Fluid Mechanics Interview Questions

Reynolds number (Re) is a dimensionless ratio of inertial forces to viscous forces: Re = rho*v*D/mu, where rho is density, v is velocity, D is characteristic length, and mu is dynamic viscosity. It indicates flow regime: Re < 2100 for laminar flow (smooth, parallel streamlines), Re > 4000 for turbulent flow (chaotic, mixing), and 2100-4000 for transitional flow. Reynolds number is fundamental to predicting friction factors, heat transfer coefficients, and mass transfer rates.

Bernoulli's equation states that for steady, incompressible, inviscid flow along a streamline: P/rho + v^2/2 + gz = constant, representing pressure energy, kinetic energy, and potential energy per unit mass. Assumptions: steady flow, incompressible fluid, no friction (inviscid), flow along a streamline, and no energy added or removed. For real pipe flow, modified forms include friction losses (Darcy-Weisbach) and pump work terms.

A centrifugal pump uses a rotating impeller to add velocity to fluid, which is then converted to pressure in the volute casing. Liquid enters axially at the impeller eye, is accelerated radially outward by the spinning vanes, exits at high velocity into the volute, and the expanding volute converts kinetic energy to pressure energy. Centrifugal pumps are the most common pump type in the process industry, handling flows from small to very large and providing continuous, non-pulsating flow.

Head is energy per unit weight of fluid, expressed in meters or feet of fluid, independent of fluid density. Pressure is force per unit area, measured in bar or psi, and depends on fluid density. They are related by: Pressure = Head x rho x g. Using head allows pump performance to be specified independently of the fluid being pumped - a pump develops the same head regardless of fluid density, though the pressure rise varies. This makes pump curves universal for any liquid.

NPSH (Net Positive Suction Head) is the absolute pressure head at the pump suction above vapor pressure. NPSHa (available) is provided by the system: NPSHa = P_atm/rho*g + h_static - h_friction - P_vapor/rho*g. NPSHr (required) is specified by the pump manufacturer. If NPSHa < NPSHr, cavitation occurs - vapor bubbles form and collapse causing noise, vibration, impeller damage, and loss of head. Adequate NPSH margin (typically NPSHa > NPSHr + 0.5-1m) is essential.

Positive displacement (PD) pumps trap a fixed volume of fluid and force it through the discharge. Types include reciprocating (piston, plunger, diaphragm) and rotary (gear, screw, lobe, vane). PD pumps are used for: high-pressure applications (up to 1000+ bar), accurate metering/dosing, viscous fluids (where centrifugal efficiency drops), low flow rates, self-priming needs, and handling shear-sensitive fluids. They provide nearly constant flow regardless of pressure, unlike centrifugal pumps.

The Darcy friction factor (f) relates frictional pressure drop to flow velocity in pipes via the Darcy-Weisbach equation: dP = f*(L/D)*(rho*v^2/2). For laminar flow: f = 64/Re. For turbulent flow, f depends on Re and relative roughness (e/D), determined from the Moody chart or Colebrook equation. Typical values: smooth pipes 0.01-0.02, rough pipes up to 0.05. The friction factor is essential for calculating pressure drops and sizing pumps for piping systems.

Design velocities balance pressure drop (energy cost) against pipe cost (capital). Typical ranges: liquids in suction lines 0.5-1.5 m/s (to ensure adequate NPSH), liquids in discharge 1.5-3 m/s, gravity drain lines 0.5-1 m/s, gases at low pressure 10-20 m/s, gases at high pressure 15-30 m/s, and steam 20-40 m/s. Erosion limits apply for solids-laden streams or corrosive fluids. Economic velocity analysis may optimize for specific applications.

An orifice plate is a thin plate with a sharp-edged hole inserted in the pipe. It creates a pressure drop proportional to flow velocity squared. By measuring the pressure difference upstream and at the vena contracta (downstream constriction), flow can be calculated using: Q = Cd*A2*sqrt(2*dP/rho), where Cd is the discharge coefficient (typically 0.6-0.65). Orifice plates are simple, reliable, and inexpensive but cause permanent pressure loss (40-80% of measured dP).

