Flow in Pipes - Cheat Sheet
Your last-minute companion for pipe flow calculations, regime identification, and head-loss quantification. Covers Reynolds number, Darcy-Weisbach, Manning, minor losses, and series/parallel networks.
Reynolds Number & Flow Regime
Formulas
Re = vD/ν = (ρvD)/μ
Meaning
v = velocity (m/s); D = pipe diameter (m); ν = kinematic viscosity (m²/s); ρ = density (kg/m³); μ = dynamic viscosity (Pa·s)
Watch out
Use kinematic viscosity (ν), not dynamic (μ). For water at 20°C: ν = 1×10⁻⁶ m²/s. Diameter MUST be in metres.
When to use
Always first — determines if flow is laminar, transitional, or turbulent.
f = 64/Re (laminar only)
Meaning
f = Darcy friction factor; Re = Reynolds number
Watch out
This is exact for laminar. Turbulent f comes from Moody chart (depends on Re AND relative roughness ε/D).
When to use
ONLY when Re < 2000 (laminar). Do NOT use for turbulent flow.
Common values
Value
1 × 10⁻⁶ m²/s
Symbol
ν
Quantity
Water kinematic viscosity at 20°C
Value
4 × 10⁻⁵ m²/s
Symbol
ν
Quantity
Oil kinematic viscosity at 20°C (typical)
Value
2000
Symbol
Re_crit
Quantity
Laminar/turbulent threshold (lower)
Value
4000
Symbol
Re_turbulent
Quantity
Turbulent threshold (upper)
Important facts
- Regime boundaries: Re < 2000 (laminar), 2000–4000 (transition), Re > 4000 (turbulent).
- Most engineering flows are turbulent (Re > 4000).
- Laminar friction factor is independent of roughness — depends ONLY on Re.
- Turbulent friction factor depends on both Re AND relative roughness ε/D.
- Relative roughness ε/D: ε = absolute roughness of pipe material (mm).
Key definitions
Laminar flow
Example
Oil flowing slowly through a small pipe; viscous forces dominate.
Smooth, orderly flow in parallel layers; Re < 2000; friction factor f = 64/Re.
Turbulent flow
Example
Water gushing from a tap; inertial forces dominate.
Chaotic, eddying flow with random velocity fluctuations; Re > 4000; f from Moody chart.
Transitional (critical zone)
Example
Flow regime unpredictable; do NOT design for this zone.
Unstable region between laminar and turbulent; 2000 < Re < 4000; avoid for design.
Kinematic viscosity
Example
Water at 20°C: ν = 1×10⁻⁶ m²/s; oil at 20°C: ν ≈ 4×10⁻⁵ m²/s.
Ratio of dynamic viscosity to density: ν = μ/ρ (m²/s); measure of fluid's resistance to motion.
Diagrams to know
- Moody chart: axes are Re (log scale, horizontal) and f (log scale, vertical); curves show laminar line, transition zone, and turbulent curves for different ε/D.
- Velocity profile: laminar (parabolic), turbulent (nearly flat with boundary layer).
Major Losses – Darcy-Weisbach Equation
Formulas
h_f = f(L/D)(v²/2g)
Meaning
h_f = head loss due to friction (m); f = Darcy friction factor (dimensionless); L = pipe length (m); D = pipe diameter (m); v = mean flow velocity (m/s); g = 9.81 m/s²
Watch out
f is NOT constant — it depends on Re (and roughness for turbulent). h_f ∝ v² so doubling velocity quadruples loss. L/D ratio is critical.
When to use
Always use for major (friction) losses in pipes. Works for any diameter, material, and regime.
Velocity v = Q/A = Q/(π D²/4)
Meaning
Q = discharge (m³/s); A = cross-sectional area (m²); D = diameter (m)
Watch out
Area = πD²/4, not πD. D must be in metres; result v is in m/s.
When to use
Convert discharge to velocity before calculating Re or head loss.
Common values
Value
9.81 m/s²
Symbol
g
Quantity
Gravity acceleration
Value
0.045 mm
Symbol
ε
Quantity
Steel pipe absolute roughness
Value
0.0015 mm
Symbol
ε
Quantity
PVC pipe absolute roughness
Value
0.3–3 mm (range)
Symbol
ε
Quantity
Concrete pipe absolute roughness
Important facts
- h_f is proportional to v² — doubling velocity quadruples the loss.
- h_f is proportional to L/D — longer pipes and smaller diameters increase loss dramatically.
