Fluid flow and pumps in process plants

In short

Fluid flow and pumps covers how liquids and gases move through process piping, how much pressure is lost doing it, and how pumps and compressors supply that pressure. It rests on three balances — mass (continuity), mechanical energy (Bernoulli with friction) and momentum — plus the Darcy-Weisbach friction equation and pump characteristic curves. Every chemical plant, water utility, refinery and pharma unit sizes pipes, selects pumps and solves cavitation and flow-measurement problems with exactly this material. It is heavily examined in GATE CH (Fluid Mechanics and Mechanical Operations section), in university Fluid Mechanics / Unit Operations-I papers, and in technical rounds at Reliance, IOCL, BPCL, ONGC, L&T Hydrocarbon, Tata Chemicals, UPL, Aarti Industries, Sun Pharma, Thermax, KSB, Kirloskar Brothers and engineering consultants such as Jacobs and Toyo.

Explained

Fluid properties and flow regimes

• Fluid: a substance that cannot sustain shear at rest. Newtonian fluid: shear stress τ = μ(du/dy); water, air, most light organics. Non-Newtonian: pseudoplastic (polymer solutions, paints) and dilatant (starch slurry) follow the power law τ = K(du/dy)ⁿ, with n < 1 and n > 1 respectively; Bingham plastic (toothpaste, drilling mud, sewage sludge) has a yield stress instead, τ = τ₀ + μ_p(du/dy).
• Viscosity μ (Pa·s; 1 cP = 10⁻³ Pa·s) falls with temperature in liquids, rises in gases. Kinematic viscosity ν = μ/ρ (m²/s; 1 cSt = 10⁻⁶ m²/s).
• Reynolds number Re = ρuD/μ = inertia/viscous forces. In a circular pipe: laminar Re < 2,100, transition 2,100–4,000, turbulent Re > 4,000. Most plant lines run turbulent (Re 10⁴–10⁶).
• Velocity profile: laminar is parabolic with u_max = 2u_avg; turbulent is blunt with u_max ≈ 1.2–1.25 u_avg, and has a viscous sub-layer at the wall where most of the resistance sits.
• Boundary layer: the thin region near a surface where velocity rises from zero to free-stream. No-slip condition at the wall is why friction exists at all. Entrance length for fully developed flow ≈ 0.05 Re·D (laminar), ≈ 25–50 D (turbulent).
• Compressible or not: treat gas flow as incompressible if Mach number < 0.3 or pressure drop < ~10% of inlet absolute pressure; otherwise use compressible (isothermal or adiabatic) pipe-flow equations. Maximum gas velocity in a pipe is limited by choking at Ma = 1.

Continuity, Bernoulli and the mechanical energy balance

• Continuity (steady, one inlet/outlet): ṁ = ρ₁A₁u₁ = ρ₂A₂u₂; for incompressible flow Q = A₁u₁ = A₂u₂.
• Bernoulli (ideal, incompressible, steady, along a streamline): p/ρg + u²/2g + z = constant — pressure head + velocity head + elevation head. Valid only for frictionless flow with no work.
• Real (extended) Bernoulli / mechanical energy balance: adds pump work and friction loss, and a kinetic-energy correction factor α (α = 2 laminar, ≈ 1.05 turbulent, usually taken as 1).
• Momentum balance: used for forces on bends, reducers and nozzles, and for thrust on pipe supports — ΣF = ṁ(u_out − u_in). Examined as "force on a 90° bend".
• Flow work vs shaft work: the pump adds shaft work; the head it must supply equals static lift + pressure difference between vessels + total friction, not just the lift.

