Basics of Fluid Mechanics: Complete Guide

Fluid mechanics is the silent physics of the cement plant: every fan, every duct, every pump, every air slide, every pneumatic conveyor and every filter operates on the laws of the fluids: the kiln draught is a gas flow, the slurry of the old wet process was a liquid flow, the clinker transport by the air is a two-phase flow: the engineer who reads the numbers of the plant, the meters, the pressures, the fan curves and the duct velocities, reads them in the language of the fluid mechanics.

The Complete Cement Technical Package (931 files including the books, the courses, the Excel tools and the presentations: $249.99 one-time: instant download via the PayPal payment) includes the dedicated fluid and fan engineering titles: the fan handbooks, the ductwork design chapters, the flow measurement guides and the air slides texts: this article is the readable foundation that makes those documents useful: the definitions, the equations and the numbers of the fluid mechanics of the cement industry: the reader leaves with the complete toolkit of the flow.

This page is written for the cement engineer, not the theoretical physicist: the derivations appear only where they serve the plant numbers: the target is the ability to calculate a duct, to read a fan, to judge a pump and to understand why the flow behaves as it does: the values and the tables of the article follow the engineering practice of the industry, and the package holds the deeper texts for the design work: the foundations first.

1. Why the Cement Engineer Needs the Fluid Mechanics

The cement plant is one large flow network: the process air of the kiln, the cooling air of the cooler, the transport air of the mill, the water of the cooling circuits and the oil of the hydraulic systems: the engineer touches the fluids in every equipment:

• The process gas flow: the preheater, the kiln and the cooler move thousands of normal cubic meters per hour of air: the performance of every thermal exchange depends on the velocity of the gas;
• The fans: the main fans, the cooler fans, the mill fans: each a fluid machine that converts the rotating energy into the pressure and the flow: the largest consumers of the electric energy of the plant, after the mills;
• The ducts and the bends: the gas travels through the expansion chambers, the cyclones, the mills and the filters; every bend and every restriction costs friction pressure, and the friction losses sum into the fan duty;
• The pumps: the water of the conditioning towers, the cooling water circuits, the slurry of the wet plants, the fuel oil of the burners: the pumps of the cement plant move tons of liquid every hour;
• The air slides and the pneumatic conveying: the cement powder is transported on films of air and through the pipes of air: the fluidization is fluid mechanics at the industrial scale: the porosity of the air slide, the velocity of the conveying air;

The flow network is the blood system of the plant: the same flow discipline covers the kiln gas and the ball mill vent: the engineer who computes the flows and the losses holds the natural language of every system: the fluid mechanics of the cement plant: fluid knowledge, plant power.

2. The Properties of the Fluids: The Matter the Plant Moves

The behavior of every flow follows from the properties of the medium, and the engineer of the cement plant handles four main fluids: the air and the flue gas, the water, the oils and, in special circuits, the slurries:

Fluid	Typical density	Typical dynamic viscosity	Notes for the cement plant
Air at 20 °C, 1 bar	1.20 kg/m3	18 × 10-6 Pa · s	The standard of the fan calculation
Flue gas at 200 °C	0.75 – 0.8 kg/m3	26 × 10-6 Pa · s	The hot gas of the ducts of the kiln
Water at 20 °C	998 kg/m3	1.0 × 10-3 Pa · s	The cooling and the conditioning
Fuel oil (heavy)	950 – 990 kg/m3	0.05 – 0.4 Pa · s	The burner fuel, the hot viscosity
Hydraulic oil	850 – 900 kg/m3	0.03 – 0.1 Pa · s	The hydraulic systems of the kiln

The dynamic viscosity measures the fluid’s internal friction and the kinematic viscosity, its ratio to the density, is the number that appears in the Reynolds calculation: the numbers of air change strongly with the temperature: the gas at the kiln entrance occupies five times the volume of the same mass at the ambient: the fans of the plant are specified with the working temperature and the altitude: the properties determine the flows: the numbers of the table, the basis of every duct design.

