Precision-Bore Capillary Tube & Water Jacket
Calibrated borosilicate glass capillary of uniform internal radius r = 0.250 ± 0.001 mm and length L = 15.00 ± 0.02 cm encased in an optical circulating water jacket.
Chemistry / Poiseuille Capillary Viscosity
FREE TO EXPLORELABORATORY 08 · NATURAL SCIENCES
Determination of Dynamic Viscosity via Poiseuille Capillary Flow and Hydrostatic Head
Determine the absolute dynamic viscosity of ultra-pure water at 20.0 °C by verifying the Hagen-Poiseuille law of laminar capillary flow across systematic hydrostatic pressure gradients, demonstrating Reynolds number laminar stability, and extracting dynamic viscosity using ordinary least-squares regression. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
VOLUMETRIC CAPILLARY FLOW RATE Q—
MEASUREMENT STATUS
Ready to dispense 20.0 cm of liquid.
Adjust hydrostatic head V, then weigh the dispensed aliquot.
Mass observations are determined by the high-precision thermodynamic equation of state for pure liquid water. Readings reflect thermal equilibrium and analytical balance force restoration.
Physical chemistry assumptions and metrological limits
The determination of absolute dynamic viscosity via Poiseuille capillary flow is subject to specific experimental constraints: (1) Capillary Radius Fourth-Power Sensitivity: Because volumetric flow rate scales with r⁴, microscopic manufacturing variations or slight non-circular ellipticity in capillary bore diameter represent the primary source of systematic instrumental uncertainty. (2) End-Effect Kinetic Perturbations: At the entrance and exit of the capillary, fluid streamlines accelerate and decelerate, dissipating kinetic energy; while the high aspect ratio (L/r = 600) minimizes Couette end-effects, a slight residual pressure loss (<0.2%) persists. (3) Surface Dust Occlusion: Airborne particulate matter or dust fibers settling in the feed reservoir can lodge in the 0.25 mm capillary entrance, partially obstructing flow. (4) Meniscus Curvature at Discharge: Surface tension forces at the capillary outlet orifice create a slight capillary backpressure that must be minimized by submerged delivery or consistent drop detachment. The Poiseuille capillary flow model incorporates the hydrodynamic relation Q = [ (π · r⁴ · ρ · g · 10⁴ · 60) / (8 · L · η) ] · Δh, where Q is in mL/min and Δh is in cm. Calibrated apparatus parameters: capillary radius r = 0.000250 m (0.250 mm), length L = 0.150 m (15.00 cm), water density ρ = 998.2 kg/m³ at 20.0 °C, and standard gravity g = 9.80665 m/s². The geometric constant is K_geom = (π · r⁴ · ρ · g · 10⁴ · 60) / (8 · L) = 6.006263 × 10⁻⁵. Inserting the CIPM reference viscosity of water η = 0.0010020 Pa·s (1.0020 mPa·s) yields the theoretical slope m_slope = K_geom / η = 0.0599427 mL/(min·cm). The Reynolds number Re = (2 · r · v · ρ) / η ranges from 25.3 at Δh = 10.0 cm to 88.7 at Δh = 35.0 cm, confirming that flow remains well below the critical laminar threshold (Re_crit ≈ 2000). Linear regression across six hydrostatic increments absorbs any slight discharge meniscus resistance or cathetometer zero-offset into the intercept Q₀ = 0.000 mL/min, insulating the dynamic viscosity calculation against baseline delivery artifacts.
Analytical chemistry apparatus & tools.
Constant-Head Overflow Reservoir & Cathetometer
Heavy borosilicate reservoir with an adjustable overflow weir and precision vernier cathetometer to establish and measure stable hydrostatic heads from 10.0 to 35.0 cm.
Circulating Thermostatic Water Bath
Refrigerated/heating bath circulator maintaining the jacketed capillary and feed water at 20.0 ± 0.05 °C monitored by a four-wire calibrated platinum RTD sensor.
Class A Calibrated Micro-Burette & Receiving Vessel
10.00 mL receiving burette with 0.01 mL graduation markings to collect and measure effluent discharge volume with ±0.005 mL volumetric reading accuracy.
Digital Precision Quartz Chronometer
Laboratory stopwatch with 0.01 s time resolution to record timed collection intervals (300.0 s) for flow rate determination.
Chromic-Sulfuric Acid Wash Station & Vacuum Line
Acid cleaning apparatus to thoroughly degrease capillary inner walls and remove particulate matter before measurement, guaranteeing a no-slip hydrophilic glass boundary.
FOLLOW THE METHOD
A reason behind every step.
Determine the absolute dynamic viscosity of ultra-pure water at 20.0 °C by verifying the Hagen-Poiseuille law of laminar capillary flow across systematic hydrostatic pressure gradients, demonstrating Reynolds number laminar stability, and extracting dynamic viscosity using ordinary least-squares regression. Suggested independent volumetric settings: 10.0, 15.0, 20.0, 25.0, 30.0, 35.0 cm.
01
Capillary Cleaning and Degreasing
Flush the precision capillary tube sequentially with warm chromic-sulfuric acid cleaning solution, copious amounts of deionized water, absolute ethanol, and filtered dry air to ensure an immaculate, fully hydrophilic glass surface free of dust or grease films.
02
Thermostatic Temperature Equilibration
Mount the capillary horizontally inside the water jacket and connect the circulating bath set to 20.0 °C. Circulate deionized water through the system for 15 minutes to guarantee thermal equilibrium, verified by an immersion thermometer.
03
Hydrostatic Head Adjustment
Adjust the vertical height of the overflow weir to establish the lowest experimental pressure head (Δh = 10.0 cm), measured relative to the capillary centerline using a vernier cathetometer. Ensure continuous overflow to maintain an invariant liquid meniscus.
04
Capillary Flow Initiation and Bubble Purging
Open the feed stopcock, allow fluid to establish steady laminar flow through the capillary, and inspect the capillary bore under backlighting to verify complete absence of trapped microscopic air bubbles.
05
Timed Volumetric Effluent Collection
Place a dry, tared receiving vessel under the capillary outlet and simultaneously start the digital timer. Collect effluent for exactly 300.0 seconds (5.00 minutes), record the delivered volume V to ±0.005 mL, and calculate the volumetric flow rate Q = V/t in mL/min.
06
Multi-Head Systematic Flow Series and Regression
Increase the hydrostatic head in 5.0 cm increments up to 35.0 cm, recording flow rates across all six settings. Fit the flow rate against head via ordinary least-squares regression to extract absolute dynamic viscosity η and evaluate laminar Poiseuille linearity.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into quantitative chemical insight.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
ORDINARY LEAST-SQUARES FIT · m = ρ·V + m₀
Q = [π·r⁴·ρ·g / (8·η·L)] · Δh + Q₀ ==> Q = 0.05994 · Δh
| # | Hydrostatic pressure head Δh (cm) (cm) | Volumetric capillary flow rate Q (mL/min) | Hydrostatic pressure head Δh (cm) | Volumetric flow rate Q (mL/min) | Remove |
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