Friction losses in pipes and fittings

• Darcy-Weisbach: h_f = f(L/D)(u²/2g) with the Moody (Darcy) friction factor f. Beware notation: the Fanning friction factor f_F = f/4, and Indian textbooks (McCabe, Coulson) often use Fanning — state which you are using.
• Laminar: f = 64/Re (Fanning 16/Re), from Hagen-Poiseuille; pressure drop ∝ u and ∝ 1/D⁴ at fixed Q, and is independent of roughness.
• Turbulent: f from the Moody chart or Colebrook-White equation, function of Re and relative roughness ε/D. Blasius: f = 0.316/Re^0.25 for smooth pipe, 4,000 < Re < 10⁵. In the fully rough regime f depends on ε/D alone.
• Typical roughness ε: drawn tubing 0.0015 mm, commercial steel 0.045 mm, galvanised iron 0.15 mm, cast iron 0.26 mm, concrete 0.3–3 mm. Scaling and corrosion raise ε over years — add a fouling allowance.
• Minor losses: h = K(u²/2g). Typical K: 90° standard elbow 0.75, 45° elbow 0.35, gate valve fully open 0.17, globe valve open 6–10, swing check valve 2, tee (through branch) 1.0, sudden exit 1.0, sudden entrance 0.5 (0.05 if rounded). Alternatively use equivalent length L_e/D (90° elbow ≈ 30, gate valve ≈ 8, globe valve ≈ 340).
• Sudden enlargement: h = (u₁ − u₂)²/2g (Borda-Carnot). Sudden contraction: h ≈ 0.5(u₂²/2g) approximately.
• Economic pipe size: balances capital cost (larger pipe) against pumping cost (smaller pipe). Common design velocities: pump suction 0.6–1.5 m/s, pump discharge/liquid lines 1.5–3 m/s, gravity lines 0.5–1 m/s, steam 20–40 m/s, process gas 10–30 m/s.

Pumps: types, selection and characteristics

• Centrifugal (rotodynamic): impeller adds kinetic energy, the volute or diffuser converts it to pressure. Types — radial, mixed and axial flow; single/multistage; end-suction, split-casing, vertical turbine, submersible, canned/magnetic-drive (no seal, for hazardous duty). Handles large flows at moderate head; flow varies with head; must usually be primed; self-regulating against a throttled discharge.
• Positive displacement (PD): traps and displaces a fixed volume per stroke or revolution. Reciprocating — piston, plunger, diaphragm (metering/dosing). Rotary — gear, lobe, screw, vane, progressive cavity, peristaltic. Nearly constant flow regardless of head, self-priming, handles high viscosity and high pressure; never throttle or valve-off the discharge — pressure rises until something fails, so a relief valve is mandatory.
• Special pumps: jet pump/ejector (steam or water motive fluid, no moving parts, for vacuum and slurry), air-lift pump, hydraulic ram, airless diaphragm pumps for corrosive acid duty.
• Characteristic curve: H falls as Q rises (for radial impellers); efficiency η peaks at the best efficiency point (BEP); power rises with Q. System (resistance) curve: H_sys = static head + KQ². The operating point is where the two curves intersect — select so it lies near BEP (ideally 80–110% of BEP flow).
• Control of flow: discharge throttling (simple, wasteful), variable frequency drive (energy-efficient, now standard for large duties), impeller trimming, bypass/recirculation, parallel/series pumping. Never throttle the suction — it causes cavitation.
• Series vs parallel: series adds heads at the same flow (high-head duty); parallel adds flows at the same head (but each pump delivers less than alone because the system curve steepens).
• Priming, minimum flow and seals: centrifugal pumps need a flooded suction or priming; running at near-zero flow overheats the casing (hence minimum-flow bypass); sealing by gland packing, mechanical seal (single/double with flush plan) or seal-less design.

NPSH and cavitation

• Cavitation: if the pressure at the impeller eye falls to the liquid's vapour pressure, vapour bubbles form and collapse violently downstream — noise, vibration, pitted impeller, falling head and flow.
• NPSH available (NPSHa) = (p_atm or p_vessel − p_vapour)/ρg + z_static − h_f,suction, where z is positive for flooded suction and negative for a lift. It is a property of the installation.
• NPSH required (NPSHr) is a property of the pump from the manufacturer's test curve and rises with flow. Design rule: NPSHa ≥ NPSHr + 0.5 to 1 m margin (API 610 practice asks for a margin; many specs use ~1 m or 10%).
• Remedies: raise the suction vessel, lower the pump, shorten/enlarge the suction line, reduce suction fittings, cool the liquid (lowers p_vap), reduce flow, use a lower-NPSHr or double-suction pump, add an inducer or a booster pump.
• Hot or volatile liquids (boiling-point feed, LPG, light hydrocarbons) have p_vap ≈ p_vessel, so NPSHa is almost entirely the static liquid level — these services are the classic cavitation interview question.
• Suction specific speed Nss flags cavitation-prone selections; high values indicate a narrow stable operating band.