3. The Pressure and the Head: The Language of the Fans and the Pumps

The pressure is the fluid’s energy density: the cement engineer reads the process pressures in the millibars, the head of the water column and the kilopascals, and the equivalence between the units is an everyday tool:

• The pressure definition: the force of the fluid over the area: the static pressure of the gas in a duct, the dynamic pressure of its velocity, and their sum, the total pressure:
• The hydrostatic head: the pressure at the depth of a liquid: p = density × g × h: the manometer, the U-tube and the piezometer read the head directly: the level of the silo, the standpipe of the cooling tower:
• The unit conversions: 1 bar = 100 kPa = 10,000 mm WG (approx: 1 mm WG = 9.81 Pa): the fan curves and the plant instruments still mix the units, and the engineer converts daily;
• The gauge and the absolute: the plant pressures are the gauge values, and the absolute readings include the atmosphere: the fan and the gas-flow calculations use the absolute pressures wherever the density matters: the vacuum of the kiln exhaust, the negative gauge: the world of the draught;
• The pressures of the system: the kiln inlet fan inlet: the -5 to -30 millibar range: the pressure boxes of the cyclone stages: the air slide: the pressure of the filter: the pressure map of the plant: the flow conductor of the diagram:

The pressure is the most measured quantity of the cement gas engineering: the pressure-drop calculations of the ducts, the fan curves and the control loops all speak in the pressure: the mill bar and the water gauge live side by side on the drawings: the engineer who converts naturally between them moves at home in any of the world’s plants: the pressure: the first medium of the fluid.

4. The Continuity and the Bernoulli Equation: The Energy of the Flow

Two equations rule the flow of the fluids in the plant, and the cement engineer applies them daily without calling the theorems by name:

• The continuity (mass balance): what flows in, flows out: Flow = density × area × velocity: the same mass passes every section of a duct: a duct narrowing to half the area doubles its velocity: the basis of the cyclone inlet calculations and the duct sizing:
• The Bernoulli equation: along a stream of the ideal fluid, the sum of the static pressure, the dynamic pressure and the elevation head is constant: p + ½ρv2 + ρgh = constant:
• The dynamic pressure: the ½ρv2 term: the pressure the velocity would convert if the flow stopped; at 15 m/s of air, the dynamic pressure is about 135 Pa: the number that sizes the pitot tube: the airflow measurement of the fan tests:
• The elevation term: for the gases it is negligible, for the liquids it is the head: the difference between the suction and the discharge levels of a pump is the elevation term of the balance:
• The friction losses in the system: the friction losses, the bends and the fittings appear as the lost head: the practical plant equation: the total energy in = the useful energy out + the losses: this is the whole of the duct and the pump design: the energy book of the flow:

The Bernoulli energy balance is the base of the venturi measure, the fan test, the pump curves and the pressure drops: the engineer who does the balance around the pipe uses the Bernoulli without the fanfare: the understanding of the terms, the near the resolved measurement: the law of the flow of the plant and the book of its energy.

5. The Reynolds Number: The Flow Regimes of the Cement Fluids

The dimensionless number of Reynolds decides whether the flow is the orderly laminar layers or the chaotic mixing of the turbulent flow, and the Reynolds numbers describe nearly every flow of the plant:

Flow example	Re range	Regime	The meaning in the plant
Water in the small cooling pipes	below 2300	Laminar	The heat transfer suffers, the deposit the solids
Water in the main pipes	10,000 – 100,000	Turbulent	The normal pipe flow: the friction table of Moody
Air in the plant ducts	100,000 – 1,000,000	Turbulent	The transport of the dust, the uniform velocity
Air around the particles in the cyclones	1,000 – 100,000	Mixed	The separation of the dust of the cyclone
The oil film of the bearings	< 100	Laminar	The hydrodynamic bearing of the mills and the kiln

The Reynolds number is computed from the velocity, the hydraulic diameter, the density and the dynamic viscosity: the laminar flows are the smooth straight lines, and the turbulence mixes the flow, the heat and the dust: the cyclone requires its range of Reynolds to separate the fines, the bearing oil film requires the laminar to carry the load: the professional number: the regime of each flow of the plant: the flow of the fluid, the orders of the physics.