- For laminar flow, f = 64/Re is exact; independent of pipe roughness.
- For turbulent flow, f depends on both Re and ε/D; use Moody chart or Colebrook-White equation.
- Velocity head = v²/(2g); with g = 9.81, v²/(2g) = 0.0510 v² (v in m/s).
Key definitions
Major loss
Example
h_f in 500 m of pipe typically >> minor losses from fittings.
Head loss due to friction between fluid and pipe wall over the pipe length; dominates long pipes.
Darcy friction factor (f)
Example
Laminar: f = 0.064 at Re = 1000. Turbulent: f ≈ 0.02–0.03 depending on Re and ε/D.
Dimensionless coefficient describing friction; = 64/Re (laminar) or from Moody chart (turbulent); accounts for roughness.
Relative roughness
Example
Steel: ε ≈ 0.045 mm; PVC: ε ≈ 0.0015 mm; concrete: ε ≈ 0.3–3 mm.
Ratio ε/D where ε = absolute roughness of pipe interior (mm); determines Moody chart position.
Diagrams to know
- Moody chart with laminar line, transition zone, and turbulent curves.
- Pipe friction loss vs. velocity (parabolic curve).
- Energy grade line (EGL) and hydraulic grade line (HGL) on a pipe profile.
Manning & Hazen-Williams Equations
Formulas
h_f = (6.35 n² L v²) / D^(4/3) [SI, full pipes]
Meaning
n = Manning's roughness coefficient; L = length (m); v = velocity (m/s); D = diameter (m); h_f = head loss (m)
Watch out
This is the SI form. Manning's n is dimensionless but NOT the same as friction factor f. Typical n: 0.009–0.015 for smooth pipes.
When to use
Alternative to Darcy-Weisbach; commonly used for full pipes and open channels in practice.
v = (1/n) R^(2/3) S^(1/2)
Meaning
R = hydraulic radius (m) = D/4 for full pipes; S = slope = h_f/L (dimensionless); v = velocity (m/s)
Watch out
For full circular pipes, R = D/4. S is the energy slope, NOT channel bed slope. h_f = S × L.
When to use
Manning's equation in standard form; rearrange to find v given slope, or slope given v.
v = 0.849 C R^(0.63) S^(0.54) [Hazen-Williams]
Meaning
C = roughness coefficient (dimensionless, 80–150 for water pipes); R = hydraulic radius (m); S = slope (dimensionless)
Watch out
C is NOT the same as Manning's n or Darcy's f. C range: 80–150; typical: C = 100–130 for steel/PVC. Only for water.
When to use
Hazen-Williams is popular for water distribution design; simpler than Darcy-Weisbach for practitioners.
Common values
Value
0.009–0.010
Symbol
n
Quantity
Manning's n – smooth pipes
Value
0.012–0.015
Symbol
n
Quantity
Manning's n – typical steel
Value
140
Symbol
C
Quantity
Hazen-Williams C – new steel
Value
80–90
Symbol
C
Quantity
Hazen-Williams C – old corroded
Important facts
- Manning is intuitive: v increases with R and slope, decreases with roughness n.
- Hazen-Williams is simpler empirically but less physically grounded than Darcy-Weisbach.
- All three (Darcy, Manning, Hazen-Williams) give the same h_f if coefficients are matched.
- Manning works for open channels AND full pipes; Darcy-Weisbach is more fundamental.
- Hazen-Williams is widely used in water supply design in the Philippines and USA.
Key definitions
Manning's roughness coefficient (n)
Example
Glazed concrete: n ≈ 0.010; old steel: n ≈ 0.015.
Empirical coefficient describing pipe/channel roughness; 0.009–0.013 (smooth) to 0.015–0.03 (rough).
Hazen-Williams coefficient (C)
Example
New steel: C = 140; old corroded steel: C = 80–90.
Empirical roughness coefficient for water; typically 80–150; higher C = smoother, lower loss.
Hydraulic radius (R)
Example
200 mm pipe: R = 0.05 m.
Cross-sectional area divided by wetted perimeter; for full circular pipe: R = D/4.
Diagrams to know
- Roughness coefficient comparisons: table of n values for different pipe materials.
- Manning vs. Darcy-Weisbach head-loss curves.
Minor Losses
Formulas
h_m = K (v²/2g)
Meaning
h_m = minor head loss (m); K = loss coefficient (dimensionless); v = velocity upstream of loss (m/s); g = 9.81 m/s²
Watch out
K depends on geometry and flow direction. Use velocity at the point of loss. K is usually given in tables; typical: 0.5–4.
