🔧 Energy Losses in Pipes
A virtual re-creation of the pipe-friction experiment. Run the low-flow part on the water manometers and the high-flow part on the differential pressure gauge, measure discharge by timed collection, and determine the Darcy–Weisbach friction factor across laminar, transitional and turbulent regimes.
Objective
To investigate head loss due to friction in a pipe, and to determine the associated friction factor under a range of flow rates and flow regimes — laminar, transitional, and turbulent.
Theory
Applying the energy equation to a horizontal pipe of uniform section, the head loss between two tappings is proportional to the measured pressure difference. The Darcy–Weisbach equation relates it to the flow:
hL = f·(L/D)·(v²/2g) • laminar: f = 64/Re • turbulent (smooth, Blasius): f = 0.316/Re0.25 • Re = vD/ν • v = Q/A • 1 bar ≡ 10.2 m water
For laminar flow (Re < ~2300) f depends only on Re; for turbulent flow it depends on Re and pipe roughness (Moody chart). In the transitional band (~2300–4000) no reliable formula exists. Viscosity ν falls as the water warms, so temperature changes Re at the same flow rate — sometimes enough to change the regime.
Apparatus
Hydraulics bench; pipe-friction apparatus (vertical test pipe with two pressure tappings, constant-head tank, flow-control valve, air-bleed valve); water manometers (low flows) and differential pressure gauge (high flows); stopwatch, measuring cylinder, thermometer. Test pipe: L = 0.50 m, D = 3.0 mm (smooth)
Procedure — perform it here
Observations & Computations
L = 0.50 m, D = 3.0 mm, A = 7.07×10⁻⁶ m². Take ~8 low-flow readings (lowest hL ≈ 30 mm) and ~10 high-flow readings at increasing valve openings. fexp = hL·2gD/(L·v²); fth = 64/Re (laminar) or 0.316/Re0.25 (turbulent).
| No. | Part | T (°C) | Vol (mL) | t (s) | Q (mL/s) | v (m/s) | hL (mm) | Re | fexp | fth | Regime |
|---|---|---|---|---|---|---|---|---|---|---|---|
| No observations yet — run a timed collection, then press “Record reading”. | |||||||||||
Friction factor vs Reynolds number (log–log)
Your recorded points plotted against the laminar line f = 64/Re and the Blasius smooth-pipe curve — the same graph your report asks for. The shaded band is the transitional zone.
Report Questions & Precautions
What is the critical Reynolds number in this experiment?
The transition from laminar to turbulent flow occurs around Re ≈ 2300 for pipe flow. On the f–Re plot it shows as the departure of the data from the 64/Re line; fully turbulent behaviour is established beyond Re ≈ 4000.
How does head loss depend on velocity in each regime?
Laminar: f = 64/Re makes hL ∝ v (linear). Turbulent (Blasius): f ∝ Re−0.25 makes hL ∝ v1.75; for fully rough pipes it approaches v². A log-log plot of hL vs v reveals these slopes directly.
What is the significance of temperature to the head loss?
Viscosity drops sharply as water warms (ν ≈ 1.31×10⁻⁶ m²/s at 10 °C → 0.66×10⁻⁶ at 40 °C), raising Re at the same discharge. In the laminar range this lowers f and thus hL; it can also push the flow across the transition. Always record the water temperature.
Why might results disagree with the Moody diagram?
Experimental errors in timed collection and manometer reading, entrapped air, temperature drift, entrance/exit development lengths, and the finite spacing of tappings all scatter f. Aging, scaling, corrosion and biological growth roughen real pipes over time, moving them off the smooth-pipe curve.
Precautions: purge all air from the manometer and gauge connections before reading; take the zero-flow gauge reading; keep the collection time long enough for an accurate volume; measure water temperature with every set.