6. The Friction Losses: The Ducts, the Pipes and the Minor Fittings

The real flows lose energy to the friction of the walls and the disturbances of the fittings: the friction losses of the long ducts and the pipes are the largest operating cost of the fans and the pumps:

• The wall friction of the pipes: the friction factor from the Moody diagram depends on the Reynolds number and the relative roughness: the loss is proportional to the friction factor, the length, the velocity squared and inversely the diameter:
• The roughness of the cement ducts: the steel ducts of the process: 0.03 to 0.15 mm: the worn and the coated ducts; after years the surfaces of the process the friction factor rises: the fan duty creeps:
• The velocity head: the losses are expressed in the number of the velocity heads: the pipe bend about 0.2-0.5 heads, the 90-degree elbows 0.2-1.0, the valves 0.5 to 5:
• The fittings: the sudden enlargement, the contraction, the tees and the dampers: each a velocity head multiplier: the tables of the loss coefficients are the everyday reference of the plant designer:
• The equivalent length method: each fitting is converted into the equivalent meters of the straight pipe: the painful but practical way to sum the losses or the pipelines: the method of the package’s tools:

The friction analysis of a duct system is a few hours’ spreadsheet work and the reward is the fan efficiency: the losses that the design route: the half of the duct pressure is often absorbed by the hydraulics: the engineer who reduces a few fittings reduces the pressure requirement: the principle of the loss: the turbine of the fan.

7. The Flow Measurement: The Pitot, the Orifice and the Magnetic Method

The plant must measure the flows of its fluids, and each meter relies on the fluid mechanics of its own design:

• The pitot tube: measures the dynamic pressure and computes the velocity: the standard instrument of the duct traverses: the correction factors of the inlet and the outlet heads; the velocity profile; the traverse of the circular ducts:
• The orifice plate: the plate with the hole: the pressure difference across; the flow proportional to the root of the differential: the calibration of the discharge coefficient; the fixed loss between the permanent: the K-factor: the daily measurement of the auxiliary flows:
• The venturi: the tapered throat: the lower loss than the orifice: the permanent of the flow measurement of the low-pressure process lines when the energy matters:
• The thermal mass meter: sensing the heat removal of the flowing gas: the low flow and the mass control: the coal mill air of the modern plants:
• The magnetic-inductive meters: the water pipes: the voltage induced by the conductive liquid in the magnetic field: no moving parts: the cooling water circuits of the plant: the standard instruments:

The measurement is the information of the control: the O2, the fuel and the air flow measurements under the combustion: the errors of the flow measurements become the errors of the mass balances of the plant; the instrument engineer checks the pitot of the fan and the orifice of the aux every shutdown: the fluid of the measurement, the data of the operator.

8. The Fans in the Plant and the Fan Laws

The fans of the cement plant turn the motor power into the pressure and the flow: the fan curves, the operating point and the fan laws are the daily arithmetic of the process engineer:

• The fan curve: the fan is specified by the curve of the pressure against the flow at a given speed: the operating point is the crossing of the fan curve and the system curve:
• The system curve: the resistance of the system rises with the square of the flow: the duct, the filters, the preheater: the system pressure climbs: the design point: the operating point:
• The fan laws: the flow changes proportionally to the speed, the pressure with the square of the speed and the power with the cube: the three laws are the arithmetic of the fan speed control: the VFD dial of the rpm is the direct wallet of the plant:
• The specific fan power: the power consumed per cubic meter per second per pascal: the SFP of the plant: the fan efficiency: the optimization target: the fan efficiency of the tested fan 85 percent against 60:
• The surge and the stall: the flow falls below the stable point: the reversal, the vibration and the noise: the protection of the surge controllers on the large fans: the operating envelope of the fan system:

The fans consume between 10 and 20 percent of the electricity of the cement plant: the fan efficiency program of the plant is one of the best savings of the industry: the variable speed drives, the blade adjustments, the duct cleanings and the filter states: the calculation: one percent of the fan efficiency is the money of the year: the fan laws of the flow: the cube of the speed, the power of the saving.