When to use
Every fitting, bend, valve, entrance, exit, or transition. Sum all K values for total minor loss.
h_sudden_expansion = (v₁ - v₂)²/(2g)
Meaning
v₁ = velocity in smaller pipe (m/s); v₂ = velocity in larger pipe (m/s); h = head loss in expansion (m)
Watch out
This is a special formula; it's NOT K × v²/2g. Loss depends on VELOCITY DIFFERENCE, not absolute velocity.
When to use
Sudden pipe enlargement (no tapered transition); also equivalent to K = (1 - A₁/A₂)² / (A₂/A₁)².
Total head loss = h_f + Σh_m = h_f + K_total (v²/2g)
Meaning
Sum all friction losses and minor losses.
Watch out
h_f and h_m have different velocity references; use consistent v (usually the pipe velocity). If pipes differ in diameter, recalculate v for each section.
When to use
Final step: calculate total energy loss in the pipe system.
Common values
Value
0.5
Symbol
K
Quantity
Sharp entrance
Value
0.05–0.1
Symbol
K
Quantity
Rounded entrance (r/D = 0.1)
Value
0.9–1.0
Symbol
K
Quantity
90° elbow, smooth
Value
0.4–0.5
Symbol
K
Quantity
45° elbow
Value
1.0–1.5
Symbol
K
Quantity
Tee (perpendicular branch)
Value
0.2
Symbol
K
Quantity
Gate valve (open)
Value
4–6
Symbol
K
Quantity
Globe valve (open)
Value
1.0
Symbol
K
Quantity
Exit to atmosphere/tank
Important facts
- h_m ∝ v² — doubling velocity quadruples the minor loss.
- Minor losses are often NEGLIGIBLE in long pipes but significant in short, complex networks.
- K values are tabulated for common fittings; manufacturers provide data.
- Sharp entrance K = 0.5; rounded entrance K ≈ 0.05–0.2 (better design).
- Exit loss K = 1.0 means all the kinetic energy v²/2g is dissipated.
- Gradual transitions (diffusers, bends) have lower K than abrupt changes.
Key definitions
Minor loss (local loss)
Example
A 90° elbow with K = 0.9 in a 3 m/s flow loses 0.9 × 3²/(2×9.81) = 0.41 m.
Head loss due to fittings, bends, valves, entrances, exits, or diameter changes; proportional to velocity head v²/2g.
Loss coefficient (K)
Example
Sharp entrance K = 0.5, elbow K = 0.9, globe valve K = 4–6.
Dimensionless number relating minor loss to velocity head; depends on fitting type and geometry.
Entrance condition
Example
Pipe intake from a reservoir: rounded entrance K = 0.1; sharp intake K = 0.5.
Flow entry into pipe; sharp-edged (K = 0.5) or rounded (K ≈ 0.1–0.2).
Exit loss
Example
Pipe discharge into a tank: h_exit = 1.0 × v²/(2g) = v²/(2g).
Loss when flow leaves a pipe into a reservoir or atmosphere; K = 1.0 (all kinetic energy dissipated).
Diagrams to know
- Minor loss coefficients table: entrance types, elbows, valves, tees, exits.
- Energy loss at sudden expansion: velocity decrease and eddy formation.
- Velocity head recovery in diffuser vs. loss in sudden expansion.
Pipes in Series
Formulas
Q_in = Q₁ = Q₂ = Q₃ = ... (same discharge everywhere)
Meaning
Discharge is constant throughout series pipes.
Watch out
Velocity changes if diameter changes! v = Q/A, so if D decreases, v increases.
When to use
Always true for series pipes (continuity equation): what flows in must flow out.
h_L,total = h₁ + h₂ + h₃ + ... = Σ(h_f + h_m)_i
Meaning
Total head loss is the sum of friction losses and minor losses in each pipe segment.
Watch out
Each pipe may have different diameter, length, material, and friction factor. Calculate h_f and h_m separately for each, then sum.
When to use
Calculate total energy loss in a series pipe system.
Equivalent pipe: f_eq (L_eq/D_eq) (v²/2g) = Σ [f_i (L_i/D_i) (v_i²/2g)]
Meaning
A single 'equivalent' pipe can replace a series of pipes if it produces the same head loss.
Watch out
L_eq and D_eq are not simple sums; they depend on Q and the matching condition.
When to use
Simplify series networks for analysis; rarely needed in PRC exam but conceptually important.
Important facts
- Continuity: Q in = Q out everywhere; discharge never changes in series.