Flow measurement and other devices

• Head (differential-pressure) meters: orifice plate (cheap, high permanent loss, C_d ≈ 0.61), venturimeter (low loss, C_d ≈ 0.98, costly), flow nozzle (intermediate), pitot tube (point velocity). All give Q ∝ √Δp, so turndown is poor (about 3:1).
• Variable-area: rotameter — float rises until drag balances weight; Δp constant, area varies; good turndown, needs vertical mounting.
• Others: electromagnetic (conductive liquids only, no obstruction), ultrasonic/transit-time (clamp-on, non-intrusive), turbine, vortex-shedding, Coriolis (direct mass flow, highest accuracy, used in custody transfer and dosing), thermal mass (gases), weirs and notches for open channels.
• Valves: gate and ball for isolation (low loss), globe and needle for throttling, butterfly for large low-pressure lines, diaphragm for corrosive/sterile service, check valve to prevent reverse flow, control valve with Cv sizing, and pressure relief/safety valve as the mandatory last line of protection.
• Water hammer: sudden valve closure sends a pressure wave of speed a = √(K/ρ) (about 1,200–1,400 m/s in water in a rigid pipe); Joukowsky surge Δp = ρ a Δu. Controlled by slow-closing valves, surge vessels and air chambers.

Indian standards, codes and practice

• Piping design for process plants follows ASME B31.3 (Process Piping); power piping B31.1; cross-country liquid/gas pipelines B31.4/B31.8 and the relevant Petroleum and Natural Gas Regulatory Board (PNGRB) technical standards and OISD guidelines.
• Common Indian pipe and fitting standards: IS 1239 (mild steel tubes and tubulars, medium/heavy class), IS 3589 (steel pipes for water and sewage), IS 1536/IS 1537 (cast iron pressure pipes), IS 4985 (unplasticised PVC pipes), IS 4984 (PE pipes for water supply), IS 14333 (HDPE pipes for sewerage), IS 1538 (CI fittings). Flanges to ASME B16.5 or IS 6392. Quote editions from the current BIS catalogue — several older IS numbers have been revised or withdrawn.
• Pump standards: IS 5120 (technical requirements for rotodynamic special-purpose pumps), IS 9137 (acceptance tests for centrifugal, mixed flow and axial pumps — class C), IS 11346 (centrifugal monoset pumps for clear cold water, agricultural duty), IS 8034 (submersible pump sets), IS 6595 (horizontal centrifugal pumps for clear cold water); refinery and petrochemical duties are specified to API 610 (centrifugal), API 674 (reciprocating) and API 676 (rotary).
• Energy and efficiency: the Bureau of Energy Efficiency (under the Energy Conservation Act, 2001 as amended) runs star labelling for agricultural and monoblock pump sets, and mandatory energy audits for designated consumers — pumping is often 20–30% of a plant's electricity bill, so VFDs and right-sizing are standard energy-audit recommendations.
• Safety and statutory: process plant piping and rotating equipment fall under the Occupational Safety, Health and Working Conditions Code, 2020 (in force from 21 November 2025, replacing the Factories Act, 1948), plus the Static and Mobile Pressure Vessels (Unfired) Rules for LPG/pressure service and the Petroleum Rules for hydrocarbon transfer. Hazardous-service pumps need seal-less or double-seal design under MSIHC/chemical accident rules.