9. The Pumps and the NPSH: The Cavitation of the Water Circuits

The pumps of the plant follow the same physics and add the liquid special: the cavitation, when the local pressure falls below the vapor pressure of the liquid and the pump starts to crumple:

• The pump curve: the flow against the head of the pump at the speed: the net positive suction head (the NPSH): the pump’s energy to stay safe from the vapor: the NPSH required by the pump versus the NPSH available of the system:
• The cavitation: the low pressure evaporates the fluid locally, the bubbles collapse violently when they reach the higher pressure, the metal is attacked: the damaged impeller and the pump noise: the classic problem of the hot water pump at the suction stroke:
• The required margin: the available NPSH should pass the required by 0.5 to 1 meter: the pump suction pipe kept short and the strainer clean: the elevation of the pump relative to the tank:
• The slurry and the abrasion: the pumps of the wet-process plants carry the mill slurries: the solids wear the impellers: the large clearances, the rubber-lined housings and the ceramic choices protect the duty:
• The efficiency of the duty: the pump is most efficient near the best-efficiency point: the throttled valve shift the operating point: the VFD saves: the pump efficiency of the plant: the kW of the water:

The pumping systems of the plant are quiet, but their failures are loud: the cavitated impellers, the worn seals and the dying flows: the pump curve in the operation file holds the answers: the fluid mechanics of the NPSH explains why the pump whines while the flow dies: the suction vessel, the strainer and the elevation decide the health of the liquid system: the pumps of the cement plant, the flow of the plant, the condition of the pump.

10. The Gas in the Ducts and the Combustion: The Air the Flow

The combustion air systems of the kiln that form the specialty gas flows of the plant: the density changes with temperature and composition, and the flow calculations run on normal conditions:

• The normal conditions: the flow of the kiln gas is reported in the normal cubic meters per hour: at 0 degrees (or 20) and the reasonable pressure: the actual volumetric flow at the duct temperature is much larger: the fan and the duct must pass the real volume, not the normal:
• The flow of the gas mass: the flue gas at 300 degrees has about half the density of the air at 20 degrees: for the same mass flow, the duct must pass nearly double the volume: the ducts and the fans of the process are sized at the actual temperature and pressure of the gas, never at the normal conditions alone:
• The velocity of the ducts: the clean gas 12 to 18 m/s: the dust-clearing mainstream: the 14 to 20 in the process: the conveying gas of the mill 20 to 30: the Ferrari speed of the pneumatic pipes 20-35: each regime an established value of the calculus:
• The combustion air flow: the primary, the secondary and the tertiary air flows follow the fuel-to-oxygen ratios: the excess air drives the O2 in the exhaust: the dry gas losses: the O2 at the process points of 2 to 4 percent corresponds to roughly 10 to 20 percent of the excess air: the gas analysis, the daily measure of the combustion balance:
• The compressibility most effects: the fan deliveries with a pressure increase: the air density: the volumetric drops: the absolute pressure: the fan curves: the altitude of the plant: the corrections of the fan nameplate to the site condition:

The dry air of the process: the measures of the anhydrous: normal cubic meters: the fan of the damper: the same mass: the different volumes: the capacity of the equipment at the elevated conditions: the engineer of the new plants checks: race, the dry: the Nm3/h: the true volume: the stack and the fan, sized for the real: the design box: the air of the management.

11. The Special Flows of the Plant: The Coal, the Air and the Cyclones

The fluid mechanics reaches beyond the pipes of the flow: three specialty flows carry the numbers and the energies of the plant: the cyclones for the dust, the conveying the air and the coal combustion:

• The cyclone flow: the vortex of the gas turns the particles toward the wall: the separation depends on the gas velocity: the inlet velocities of 16 to 20 meters per second are the standard: the pressure drop of a cyclone stage is 5 to 8 millibars: the cyclone is the fluid separator of the tower and the mill circuits;
• The air slide: the porous fabric lets the air float the powder: the pressure drop of the slide of 20 to 50 millibars at the low volumetric passages: the fluidization state: the powder flows like the liquid: the humidity gate of each airslide its own control;
• The pneumatic conveying: the powder in the pipe: the solid-gas flow: the dense phase and the lean phase: the pickup velocity of the particles at 25 to 35 meters per second in the lean systems: the energy of the conveying and the wear of the pipe bends: the design discipline of the transport lines:
• The cement pumps: the eccentric disc pumps push the cement through the pipes to the silos: the pressure of the product pipe, the loop design, the elevation of the silo and the discharge: the whole system is the momentum balance of the two-phase medium: the pressure of the pump against the friction of the pipeline:
• The dust dynamics: the saltation of the duct: the dust falls out of the low velocity: the deposition: the dust removal of the ducts: the sections of velocities: the automatic heading:

The three specialty flows are the fluid mechanics of the powder: every day, tons of cement and raw meal travel on the air: the pressure drops of the flows, the static pressure of the air slides, the fans moving the air: the flows of the cement follow the same physics as the flows of the gas: the practical discipline of the plant, applied to the powder.