Dynamic compressors: Centrifugal (high flow, moderate pressure ratio, oil-free option), Axial (very high flow, lower pressure ratio, multi-stage). Positive displacement: Reciprocating (high pressure, lower flow, pulsating output), Rotary screw (continuous flow, oil-injected or dry), and Rotary vane (lower pressure applications). Selection depends on flow rate, pressure ratio, gas properties, and service continuity. Centrifugal dominates large continuous processes; reciprocating for high pressure or smaller intermittent duty.

Pipe fittings (elbows, tees, valves, reducers) cause additional pressure losses beyond straight pipe friction. These are typically expressed as equivalent length (Le) of straight pipe or as velocity heads (K-factor): dP = K*(rho*v^2/2). Typical K-values: 90-degree elbow 0.3-0.9, gate valve (open) 0.1-0.2, globe valve (open) 4-10, check valve 1-2. Fittings can represent significant loss in short piping runs - total fitting losses often exceed straight pipe losses in process plants.

A control valve adjusts flow by varying the restriction to flow based on a signal from a controller. Components include: body (contains flow passage and trim), trim (plug/seat that modulates flow), actuator (pneumatic, electric, or hydraulic - moves the stem), and positioner (ensures accurate stem position). The valve creates a variable pressure drop - more closure means more dP for a given flow. Valve characteristics (linear, equal percentage, quick-opening) describe how flow changes with stem position.

Newtonian fluids have constant viscosity regardless of shear rate - shear stress is directly proportional to shear rate (water, most gases, light oils). Non-Newtonian fluids have viscosity that varies with shear rate: shear-thinning (pseudoplastic - viscosity decreases with shear, like paint, polymer solutions), shear-thickening (dilatant - viscosity increases, like cornstarch slurry), Bingham plastic (requires yield stress to flow, like toothpaste), and thixotropic (time-dependent thinning). Non-Newtonian behavior affects pump selection and piping design.

Differential pressure: orifice plate (most common, simple, permanent loss), Venturi (lower loss, higher cost), flow nozzle. Velocity: turbine (high accuracy for clean liquids), vortex (wide rangeability), ultrasonic (non-invasive), magnetic (conductive liquids only). Mass flow: Coriolis (direct mass measurement, most accurate), thermal dispersion (gases). Selection depends on fluid properties, accuracy needs, rangeability, pressure drop tolerance, and maintenance requirements.

Priming is filling the pump casing and suction line with liquid before starting. Centrifugal pumps cannot pump air (air is too compressible) - they need liquid present to develop pressure. Self-priming pumps have special casing design to retain liquid for re-priming. Priming methods: foot valve in suction line (maintains liquid), vacuum priming systems, flooded suction (liquid level above pump), and manual filling. Failure to prime causes no flow, overheating, and potential seal damage.

The pump curve (H vs Q) shows head developed at various flows - it decreases as flow increases for centrifugal pumps. The system curve shows head required by the piping system - it increases with flow squared due to friction. The operating point is where curves intersect. System curve shifts up with increased resistance (valve closure, fouling); pump curve shifts with speed changes or impeller trimming. Understanding this interaction is crucial for pump selection and troubleshooting flow problems.

Affinity laws relate pump performance parameters to speed changes: Q2/Q1 = N2/N1 (flow proportional to speed), H2/H1 = (N2/N1)^2 (head proportional to speed squared), P2/P1 = (N2/N1)^3 (power proportional to speed cubed). Applications: predict performance at different speeds, evaluate VFD (variable frequency drive) energy savings, and estimate impeller diameter changes. Limitations: only valid for geometrically similar conditions, inaccurate at low speeds or significant efficiency changes.