- Velocity changes if diameter changes: v = Q/A = Q/(πD²/4).
- Total head loss = sum of all individual h_f and h_m.
- If one pipe is much longer or rougher, its loss dominates.
- Series networks are easier to analyze than parallel because Q is known everywhere.
Key definitions
Series pipes
Example
100 m of 200 mm pipe followed by 50 m of 150 mm pipe: Q is same throughout, but v increases in the 150 mm section.
Pipes connected end-to-end such that the same discharge flows through each; head losses add.
Equivalent pipe
Example
Series of 2 pipes might be replaced by 1 equivalent pipe of length L_eq and diameter D_eq.
A single hypothetical pipe that produces the same head loss as a series combination for the same Q.
Diagrams to know
- Series pipe schematic: three pipes of different diameters, Q same in all, h_L adds.
- Energy grade line (EGL) profile: continuous drop through each pipe and fitting.
Pipes in Parallel
Formulas
h_L,1 = h_L,2 = h_L,3 = ... (same head loss across all branches)
Meaning
The pressure drop (head loss) is identical for each parallel branch.
Watch out
Discharges Q_i are different, but ALL branches experience the same h_L. This is NOT obvious.
When to use
Fundamental rule for parallel pipes: water 'chooses' path of least resistance but both end points have same elevation.
Q_in = Q₁ + Q₂ + Q₃ + ... (discharges add)
Meaning
Total discharge is the sum of discharges in each branch.
Watch out
Do NOT assume equal discharge in each branch unless diameters and lengths are equal.
When to use
Continuity for parallel branches; what flows in splits and recombines.
For two parallel pipes: Q₁/Q₂ = (h_L,2 / h_L,1)^n, where n ≈ 0.5–1 depending on regime
Meaning
Discharge ratio depends on head-loss ratio; for laminar n ≈ 1, turbulent n ≈ 0.5.
Watch out
This is approximate. For exact solution, set h_L,1 = h_L,2 and solve simultaneously.
When to use
Quick estimation of discharge split in parallel pipes (but solve h_L,1 = h_L,2 rigorously).
Important facts
- Parallel head losses are EQUAL, not discharges.
- Flow preferentially uses the lower-resistance path (larger diameter, shorter length).
- Total discharge is the sum: Q_total = Q₁ + Q₂ + ...
- For laminar parallel pipes: Q_i ∝ 1/L_i (inversely proportional to length if diameters equal).
- For turbulent parallel pipes: Q_i ∝ D_i^2.5 (stronger dependence on diameter).
Key definitions
Parallel pipes
Example
Water divides into two pipes at a junction and recombines downstream; both branches have same pressure drop.
Pipes connecting the same two points; same head loss across all branches, but discharges split.
Equivalent pipe for parallel
Meaning
Pipe of diameter D_eq and length L_eq such that h_L,eq = h_L,parallel at Q_total.
A single pipe that passes total Q with the same head loss as the parallel combination.
Diagrams to know
- Parallel pipe schematic: two branches from point A to point B, h_L same, Q different.
- Energy grade line: same drop across both branches despite different paths.
Reactions or equations
h_L = f₁(L₁/D₁)(v₁²/2g) = f₂(L₂/D₂)(v₂²/2g)
Note
This is the key equation for parallel pipe problems: equate h_L values and solve.
Conditions
Both branches have same h_L; set equal to find v₁ and v₂, then Q_i = v_i × A_i.
Pipe Networks & Hardy Cross Method
Formulas
Loop energy equation: Σ(h_L) = 0 (around any closed loop, net head loss = 0)
Meaning
The sum of head losses around a closed loop must be zero (energy conserved).
Watch out
Assign direction to flow and sign to h_L carefully: h_L positive if flow is in assumed loop direction, negative if opposite.
When to use
Setting up Hardy Cross iteration; write this equation for each loop in the network.
Continuity at node: Σ(Q_in) = Σ(Q_out)
Meaning
Discharge in equals discharge out at every junction.
Watch out
Every node must satisfy continuity; this gives one equation per node.
When to use
Writing equations for multiple junctions in a network.
Hardy Cross correction: ΔQ = -Σ(h_L) / [2Σ(h_L/Q)]
Meaning
ΔQ = correction to assumed flows in a loop; iterate until ΔQ → 0.
Watch out
This is an iterative algorithm: assume flows, calculate h_L, correct, repeat. Modern software is faster, but PRC may test the concept.
When to use
Solving multi-loop networks by successive approximation (hand calculation method).
