Problem statement and knowns/unknowns
It provides a compact pipeline for fluid checks in internal flow systems where pressure-loss and head-availability questions drive design decisions.
- Calculate flow velocity and Reynolds number from fluid and pipe inputs.
- Estimate Darcy friction factor and line pressure drop.
- Evaluate head balance and rough pump power requirement.
Recommended workflow
Update property and geometry rows first. Then inspect `Re`, `f`, and `dp` before using the Bernoulli rows to understand remaining head margin.
Assumptions, validity limits, and unit discipline
- The default rows assume steady, single-phase, incompressible internal flow in a full pipe.
- Swamee-Jain is intended for turbulent flow. Treat it as valid when `Re` is above roughly 5000 and relative roughness `eps/D` is in normal engineering ranges.
- For laminar flow use `f=64/Re`; for transition (`Re` about 2300 to 4000), friction-factor estimates are uncertainty-sensitive.
- Use consistent SI units: `rho` in kg/m^3, `mu` in Pa*s, `D` and `L` in m, `Q` in m^3/s, pressure in Pa.
Derivation and governing equations
Re = rho*v*D/mu
DeltaP = f*(L/D)*(rho*v^2/2)
hf = DeltaP/(rho*g)FAQ
Is this valid for compressible gas flow?
This starter assumes incompressible behavior. For compressible flows, replace the pressure-drop model with a suitable gas-flow relation.
Can I add minor losses?
Yes. Add a `K_total*(rho*v^2/2)` term to pressure-drop rows for fittings and bends.
Worked example (interpreted)
Step 1: Baseline inputs produce Re=190,224 (clearly turbulent for this line).
Step 2: Turbulent branch gives f=0.01934, dp=28.87 kPa, and hf=2.949 m.
Step 3: Bernoulli check gives head_loss_balance≈0, confirming internal consistency.
Interpretation: line losses dominate but are internally consistent. Minor-loss rows then raise total pressure-drop and pump-power estimates for realistic fittings.
When this model is invalid
| Condition | Why invalid | Use instead |
|---|---|---|
| Laminar or transition regime | Swamee-Jain is a turbulent relation. | Use laminar row f_lam=64/Re or transition-appropriate correlation. |
| Compressible/high-Mach flow | Incompressible Bernoulli assumptions fail. | Compressible-flow energy equation with property variation. |
| Minor losses dominate | Major-loss-only model underpredicts total drop. | Use K_total and dp_total branch rows. |
How to validate your worksheet
Re_lam_marginandRe_turb_marginshow regime distance from boundaries.head_loss_balanceshould be near zero.invalidity_proxy=4000-Repositive means turbulent Swamee-Jain assumptions are not safe.
Domain-specific variants in this template
The worksheet includes laminar branch rows plus minor-loss sensitivity rows so you can compare model families inside one notebook.
Practice problems (with answer outlines)
Practice 1
Reduce flow rate until transition regime and compare friction branches.
Outline: Recompute Re; use both laminar and turbulent relations to quantify model divergence.
Practice 2
Increase K_total and report new dp_total and pump power.
Outline: Evaluate incremental minor-loss term then propagate to total pressure and power rows.
References and standards
- White, Fluid Mechanics (foundational derivations). Book page.
- ASME MFC standards for flow measurement context. ASME MFC-3M.
- Crane TP-410 (practical friction/minor-loss design data). Reference site.