Mechanical seals: industry standard, versatile, field-maintainable, but leak pathway exists and seals are wear items. Sealless options: Magnetic drive pumps (magnets couple motor to impeller through containment shell - zero leakage but efficiency loss from eddy currents, temperature limits), Canned motor pumps (motor rotor in process fluid - compact, suitable for high pressure, but bearing wear in fluid). Sealless preferred for toxic, carcinogenic, or expensive fluids; mechanical seals for high temperature, abrasive, or when efficiency is critical.

Surge occurs in centrifugal/axial compressors when flow drops below the minimum stable flow, causing flow reversal and violent pressure oscillations. It damages seals, bearings, and impellers. Prevention: anti-surge control system that maintains flow above surge limit by recycling gas or opening a vent. Surge margin (typically 10-15% above surge line) accounts for control system response time. Surge detection uses flow/pressure measurements to calculate proximity to surge, triggering protective action.

Piping stress analysis verifies that piping systems can withstand loads from pressure, temperature, weight, and external forces. Required for: high temperature/pressure systems (thermal expansion stress), large diameter piping, piping connected to sensitive equipment (pumps, compressors, vessels with nozzle load limits), and code requirements (ASME B31.3). Analysis uses software (Caesar II, Autopipe) to calculate stresses, support loads, and equipment nozzle loads. Flexibility is added through routing, expansion loops, or expansion joints.

Main patterns include: Stratified flow (low velocities - liquid at bottom, gas above), Wavy stratified (higher gas velocity creates waves), Slug flow (liquid slugs alternate with gas pockets - problematic for equipment), Plug flow (elongated gas bubbles in liquid), Annular flow (high gas velocity - liquid film on wall, gas core with droplets), and Dispersed bubble flow (high liquid velocity - gas bubbles dispersed in liquid). Pattern maps (Baker, Taitel-Dukler) predict pattern based on superficial velocities and fluid properties.

Cv (valve coefficient) relates flow to pressure drop: for liquids, Q = Cv*sqrt(dP/SG). Valve sizing: calculate required Cv at normal, minimum, and maximum flows; select valve with rated Cv allowing adequate travel range (typically 10-90% opening). Check for choked flow (vaporization limiting flow), cavitation, noise, and velocity limits. The installed Cv may differ from rated due to fittings (reducers, piping geometry). Undersized valves cannot achieve required flow; oversized valves give poor control resolution.

Venturi meter: gradual converging section and diffuser for pressure recovery, permanent loss only 10-20% of measured dP, higher accuracy (Cd ~0.98), but expensive and requires more space. Orifice plate: simple, inexpensive, easy to install and replace, but permanent loss 40-80% of measured dP, lower accuracy (Cd ~0.6), susceptible to edge wear. Venturi preferred for large flows where pumping cost is significant; orifice for lower flows, cost-sensitive applications, or when frequent changes are needed.

Coriolis meters directly measure mass flow (not volumetric), eliminating need for density compensation. Advantages: high accuracy (0.1-0.5%), measures density simultaneously, handles varying process conditions, bidirectional flow measurement, no straight pipe requirements, and low maintenance. Also measures fluid viscosity in some models. Limitations: high cost, pressure drop, size/weight for large flows, and sensitivity to vibration and two-phase flow. Ideal for custody transfer, batching, and high-value or variable-density fluids.

Hydraulic gradient is the slope of the hydraulic grade line (HGL), representing energy loss per unit length due to friction. HGL = elevation + pressure head; it drops along flow direction due to friction. For gravity-driven flow, the HGL slope determines flow rate. In pump systems, the pump adds energy, creating a step up in HGL. Pipeline profile is plotted against HGL to ensure positive pressure throughout (HGL above pipe centerline) and identify potential problems like vapor pockets at high points.

Minimum flow prevents: overheating (energy dissipates as heat when not transferred to fluid), cavitation and recirculation at impeller eye, mechanical damage from vibration and hydraulic forces, and bearing damage. Minimum flow is typically 10-30% of BEP flow depending on pump design. Methods to ensure: continuous recirculation line with orifice (simple but wastes energy), automatic recirculation valve (opens below setpoint), minimum flow control valve, or variable speed operation that reduces speed at low flow.

