Physical Address
304 North Cardinal St.
Dorchester Center, MA 02124
ASME Y10.2-1958 — Letter Symbols for Hydraulics
🌊 ASA Y10.2-1958 was prepared by the hydraulics symbol subcommittee under Sectional Committee Y10 on Letter Symbols and approved by the American Standards Association on June 18, 1958. Unlike the single-discipline symbol lists that precede it in the Y10 series, the Foreword states plainly that this comparatively short list of symbols is an attempt to be universal rather than comprehensive — a compromise intended to unify the widely divergent conventions of the various hydraulics subfields. The subcommittee was chaired by Prof. J. M. Robertson and included hydraulic specialists from Douglas Aircraft, the Bureau of Reclamation, the Waterways Experiment Station, Ingersoll-Rand, and the Iowa Institute of Hydraulic Research, among others.
💡 The core philosophy is “one list, many uses”: the subfields of hydraulics — turbomachinery, water waves, sediment, hydrology, industrial hydraulics, water hammer, and naval architecture — had already formed their own symbol habits. The Standard does not start from scratch; it respects existing practice and seeks the best possible compromise.
1. Scope and Subfields Covered 📌
The Foreword describes the extensive list of subfields reviewed in composing the list, the principal ones being:
- Hydraulic Turbomachinery: specific speed, head, and discharge of pumps and water turbines;
- Water Waves: drawn in part from the University of California 1951 report “Waves, Tides and Beaches: Glossary of Terms and List of Standard Symbols”;
- Sediment Transport: bed load, suspended load, and shear velocity;
- Hydrology: runoff, precipitation, and watershed parameters;
- Industrial Hydraulics: pressures, flows, and piping in hydraulic systems;
- Water Hammer: consistent with the symbols recommended by the ASME Hydraulics Division’s Water Hammer Committee in 1933;
- Naval Architecture: following the international list adopted in 1951 by the Sixth International Conference of Ship Tank Superintendents (published by SNAME).
This cross-disciplinary integration makes the Standard a “common symbol convention” linking hydraulic, mechanical, ocean, and civil engineering.
⚠️ Understand the Standard’s positioning: it aims at universality and compromise, so purely local symbols of individual subfields may be omitted or replaced by generic forms. In specialized treatises, the more rigorous branch-specific standards (e.g., ship-model test symbols) should take precedence.
2. Symbol-Selection Rules and Dimensionless Numbers 🧮
The Foreword summarizes a set of practical rules that emerged from the conceptual listing, useful for anyone adopting symbols for new or more specialized concepts:
- Angles are usually identified by Greek letters, generally those appearing early in the alphabet;
- Geometric properties (length, volume), forces, and kinematic quantities use English letters;
- Fluid properties commonly use Greek letters;
- Basic dimensionless parameters use English capital letters (with one exception, σ).
For dimensionless parameters the Standard made a far-reaching choice: in the interests of simplicity it diverged from the Aeronautical Sciences standard (Y10.7-1954, originally Z10) and chose single bold letters — R for Reynolds number, F for Froude number, and M, W, D for other basic dimensionless parameters — instead of NRe or Re. Where there is no chance of confusion with other uses of these letters, ordinary capitals (except O) may be used. The reason is evident to anyone using subscripts (RL instead of NReL), and a less complex method of typesetting.
| Dimensionless Parameter | Symbol (this Std.) | Traditional Form | Physical Meaning |
|---|---|---|---|
| Reynolds number | R | Re or NRe | Inertia vs. viscous forces |
| Froude number | F | Fr or NF | Inertia vs. gravitational forces |
| Mach number | M | Ma or NM | Flow speed vs. speed of sound |
| Weber number | W | We or NWe | Inertia vs. surface tension |
| Darcy friction factor | f | λ or f | Pipe-flow friction coefficient |
💡 The intent of boldface: the Standard recommends F, M, R, W, and D in bold face so they will not be confused with the ordinary quantities force F, mass M, and radius R; when context makes confusion impossible, ordinary capitals may be used. This “typeface distinguishes dimensionless numbers” idea was later inherited by subsequent standards.