Important facts
- Networks require BOTH loop energy equations AND node continuity equations.
- Number of independent loop equations = number of loops (meshes) in the network.
- Number of node continuity equations = (number of nodes) – 1.
- Hardy Cross is a hand-calculation method; today, computer software (EPANET, etc.) is standard.
- Convergence of Hardy Cross typically 3–5 iterations for simple networks.
- Sign convention: assume a loop direction (clockwise or counterclockwise); h_L is positive if flow matches assumed direction.
Key definitions
Pipe network
Example
Water distribution system in a city with multiple mains, branches, and loops.
System of interconnected pipes with multiple loops, junctions, and sources/sinks; requires simultaneous solution.
Loop (mesh)
Example
In a figure-8 network, there are two loops.
Closed path of pipes in a network; used to write energy equations.
Node (junction)
Example
Where a main splits into two branches.
Point where pipes meet; must satisfy continuity Q_in = Q_out.
Hardy Cross method
Example
Start with approximate flow distribution, calculate loop imbalances, correct, repeat until convergence.
Iterative algorithm for solving multi-loop networks by guessing flows, calculating corrections, and refining.
Diagrams to know
- Multi-loop network diagram with labeled pipes, nodes, and assumed flow directions.
- Hardy Cross iteration table: showing initial Q, calculated h_L, correction ΔQ, updated Q.
Must remember
- Reynolds number Re = vD/ν determines flow regime: Re < 2000 (laminar), 2000–4000 (transition), Re > 4000 (turbulent). For laminar, f = 64/Re exactly. For turbulent, f comes from Moody chart and depends on BOTH Re and relative roughness ε/D.
- Darcy-Weisbach h_f = f(L/D)(v²/2g) is the fundamental equation; valid for all flows. Major loss scales with v² — doubling velocity quadruples the loss. Always use consistent units: D in metres, v in m/s, h in metres.
- Minor losses h_m = K(v²/2g) depend on fitting geometry (K value). Sum all K values and multiply by velocity head v²/2g. Exit loss K = 1.0; sharp entrance K = 0.5; elbow K ≈ 0.9.
- Manning equation h_f = (6.35 n² L v²)/D^4/3 and Hazen-Williams v = 0.849 C R^0.63 S^0.54 are empirical alternatives; commonly used for water supply design in Philippines.
- In SERIES pipes, discharge is constant (Q same everywhere), but head losses ADD: h_L,total = h_1 + h_2 + ... Velocity changes if diameter changes.
- In PARALLEL pipes, head loss is constant (h_L same for all branches), but discharges ADD: Q_total = Q_1 + Q_2 + ... Set h_L,1 = h_L,2 to find discharge split.
- Moody chart: horizontal axis is log(Re), vertical axis is log(f), with curves for different ε/D. Laminar line f = 64/Re (straight). Turbulent curves depend on roughness.
- For water at 20°C: ν = 1×10⁻⁶ m²/s. For oil: ν ≈ 4×10⁻⁵ m²/s. These are essential for calculating Re.
- Hardy Cross method: assume initial flows, calculate loop imbalances, apply corrections ΔQ = −Σ(h_L)/[2Σ(h_L/Q)], iterate until convergence. Used for multi-loop networks.
- Total head loss = major loss (friction) + all minor losses. Don't forget entrance, bends, valves, and exit. h_m often significant in short, complex systems with many fittings.
Last minute tips
- Always start with Reynolds number: Re = vD/ν. This identifies the regime and whether you use f = 64/Re or Moody chart. Missing this is a common exam mistake.
- Check units rigorously: D must be in metres (not mm), v in m/s, L in m, ν in m²/s. Mixing cm or mm with m/s leads to wrong Re and wrong f — verify at the start.
- For pipes in series: Q is same everywhere, so calculate velocity for EACH pipe segment (v = Q/A). Diameter changes mean velocity changes — calculate h_f and h_m separately for each.
- For pipes in parallel: set h_L,1 = h_L,2 as your KEY equation. Solve this simultaneously with Q_1 + Q_2 = Q_total to find the discharge split. Don't assume equal Q in parallel branches.
- Common exam trap: confusing Manning's n, Hazen-Williams C, and Darcy's f. They are NOT the same. Know which equation to use: Darcy (all flows), Manning (full pipes & channels), Hazen-Williams (water supply).