Criteria include: pressure drop limit (available pressure, pump sizing), velocity limits (erosion, noise, vibration), economic optimization (pipe cost vs energy cost), code requirements (minimum wall thickness for pressure), two-phase flow considerations (avoid slug flow regime), control valve pressure drop allocation (typically 25-50% of system dP), and special requirements (gravity flow, self-draining, slope for two-phase). Standard pipe sizes are selected from calculated requirements, often rounding up for margin.

Parallel operation: flows add at same head - used to increase capacity or provide redundancy. Combined curve is horizontal sum of individual curves. Series operation: heads add at same flow - used for high head requirements. Combined curve is vertical sum. Parallel considerations: check valves prevent backflow through idle pump, pumps should have similar characteristics to share load, and operating point stability. Series: first pump must have adequate NPSH, second pump handles higher suction pressure.

Linear: flow proportional to opening - used when valve takes most system dP and dP is constant. Equal percentage: equal increment of opening gives equal percentage change in flow - most common, provides linear installed characteristic when valve dP varies with flow. Quick-opening: large flow change at small opening - used for on-off or relief service. Selection based on: system pressure drop distribution, process gain requirements, and rangeability needs. Equal percentage preferred for most process control applications.

Water hammer is a pressure surge caused by sudden velocity change - rapid valve closure, pump trip, or check valve slam. Pressure rise approximately dP = rho*c*dV, where c is acoustic velocity (1000-1400 m/s for water). Effects: noise, vibration, pipe rupture, equipment damage. Prevention: slow valve closure (5-10 pipe lengths travel time), surge relief valves, surge tanks or accumulators, flywheel on pumps (extends coastdown), soft-start/stop on pumps, and air chambers. Analysis using method of characteristics for critical systems.

A liquid ring pump uses an eccentric rotor in a cylindrical housing partially filled with sealing liquid (usually water). Rotation creates a liquid ring against the casing, with varying gas volume between impeller blades acting as compressing chambers. Gas is drawn in, compressed, and discharged as the ring expands and contracts. Applications: vacuum systems handling condensable vapors, wet gases, or explosive mixtures (isothermal compression). Advantages: handles liquid slugs, simple design, seals gas, and no oil contamination.

The equivalent length method converts fitting losses to equivalent straight pipe lengths: Le = K*D/f, where K is fitting K-factor, D is diameter, and f is friction factor. Total equivalent length = straight pipe length + sum of fitting equivalent lengths. Pressure drop is then calculated using Darcy-Weisbach for total equivalent length. Alternative: use K-factors directly with dP = K*(rho*v^2/2). The method simplifies calculations but assumes constant friction factor - adequate for most engineering applications.

A steam ejector uses high-pressure motive steam passing through a converging-diverging nozzle, creating supersonic flow and low pressure that entrains the suction gas. The combined stream is compressed in the diffuser section where kinetic energy converts to pressure. Key parameters: motive steam pressure and flow, suction pressure, and discharge pressure. Staging (2-6 ejectors in series with intercondensers) achieves deep vacuum. Advantages: no moving parts, handles corrosive gases, and reliable. Disadvantages: steam consumption, limited turndown.

Sizing considerations: determine relieving scenarios (fire case, blocked outlet, runaway reaction, etc.), calculate required relieving rate for each scenario, select worst case, calculate required orifice area using API 520/521 methods accounting for fluid properties, back pressure, and set pressure. Types: conventional (sensitive to back pressure), balanced bellows (tolerates back pressure variation), pilot-operated (tight closure). Verify inlet pressure drop <3% set pressure and outlet pressure within valve rating.

Considerations include: minimum velocity to prevent settling (1-2 m/s for sand, varies with particle size/density), solids concentration affecting viscosity and flow behavior, abrasion/erosion at bends and restrictions, startup/shutdown procedures (prevent settling), pump selection (hardened wear parts, large clearances), and heterogeneous vs homogeneous flow regimes. Use specialized correlations (Durand, Wilson) for pressure drop. Large particles require higher velocities; fine particles may behave as homogeneous mixture at lower velocities.

