Coupled Dual-Tank Acrylic Process Rig
Two matched vertical cylinders (22.56 cm ID, A = 400.0 cm^2 each) connected by an inter-tank flow line with isolation valve.
Chemical & Process Engineering / Two-Tank Interacting Dynamics
FREE TO EXPLORELABORATORY 41 · CHEMICAL & PROCESS ENGINEERING
Interacting vs Non-Interacting Two-Tank Liquid Level Dynamics & Coupled State-Space Modeling
Operate a two-tank interacting liquid level system with inter-tank flow coupling, apply step perturbations in primary tank feed flow ΔF_1 from 1.0 to 6.0 L/min, monitor coupled liquid level responses h_1(t) and h_2(t), evaluate second-order overdamped dynamics, and determine the steady-state interacting process gain K_p. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
TANK 2 STEADY LEVEL DEVIATION ΔH_2—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Feed Perturbation ΔF_1 = 3.0 L/min.
Adjust Feed Perturbation ΔF_1, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (1.0 to 6.0 L/min). Evaluated using an instrumented dual acrylic column process rig (A_1 = A_2 = 400.0 cm^2 = 0.0400 m^2) with inter-tank laminar capillary valve and final laminar discharge tube. Independent piezoresistive pressure level transmitters (±0.05 cm) on both vessels.
Process apparatus & industrial sensors.
Inter-Tank Laminar Capillary Restriction Valve (R_1)
Provides bidirectional linear laminar flow coupling F_12 = (h_1 - h_2) / R_1 without turbulent swirling.
Tank 2 Linear Capillary Discharge Resistor (R_2)
Discharges Tank 2 effluent to the sump with calibrated linear hydraulic resistance R_2 = 4.2500 cm/(L/min).
Dual Piezoresistive Bottom-Mounted Level Transmitters
Continuously measures hydrostatic pressures at Tank 1 and Tank 2 base with 0.02 cm level accuracy.
Servo-Controlled Inflow Feed Metering Pump
Delivers calibrated step changes in feed flow rate ΔF_1 from 1.0 to 6.0 L/min into Tank 1.
High-Speed Real-Time Data Acquisition (DAQ) Interface
Samples h_1(t), h_2(t), and feed flow F_1(t) simultaneously at 10 Hz for coupled dynamic parameter extraction.
FOLLOW THE METHOD
A reason behind every step.
Operate a two-tank interacting liquid level system with inter-tank flow coupling, apply step perturbations in primary tank feed flow ΔF_1 from 1.0 to 6.0 L/min, monitor coupled liquid level responses h_1(t) and h_2(t), evaluate second-order overdamped dynamics, and determine the steady-state interacting process gain K_p. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 L/min.
01
Level Transmitters Hydrostatic Zeroing
Fill both tanks with water; drain completely to baseline; calibrate piezoresistive transmitter zeroes to bottom datum.
02
Interacting Valve Configuration
Open inter-tank coupling valve R_1 completely; verify submerged liquid connection between tanks to enforce interacting mode.
03
Initial Baseline Steady-State Stabilization
Establish baseline feed flow F_1 = 3.0 L/min; allow levels h_1 and h_2 to stabilize at steady state for 10 minutes.
04
Positive Step Perturbation Protocol (ΔF_1 = 1.0 L/min)
Apply step increase ΔF_1 = 1.0 L/min (F_1 = 4.0 L/min); record dynamic trajectories h_1(t) and h_2(t) at 2 Hz until new steady state.
05
Step Flow Progression Across Perturbations
Step feed perturbations through ΔF_1 = 2.0, 3.0, 4.0, 5.0, and 6.0 L/min, recording S-shaped second-order step responses for each plateau.
06
Coupled Process Gain Linear Regression
Evaluate steady level deviations Δh_2; plot Δh_2 versus ΔF_1 and perform linear regression to determine interacting process gain K_p.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Two-Tank Interacting Dynamics mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
Δh_2 = K_p · ΔF_1 = 4.2500 · ΔF_1
| # | Tank 1 Flow Perturbation ΔF_1 (L/min) | Tank 2 Steady Level Deviation Δh_2 (cm) | Tank 1 feed perturbation ΔF_1 (L/min) | Tank 2 level deviation Δh_2 (cm) | Remove |
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Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
The transfer function of an interacting two-tank liquid level system G(s) = H_2'(s) / F_1'(s) is:
At steady state, the interacting process gain K_p = Δh_2 / ΔF_1 is equal to:
Compared to an identical non-interacting two-tank system, the step response of an interacting system is:
The initial slope of the Tank 2 liquid level response (dh_2/dt at t = 0) following a step change in Tank 1 inflow is:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Multi-capacity processes in chemical and process engineering—including multi-stage distillation columns, series heat exchangers, reactor cascades, and multi-compartment separators—exhibit complex dynamic responses resulting from hydraulic and thermodynamic coupling between individual stages. When two liquid storage tanks are connected such that flow between them depends on the difference between both liquid levels, the system is classified as an interacting two-tank process. In an interacting configuration, influent enters Tank 1 (area A_1 = 400.0 cm^2), flowing into Tank 2 (area A_2 = 400.0 cm^2) through an inter-tank laminar restriction of resistance R_1. Because inter-tank flow is driven by the differential hydrostatic head: F_12 = (h_1 - h_2) / R_1, the liquid level in Tank 2 exerts a direct backpressure on Tank 1, coupling both mass balance differential equations: A_1 · (dh_1/dt) = F_1(t) - (h_1 - h_2)/R_1, and A_2 · (dh_2/dt) = (h_1 - h_2)/R_1 - h_2/R_2, where R_2 is the discharge resistance of Tank 2. Transforming these coupled equations into Laplace deviation variables yields the canonical second-order overdamped transfer function: G_2(s) = H_2'(s) / F_1'(s) = K_p / (τ_1 · τ_2 · s^2 + (τ_1 + τ_2 + A_1 · R_2) · s + 1), where individual capacities are τ_1 = A_1 · R_1 and τ_2 = A_2 · R_2. Crucially, the interaction cross-term A_1 · R_2 in the linear damping coefficient increases the effective time constants, making the interacting system more sluggish (higher damping ratio ζ > 1) than an equivalent non-interacting cascade where Tank 1 discharges freely into Tank 2 through an open air gap. However, at steady state (s -> 0), all time derivatives vanish, and mass conservation requires that total effluent from Tank 2 matches primary influent: F_out = h_2 / R_2 = F_1. Consequently, the steady-state process gain K_p = Δh_2 / ΔF_1 equals the final discharge resistance R_2 = 4.2500 cm/(L/min), completely independent of inter-tank resistance R_1. In this laboratory experiment, an instrumented dual-tank benchtop trainer operates under interacting mode across feed flow step changes from 1.0 to 6.0 L/min to evaluate transient S-shaped overdamped response curves and determine K_p = 4.2500 cm/(L/min).
Δh_2 = K_p · ΔF_1 = 4.2500 · ΔF_1
Evaluated using an instrumented dual acrylic column process rig (A_1 = A_2 = 400.0 cm^2 = 0.0400 m^2) with inter-tank laminar capillary valve and final laminar discharge tube. Independent piezoresistive pressure level transmitters (±0.05 cm) on both vessels.