Key points

• Continuity - mass in = mass out; for liquids, velocity rises as area falls (u ∝ 1/D²).
• Bernoulli - pressure, velocity and elevation heads interchange; valid only without friction or work.
• Reynolds number - Re = ρuD/μ; laminar below 2,100, turbulent above 4,000 in pipes.
• Darcy-Weisbach - h_f = f(L/D)(u²/2g); friction head loss, with f from Re and ε/D.
• Fanning vs Darcy f - f_Darcy = 4 f_Fanning; mixing them gives a 4× error.
• Hagen-Poiseuille - laminar Δp = 32μLu/D²; Q ∝ D⁴, so halving diameter cuts flow 16-fold.
• Minor losses - fittings expressed as K(u²/2g) or equivalent pipe length L_e.
• Turbulent profile is flat - u_max ≈ 1.2 u_avg against 2.0 u_avg for laminar.
• Pump head is pressure-independent of fluid - a centrifugal pump develops the same head in metres for any liquid, but pressure and power scale with density.
• Operating point - intersection of pump curve and system curve; good selection puts it near BEP.
• NPSHa ≥ NPSHr + margin - otherwise cavitation; NPSHa is site, NPSHr is pump.
• Affinity laws - Q ∝ N, H ∝ N², P ∝ N³ for a centrifugal pump at constant diameter.
• PD pumps give constant flow - head is set by the system; a blocked discharge needs a relief valve.
• Series adds head, parallel adds flow - and parallel pumps each deliver less than their solo flow.
• Orifice vs venturi - orifice is cheap with high permanent loss; venturi is costly with low loss and higher C_d.
• Specific speed Ns - classifies impellers: low → radial (high head), high → axial (high flow).
• Water hammer - Δp = ρaΔu; close valves slowly and use surge protection.
• Codes - process piping to ASME B31.3; pumps to API 610 or the relevant IS; BEE star labels for pump sets.

Formulas and examples

Example 1 — Regime, friction loss and pump power for a water line Water (ρ = 1,000 kg/m³, μ = 1×10⁻³ Pa·s) flows at 20 m³/h through 150 m of 50 mm internal-diameter commercial steel pipe (ε = 0.045 mm), with 6 elbows (K = 0.75 each) and 2 gate valves (K = 0.17 each). Pump efficiency 70%, motor efficiency 92%. Static lift 12 m, both ends open to atmosphere.

1. Q = 20/3,600 = 5.556×10⁻³ m³/s. A = π(0.05)²/4 = 1.963×10⁻³ m². u = 5.556×10⁻³/1.963×10⁻³ = 2.83 m/s (within 1.5–3 m/s design range).
2. Re = 1,000 × 2.83 × 0.05 / 1×10⁻³ = 1.42×10⁵ → turbulent.
3. ε/D = 0.045/50 = 0.0009. Moody chart gives f ≈ 0.0215.
4. u²/2g = 2.83²/(2×9.81) = 8.01/19.62 = 0.408 m.
5. Straight pipe: h_f = 0.0215 × (150/0.05) × 0.408 = 0.0215 × 3,000 × 0.408 = 26.3 m.
6. Fittings: ΣK = 6(0.75) + 2(0.17) = 4.84 → h = 4.84 × 0.408 = 1.98 m.
7. Total head H = 12 + 26.3 + 1.98 = 40.3 m.
8. Hydraulic power = 1,000 × 9.81 × 5.556×10⁻³ × 40.3 = 2,196 W ≈ 2.20 kW.
9. Shaft power = 2.20/0.70 = 3.14 kW; motor input = 3.14/0.92 = 3.41 kW → select a 3.7 kW (5 HP) motor.
10. Annual energy at 8,000 h and ₹8/kWh: 3.41 × 8,000 × 8 = ₹2.18 lakh/year — which is why pipe size and efficiency matter.

Example 2 — Laminar flow of a viscous oil Oil (ρ = 900 kg/m³, μ = 0.4 Pa·s) flows at 0.5 m/s in a 40 mm pipe, 60 m long.