Systematic approach: determine fluid properties at operating temperature (viscosity affects performance derating per HI standards), calculate NPSHa accounting for vapor pressure at temperature, apply viscosity corrections to pump curves. Options to improve NPSHa: raise vessel level, reduce suction piping losses, use oversized suction line, cool suction fluid, or use inducer impeller. For high viscosity: consider positive displacement pumps (screw, gear), or oversized centrifugal with viscosity correction. May need jacketed pump for temperature control. Seal selection critical for high temperature.

Test per ASME PTC-10: measure inlet/outlet pressures and temperatures, flow rate, speed, and gas composition. Calculate: polytropic head, efficiency, power, and surge margin. Compare to guarantee point considering tolerances (typically 4% head, 4% efficiency). Account for: gas property variations from design, operating speed differences using fan laws with appropriate correction, and inlet conditions. Degradation assessment compares current test to original data. Field tests use installed instruments; shop tests use more accurate instrumentation.

Approaches include: mechanistic models (OLGA, LedaFlow) solving conservation equations with closure relationships for flow pattern, holdup, and pressure drop; empirical correlations (Beggs-Brill, Hagedorn-Brown) developed from experimental data; and CFD for detailed local behavior. Key phenomena: flow pattern transitions, liquid holdup, pressure drop, slug characteristics, and terrain effects. Model selection depends on application: steady-state for design, transient for operational scenarios (startup, pigging, slugging). Validation against field data is essential.

Cavitation occurs when local pressure drops below vapor pressure, forming and collapsing bubbles. Symptoms: noise, vibration, pitting damage downstream of trim. Diagnosis: check operating conditions against cavitation indices (Sigma, Xfz), inspect for damage during maintenance. Prevention: use anti-cavitation trim (staged pressure reduction, tortuous path), relocate valve to higher pressure location, increase back pressure, use larger valve at lower dP, or consider applying back pressure via downstream restriction. For severe cases, use specialized cavitation-resistant materials.

Transient analysis required for: long pipelines (surge travel time significant), pump trip scenarios, rapid valve operations, and check valve slam assessment. Methods: method of characteristics (MOC) - converts PDEs to ODEs along characteristic lines, most common for pipeline surge; wave plan analysis - graphical for simple systems; finite element methods - for complex systems. Analysis determines: maximum/minimum pressures, surge equipment sizing (relief valves, surge tanks, vacuum breakers), and valve closure time requirements. Software includes AFT Impulse, Pipenet, and HAMMER.

Selection factors: flow rate (centrifugal >500 m3/h typically), pressure ratio (reciprocating handles higher per stage), gas molecular weight (centrifugal favors heavier gases), turndown requirements (reciprocating better), pulsation sensitivity of process, efficiency (often similar at design point), reliability philosophy, and maintenance capabilities. Economic analysis: centrifugal has lower maintenance but higher capital for small flows; reciprocating has higher maintenance but handles wide conditions. For hydrogen or light gases at high pressure ratio, reciprocating often preferred. Consider screw compressors for intermediate range.

Slug catcher sizing accounts for: steady-state liquid inventory, terrain-induced slugs (liquid accumulation in valleys released at ramps), pigging slugs (all liquid ahead of pig), ramp-up slugs (increasing gas rate releases accumulated liquid), and operationally-induced slugs. Volume = sum of all slug sources with appropriate design margin. Transient flow simulation (OLGA) determines slug volumes for various scenarios. Design includes: residence time for gas-liquid separation, level control range, and liquid handling system capacity. Safety factor 1.5-2.0 on calculated volume.