3. Core Hydraulic Quantity Symbols 📏
Besides dimensionless numbers, the list supplies the basic quantities of hydraulic calculation, excerpted below:
| Quantity | Symbol | Remarks |
|---|---|---|
| Discharge / flow rate | Q | Water volume passing a section per unit time |
| Velocity | v (or u, w) | Point velocity; V for mean section velocity |
| Depth of flow | h (or d, y) | Open-channel flow depth |
| Head | H | Total head, pump head |
| Roughness coefficient | n | Manning’s roughness |
| Hydraulic radius | Rh | Flow area divided by wetted perimeter |
| Kinematic viscosity | ν | μ/ρ |
| Surface tension | σ | Related to the Weber number |
| Water hammer wave speed | c (or a) | Pressure-wave propagation speed in a pipe |
These symbols connect directly to classic hydraulic calculations — Joukowsky’s water-hammer formula, Manning’s uniform-flow formula, and specific-speed formulas for pumps and turbines — forming the common language of hydraulic engineering formulas.
🚨 Subscript tip: in the water-hammer field, agreement on symbols was reached with the ASME Water Hammer Committee as early as 1933, including conventions for transient pressure and wave speed. When writing transient-analysis reports, check this list and avoid inventing symbols that conflict with industry practice.
4. Engineering Practice Essentials 🛠️
- 🏗️ Hydraulic structure design: unify Q, v, h, H, and n in spillway, channel, and pipe calculations to ease design-review and shop-drawing checking.
- ⚙️ Pump and turbine selection: write specific speed and dimensionless parameters (F, R) in bold capitals so selection reports interface smoothly with vendor documentation.
- 🌊 Water hammer and transient analysis: follow this list and industry consensus for wave speed c, valve-closure time, and pressure-wave symbols, keeping transient-software input and interpretation consistent.
- 🌐 Cross-disciplinary collaboration: water resources, ocean engineering, and naval architecture projects share one hydraulic symbol set, reducing inter-discipline conflicts.
5. Frequently Asked Questions ❓
❓ Q: Why does this Standard use R for Reynolds number instead of the common Re?
A: Deliberately. To diverge from the aeronautical standard Y10.7-1954 (NRe/Re) for simplicity, single-letter R was chosen to simplify subscripts (e.g., RL) and typesetting; boldface or context must prevent confusion with radius.
A: Deliberately. To diverge from the aeronautical standard Y10.7-1954 (NRe/Re) for simplicity, single-letter R was chosen to simplify subscripts (e.g., RL) and typesetting; boldface or context must prevent confusion with radius.
❓ Q: What if the Standard conflicts with a subfield’s existing symbol habits?
A: The Standard is itself a compromise — it respects branch conventions (the 1933 water-hammer symbols, the 1951 ship-model test symbols) while seeking common ground; where a branch standard is more rigorous, follow it or explain the difference explicitly in your documents.
A: The Standard is itself a compromise — it respects branch conventions (the 1933 water-hammer symbols, the 1951 ship-model test symbols) while seeking common ground; where a branch standard is more rigorous, follow it or explain the difference explicitly in your documents.
❓ Q: Why are angles and fluid properties both written in Greek letters?
A: This is a rule the Standard observed rather than imposed — early-alphabet Greek letters often denote angles, while fluid properties (density ρ, viscosity μ) follow Greek tradition; the rule helps in choosing new symbols sensibly.
A: This is a rule the Standard observed rather than imposed — early-alphabet Greek letters often denote angles, while fluid properties (density ρ, viscosity μ) follow Greek tradition; the rule helps in choosing new symbols sensibly.
❓ Q: How are Manning’s n and the Darcy friction factor f distinguished?
A: n is used in Manning’s formula (open-channel uniform flow, dimensional L1/6), while f is used in the Darcy–Weisbach equation (pipe friction loss, dimensionless). They have different physical backgrounds and applications, and each is listed separately in the Standard.
A: n is used in Manning’s formula (open-channel uniform flow, dimensional L1/6), while f is used in the Darcy–Weisbach equation (pipe friction loss, dimensionless). They have different physical backgrounds and applications, and each is listed separately in the Standard.