1. Re = 900 × 0.5 × 0.04 / 0.4 = 45 → strongly laminar.
2. f = 64/45 = 1.422.
3. u²/2g = 0.25/19.62 = 0.01274 m.
4. h_f = 1.422 × (60/0.04) × 0.01274 = 1.422 × 1,500 × 0.01274 = 27.2 m of oil.
5. Check with Hagen-Poiseuille: Δp = 32 × 0.4 × 60 × 0.5 / 0.04² = 384/0.0016 = 2.40×10⁵ Pa; as head = 2.40×10⁵/(900 × 9.81) = 27.2 m — agrees.
6. Centreline velocity = 2 × 0.5 = 1.0 m/s; a pitot at the axis would read twice the mean.

Example 3 — NPSH check on a hot-water pump Water at 80 °C (p_vap = 47.4 kPa, ρ = 972 kg/m³) is drawn from an atmospheric tank (101.3 kPa) whose level is 2.0 m above the pump centreline. Suction friction loss is 0.8 m. The pump's NPSHr at duty is 3.5 m.

1. (p_s − p_v)/ρg = (101,300 − 47,400)/(972 × 9.81) = 53,900/9,535 = 5.65 m.
2. NPSHa = 5.65 + 2.0 − 0.8 = 6.85 m.
3. Margin = 6.85 − 3.5 = 3.35 m → safe.
4. If the same water were at 100 °C (p_vap = 101.3 kPa), the pressure term becomes zero and NPSHa = 0 + 2.0 − 0.8 = 1.2 m < 3.5 m → the pump would cavitate; raise the tank or choose a low-NPSHr pump.

Example 4 — Affinity laws and VFD saving A pump delivers 100 m³/h at 50 m head drawing 20 kW at 1,450 rpm. Demand falls to 80 m³/h.

1. Speed needed: N₂ = 1,450 × (80/100) = 1,160 rpm.
2. New head = 50 × (1,160/1,450)² = 50 × 0.64 = 32 m.
3. New power = 20 × (0.8)³ = 20 × 0.512 = 10.24 kW → saving 9.76 kW.
4. By throttling instead, head would stay near 50 m plus valve loss and power would fall only to about 17–18 kW — the VFD saves roughly 7–8 kW, about ₹4.7 lakh/year at 8,000 h and ₹8/kWh (taking a 7.3 kW average saving). Note the affinity laws assume a purely frictional system curve; with static head the saving is smaller.

Example 5 — Orifice meter An orifice (d₂ = 30 mm) in a 60 mm pipe carries water (ρ = 1,000 kg/m³); manometer Δp = 25 kPa; C_d = 0.61.

1. β = 30/60 = 0.5; β⁴ = 0.0625; 1 − β⁴ = 0.9375.
2. A₂ = π(0.03)²/4 = 7.069×10⁻⁴ m².
3. 2Δp/(ρ(1−β⁴)) = 50,000/937.5 = 53.33 → √ = 7.303 m/s.
4. Q = 0.61 × 7.069×10⁻⁴ × 7.303 = 3.149×10⁻³ m³/s = 11.3 m³/h.
5. A venturi of the same bore and Δp with C_d = 0.98 would read 0.98/0.61 = 1.61× this flow, i.e. 18.2 m³/h — the C_d difference reflects the vena contracta and losses in the orifice.

Where it is used

• Refineries and petrochemicals (Reliance Jamnagar, IOCL Panipat, HPCL, BPCL): crude transfer, reflux and bottoms pumps to API 610, hot hydrocarbon NPSH design, pipeline hydraulics to ASME B31.4 and PNGRB standards.
• Water and effluent utilities: municipal water supply (Jal Jeevan Mission schemes), ETP/STP and ZLD plants — pump-and-pipe network design, vertical turbine and submersible pumps, surge protection on long rising mains.
• Fertiliser, chemical and agrochemical plants (IFFCO, Coromandel, UPL, Aarti, Tata Chemicals): slurry and acid pumping with magnetic-drive or lined pumps, metering pumps for dosing, Coriolis meters for mass balance.
• Pharma and food processing (Sun Pharma, Cipla, Amul, Nestlé India): sanitary centrifugal and lobe pumps, diaphragm valves, CIP circulation loop hydraulics, GMP-compliant dead-leg-free piping.
• Pump and equipment manufacturers (Kirloskar Brothers, KSB India, Grundfos India, WPIL, Thermax): application engineering, curve selection, hydraulic testing to IS 9137/IS 11346, energy-efficient star-rated pump sets.
• Job roles: process/piping engineer (line sizing, hydraulic calculations, P&IDs), rotating-equipment engineer, maintenance and reliability engineer (vibration, seals, cavitation diagnosis), energy auditor (BEE-certified pump system optimisation).