Causes include: mechanical (imbalance, misalignment, bearing wear, loose components), hydraulic (cavitation, recirculation, operation away from BEP, air entrainment), and resonance (structural or acoustic). Diagnostic approach: vibration spectrum analysis - 1x rpm indicates imbalance/misalignment, 2x rpm indicates misalignment/looseness, vane pass frequency indicates hydraulic issues. Check operating point relative to BEP, verify NPSH margin, inspect bearings, check alignment, and verify foundation condition. Flow-induced vibration varies with flow rate; mechanical issues are relatively constant.

Design considerations: staged pressure reduction (multiple valves or multi-stage trim) to limit velocity at each stage, avoid choked flow (sonic velocity causes severe erosion), maintain downstream pressure above vapor pressure, use anti-cavitation trim, and proper materials (hardened trim, erosion-resistant body). Velocity limits typically <200 m/s for gases, lower for liquids with flashing. Acoustic treatment for noise: silencers, inline diffusers, heavy-wall pipe. Use specialized multi-stage pressure reducing devices for extreme cases. CFD analysis may be needed for complex geometries.

Evaluation process: establish baseline power consumption and flow profile (daily/seasonal variations), construct system curve (static head + friction), apply affinity laws to predict power at various flows. Energy savings = integral of (baseline power - VFD power) over operating profile. Key factors: proportion of static vs friction head (VFD saves more with high friction proportion), flow variation range, current control method (throttling vs recirculation), motor efficiency at reduced speed. Include VFD losses (3-5%) and motor efficiency variation. Simple payback typically 1-3 years for good applications.

Design considerations: peak relieving load (often governs sizing), back pressure limits at relief valves (<10% set pressure typically), multiple load cases (fire, power failure, cooling failure), relief device staggering in manifolds, liquid knockout capacity, and flare tip sizing for smokeless capacity. Pressure drop calculated using compressible flow equations accounting for varying density. Network analysis software handles multiple simultaneous reliefs. Include: purge gas requirements, pilot gas, steam requirements if applicable, and knockout drum sizing for liquid carryover.

Pulsation sources: discrete flow pulses from plunger action create pressure waves. Analysis: API 674/618 guidelines, acoustic simulation of piping system to find resonant frequencies, avoid coincidence with pump pulsation frequencies. Dampening methods: pulsation dampeners (gas-charged or all-liquid bladder type) sized for volume change, acoustic filters (volume-choke-volume), orifice plates (adds damping but permanent loss), and proper pipe sizing (limit velocity). Suction stabilizers prevent acceleration head problems. Complex systems require acoustic analysis software (Beta, PulsaTrol).

Considerations: apparent viscosity varies with shear rate (calculate at pump shear conditions), pressure drop correlations modified for rheological behavior (use generalized Reynolds number), NPSH may be affected by inlet conditions (shear history), and pump selection differs. For shear-thinning fluids: centrifugal may work well (high shear reduces viscosity); for thixotropic: may need initial agitation. Progressive cavity pumps handle wide viscosity range with minimal shear. Diaphragm pumps for shear-sensitive fluids. Test with actual fluid or accurate rheological data essential.

Dry gas seals use a thin gas film (microns) between rotating and stationary faces, created by spiral grooves that pump gas inward. Advantages over wet seals: no oil contamination, lower power loss, higher reliability. Operating concerns: clean dry seal gas essential (filtration, conditioning), proper pressure control for seal gas supply, monitoring seal vent flows (primary, secondary, tertiary), and temperature monitoring. Tandem seal arrangement provides backup. Contamination or loss of seal gas causes rapid failure. Proper commissioning and operating procedures critical.

Design considerations: target pressure and time (typically to safe level within 15 minutes for fire scenario), minimum metal temperature during blowdown (Joule-Thomson cooling can cause brittle fracture), flare system capacity, liquid dropout and disposal, and blowdown valve sizing. Use transient simulation to model pressure/temperature profiles. Size orifices or valves for controlled rate that prevents excessive cooling. Material selection must handle minimum temperature. Segment long pipelines with intermediate valves. Consider automated blowdown for rapid response to fire detection.