently. Applying blower-inlet density to the whole pipe can materially distort the result.
Stepped bores, coolers and receivers create additional boundaries where the local condition should be updated.
Add the Complete Clean-Gas Path
Pipeline friction is not the complete air-only duty. The total should include clean and maximum normal losses through:
- Inlet filter and silencers.
- Discharge check valve and supply pipe.
- Feeder air path where applicable.
- Empty conveying line.
- Cyclone or receiver entry.
- Receiver filter and vent duct.
Using a clean filter value alone may understate the highest normal blower pressure. The calculation should preserve separate clean and fouled cases.
Validate the Result
During commissioning, an empty-line test can compare measured pressure with the calculated baseline at approved airflow points. If measured resistance is higher, investigate actual bore, valve position, hose condition, debris, filter loading and instrument basis before changing blower speed.
The calculation and test should use compatible flow reference conditions. A standard-volume reading cannot be inserted directly as local actual pipe volume.
Glossary
Darcy friction factor: Dimensionless factor used in the Darcy-Weisbach relationship for straight-pipe friction.
Equivalent resistance: Combined pressure-loss effect of defined pipework and components at a stated flow condition.
Local loss coefficient: Dimensionless coefficient representing clean-gas loss through a fitting or geometry change.
Relative roughness: Ratio of effective internal surface roughness to pipe diameter.
Sectional calculation: Method that divides a compressible pipeline into local segments with updated gas conditions.
Straight-pipe loss: Pressure reduction caused by wall friction along a defined uniform pipe length.