Comparison tables
Flow Regime – Reynolds Number Thresholds
| Flow Type | Reynolds Number Range | Friction Factor f | Characteristics | Velocity Profile |
|---|---|---|---|---|
| Laminar | Re < 2000 | f = 64/Re (exact) | Smooth, orderly, parallel layers; viscous-dominated | Parabolic (maximum at center) |
| Transitional (Critical) | 2000 < Re < 4000 | Unstable; avoid for design | Unstable flow; mix of laminar & turbulent | Transitioning from parabolic to flat |
| Turbulent | Re > 4000 | From Moody chart (f vs Re, ε/D) | Chaotic, eddying; inertia-dominated | Nearly flat (logarithmic boundary layer) |
Head Loss Equations – When to Use
| Equation | Applies To | Friction Factor/Coefficient | Pros | Cons | Common in PRC? |
|---|---|---|---|---|---|
| Darcy-Weisbach: h_f = f(L/D)(v²/2g) | All pipes, any regime (laminar & turbulent) | f from Moody chart or Colebrook-White | Physically rigorous; works for all conditions | Requires Moody chart or iterative solver for f; more complex | YES – fundamental equation |
| Manning: h_f = (6.35 n² L v²)/D^4/3 | Full pipes & open channels | n = Manning's coefficient (0.009–0.03) | Intuitive; good for design practice; empirical | Not as theoretically rigorous; limited to full flow; less accurate for very high Re | YES – common in hydraulics |
| Hazen-Williams: v = 0.849 C R^0.63 S^0.54 | Water pipes (pressure & gravity lines) | C = coefficient (80–150) | Simpler than Darcy; widely used in industry | Empirical; only for water; less accurate for low Re or extreme conditions | YES – water supply design |
Minor Loss Coefficients (K values) – Common Fittings
| Component | Configuration | K Value | Notes |
|---|---|---|---|
| Entrance | Sharp-edged (abrupt) | 0.5 | Typical intake; minimum K ≈ 0.5 |
| Entrance | Rounded (r/D = 0.1) | 0.05–0.1 | Better design; much lower loss |
| Entrance | Bell-mouth (fully rounded) | 0.03–0.05 | Excellent; used in high-head systems |
| Elbow | 90° smooth | 0.9–1.0 | Standard long-radius elbow |
| Elbow | 45° smooth | 0.4–0.5 | Lower loss than 90° |
| Tee | Through (main line) | 0.6 | Straight flow through branch |
| Tee | Perpendicular (side exit) | 1.0–1.5 | Higher loss; flow deflection |
| Valve (fully open) | Gate (low K) | 0.2 | Minimal obstruction when open |
| Valve (fully open) | Check (one-way) | 0.5–1.0 | Prevents backflow; some loss |
| Valve (fully open) | Globe (high K) | 4–6 | More obstruction; throttling valve |
| Valve (fully open) | Butterfly (partial close) | 0.5–1.5 (or more if throttled) | Variable depending on position |
| Exit | Exit to tank/atmosphere | 1.0 | All kinetic energy v²/(2g) lost |
| Sudden Expansion | Abrupt diameter increase | Special: h = (v₁−v₂)²/(2g) | Depends on velocity ratio, NOT just K |
| Sudden Contraction | Abrupt diameter decrease | 0.3–0.5 | Based on vena contracta effect |
Series vs. Parallel Pipes – Key Differences
| Property | Series Pipes | Parallel Pipes |
|---|---|---|
| Discharge (Q) | Same in all pipes (Q_in = Q_1 = Q_2 = ...) | Splits among branches (Q_in = Q_1 + Q_2 + ...) |
| Head Loss (h_L) | Adds (h_L,total = h_1 + h_2 + ...) | Same across all branches (h_L,1 = h_L,2 = ...) |
| Velocity (v) | Changes if diameter changes (v = Q/A) | Different in each branch (v = Q/A for each) |
| Analysis approach | Sequential: h_f and h_m calculated for each pipe; sum for total | Simultaneous: set h_L,1 = h_L,2, solve for Q_1 and Q_2 |
| Example | Pipe 1 (200 mm, 100 m) → Pipe 2 (150 mm, 50 m); same Q throughout | Two pipes from point A to point B in parallel; same h_L, different Q |
Diagrams
Pipe Flow Analysis Decision Tree
Decision flowchart for systematic pipe flow analysis: start with velocity, determine regime (Re), select friction factor source, calculate major and minor losses, sum for total.
Flow in Pipes – Key Concepts Map
Hierarchical concept map showing the structure of pipe flow analysis: flow regime identification, major loss equations, minor loss fittings, and series/parallel configurations.