12. The Losses in the Branches and the Balancing of the Systems

When the fan serves several branches, each branch must deliver its design flow and the balancing of the network is one of the most common commissioning jobs in the plant:

• The parallel branches: the flow of the fan splits among the branches proportionally to the inverse resistance: the high resistance branch takes less: the preferred branch robs the colleague: the classic of the manifold:
• The dampers: the slide and the louver dampers add the controllable resistance and the plant sets the design flows: the butterfly valves of the cooler ducts: the trim position of each damper is fixed by the balance: the logic of the flow control rests on the measured setpoints:
• The balancing by the pressure: the static pressure of the branches is measured and equalized at the designed flow: the pitot checks of the flow: the commissioning and the rebalance: the calibration of the damper positions:
• The leakage: the false air of the filter, the seals and the cracks: the leak means the dilution: the O2 anomalies and the fan flow: the leak hunt with the smoke and the pressure test: the standby:
• The system curve construction: the designers construct the curve of each branch and the combined curve of the network: the operating point of the fan at the interplay of the branches: the math graph: the engineering of the flow control:

The balance of the division of the flows lives in the plant’s everyday adjustments: the value of the balancing: the combustion controls that still read the O2, the kiln that needs the designed flow: the less the damping, the better the energy: the balanced system: the flow of the design: the adjustments of the dampers: the discipline of the hydrail of the branches.

13. Frequently Asked Questions

Do I need calculus for the fluid mechanics of the plant?

The plant application uses the arithmetic: the continuity, the Bernoulli, the Reynolds, the fan laws and the loss coefficients are the equations in the everyday formulas: the calculus appears in the deep design texts of the package, but the engineer of the operation and the audit works with the numbers directly: the equations on one page, the values in the tables.

Why does the flow double when the diameter doubles?

The area of a pipe grows with the square of the diameter: at the same velocity, a pipe of double the diameter carries four times the flow: the diameter is the language of the duct sizing: the engineer who quotes the velocity and the area simultaneously, in meters per second and cubic meters per hour, owns the continuity: the inverse is the same: half the diameter at the same flow means the velocity quadruples.

What flow speeds are economical for the gas ducts?

The pressure and the dust: the velocities of 14 to 20 meters per second in the process ducts, 12 to 18 in the clean gas ducts and 20 to 30 in the conveying ducts: above the balance the higher velocity costs pressure, below it the dust drops out: the velocity is the central variable of the duct design: the industrial ranges fill the design tables of the handbooks.

The fans the plant: why is the cube of the change so important?

The fan laws: the power follows the cube of the speed: a speed increase of 10 percent raises the power by about 33 percent: the same, a reduction of 10 percent saves more than a quarter of the fan power: the fan speed on the VFD is the biggest single operator move of the energy program: the fluid mechanics translates the electric savings into the cube.

What is the difference between the static and dynamic pressure of a fan?

The static pressure of the fan is the pressure the fan adds to overcome the system resistance; the dynamic pressure is the ½ρv2 of the velocity head at the fan outlet; the total pressure is the sum of the two: the fans are specified by the static pressure at the flow of the fan curve: the engineer reads the nameplate and the curve with the system installed: the fan application of the plant sits between the two readings: the pressure of the utility, the sum of the states.

14. Conclusion

The fluid mechanics of the cement plant runs through every duct, fan, pump and pneumatic line: the continuity and the energy, the Reynolds and the friction, the fan laws and the NPSH: the complete toolkit of the flow: the package provides the deep handbooks, the fan charts, the loss tables and the ready Excel tools: the 931 files of the Complete Cement Technical Package: the $249.99 one-time payment: the instant download: the engineer of the flow is the engineer of the whole plant: the fluid mechanics of the cement, mastered on these pages.

The same library carries the foundations: the fan handbooks, the fluid texts and the gas designs: this article is the entry point: the numbers of the tables, the loops of the plant, every kilogram of cement carried on the air: the kiln draught, the vent and the flow: the knowledge of the fluid completes the process of the cement: the engineer of the flow, fluent in the physics.

This file is part of the Complete Cement Technical Package (931 files) available from cementequipment.org. Respective rights holders; library copy for the licensed single user.