Pressure loss
Explore how pipe diameter and length affect frictional pressure loss. Real exhaust systems also require loss models for bends and aftertreatment devices.
- 홈
- Calculators
Calculators
Calculators
CFD Lab
Model notesFlow conditions
Straight circular pipe
0.0200.080 kg/s
200700 °C
50100 mm
0.52.0 m
Pipe flow
Mean velocity 29.0 m/s Cross-section average
Illustrative mean flow only. Particle motion and pipe geometry are not to scale.
- Mean velocity
- — m/s
- Friction loss
- — kPa
- Reynolds number
- —
- Mach number
- —
Axial pressure profile
Pressure relative to outlet · kPa —
Inlet 0 m Outlet 1.2 m · 0 kPa
Temperature effects
At fixed mass flow rate and pressure, higher gas temperature reduces density and increases mean velocity. Temperature-dependent viscosity also affects pressure loss.
Validation
Detailed studies consider pulsating flow, heat transfer, turbulence and species transport. Mesh independence and comparisons with pressure and temperature measurements support model validation.
Model, assumptions and references
This educational model does not represent engine measurements or laboratory test results. It assumes fully developed, steady turbulent flow in a smooth, straight circular pipe. Exhaust gas is approximated using air properties, with uniform temperature and density at a reference absolute pressure of 101,325 Pa.
ρ = p / (RT) · A = πD² / 4 · U = ṁ / (ρA)
Re = ρUD / μ · f = 0.3164 / Re0.25
Δp = f (L/D) ρU² / 2 · Ma = U / √(γRT)
Re = ρUD / μ · f = 0.3164 / Re0.25
Δp = f (L/D) ρU² / 2 · Ma = U / √(γRT)
R = 287.05 J/(kg·K) and γ = 1.4. Sutherland’s law gives μ = 1.716×10⁻⁵ (T/273.15)1.5 (273.15+110.4)/(T+110.4) Pa·s. T is in K; D and L are in m. The Blasius correlation gives the Darcy friction factor f. The pressure profile is p(x) − pout = Δp(1 − x/L).
The model excludes pulsation, compressibility-induced density changes, entrance effects, wall heat transfer, bends, catalysts, filters and reactions. Results are straight-pipe friction estimates, not total engine backpressure or three-dimensional CFD predictions.
References: NASA · Equation of State / NASA · Reynolds Number / MCEER · Pipe Friction Models (PDF)