Interview questions

• Q: Why does a centrifugal pump develop the same head for water and for a liquid of twice the density? A: The impeller imparts velocity, and head in metres depends on u²/g, not density; but discharge pressure and power both double because they are proportional to ρ.
• Q: What is cavitation and how do you detect it in the field? A: Vapour bubbles form at the impeller eye when local pressure drops to vapour pressure and collapse downstream; signs are crackling noise, vibration, fluctuating discharge pressure, lost head and pitted impeller vanes.
• Q: How do you increase NPSHa without changing the pump? A: Raise the suction vessel level, lower the pump, shorten or enlarge the suction line with fewer fittings, cool the liquid, or reduce the flow rate.
• Q: Why must you never throttle the discharge of a positive displacement pump? A: It displaces a fixed volume per stroke, so the pressure keeps rising until the pump, casing or piping fails — a relief valve back to suction is mandatory.
• Q: Two identical pumps are put in parallel — do you get double the flow? A: No. The combined flow is where the doubled pump curve meets the system curve; since the system curve rises as Q², total flow is typically 1.3–1.8 times single-pump flow.
• Q: What is the difference between the Darcy and Fanning friction factors? A: f_Darcy = 4 f_Fanning; Darcy is used with h_f = f(L/D)(u²/2g) and Fanning with h_f = 4f(L/D)(u²/2g) — using the wrong one gives a 4× error.
• Q: Is pressure drop proportional to flow or to flow squared? A: Proportional to u in laminar flow (Hagen-Poiseuille) and roughly to u^1.8–2 in turbulent flow; most plant lines behave as Δp ∝ Q².
• Q: Why does roughness not matter in laminar flow? A: Roughness peaks are buried inside the thick viscous layer and the loss is set entirely by viscous shear, so f = 64/Re regardless of ε.
• Q: Where would you use a venturimeter instead of an orifice plate? A: When permanent pressure loss must be low (large water mains, long pumping costs) or the fluid carries solids that would erode or block an orifice.
• Q: What does the best efficiency point mean in selection, and what happens far from it? A: It is the flow at which the pump is most efficient and hydraulically stable; running far right raises NPSHr and power, far left causes recirculation, vibration, overheating and shaft deflection.
• Q: A pump is running but delivering no flow — what do you check? A: Loss of prime or air lock, closed or blocked suction valve, clogged strainer, wrong rotation direction, suction lift exceeding NPSHa, or vapour-locking of a hot liquid.
• Q: How does a VFD save energy compared with a control valve? A: A VFD lowers speed so power falls roughly as the cube of flow, while a valve dissipates the excess head as throttling loss with the pump still near full power.

Common mistakes

• Mixing Fanning and Darcy friction factors, or quoting f = 16/Re with the Darcy form of the equation.
• Treating pump head as the static lift only, forgetting friction, fittings and the pressure difference between vessels.
• Applying Bernoulli to a real pipe without the friction term, or across a pump without the work term.
• Unit slips: cP instead of Pa·s, mm instead of m in D, kPa instead of Pa, m³/h instead of m³/s — the single commonest source of wrong answers.
• Using u_avg where the question asks for maximum (centreline) velocity in laminar flow, or forgetting α = 2 in the laminar energy balance.
• Confusing NPSHr (pump data) with NPSHa (installation), or forgetting that z is negative for a suction lift.
• Assuming the affinity laws hold for a system with a large static head, or using them across impeller diameter changes without correction.

Related topics

Dimensional analysis and similitude · Flow through packed and fluidised beds · Fluid machinery: turbines, fans and compressors · Heat transfer in process equipment · Process instrumentation and control valves · Piping design and plant utilities