CELE Hydraulics & Fluid Mechanics — Properties of FluidsCheat Sheet
A printable cheat sheet for Properties of Fluids, built for CELE reviewers who want one go-to reference in the final stretch. Covers formulas, key definitions, common question types, and the Professional Regulation Commission (PRC) — Board of Civil Engineering-specific twists you will see on CELE day.
Exam context
On the CELE 2026, the Hydraulics & Fluid Mechanics subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Properties of Fluids lands at position 1st out of 10 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Hydraulics & Fluid Mechanics on a typical CELE paper.
Properties of Fluids - Cheat Sheet
Your 30-minute revision companion for Hydraulics & Fluid Mechanics. Master density, viscosity, surface tension, compressibility, and vapor pressure. Contains all formulas, critical definitions, board-exam values, and the top 10 must-knows.
Sections
Formulas
Formula
ρ = m/V
Meaning
ρ = density (kg/m³); m = mass (kg); V = volume (m³)
Watch Out
Units: kg/m³ NOT g/cm³ (use ×1000 conversion). Water = 1000 kg/m³ exactly
When To Use
Always the starting point; convert between mass and volume
Formula
γ = ρg = ρ(9.81)
Meaning
γ = specific weight (N/m³ or kN/m³); ρ = density; g = 9.81 m/s²
Watch Out
γ for water = 9.81 kN/m³ (NOT 1000). Units must be N/m³ or kN/m³, NOT kg/m³
When To Use
When you need weight per unit volume (pressure calculations, hydrostatic force)
Formula
s = ρ_fluid / ρ_water = γ_fluid / γ_water
Meaning
s = specific gravity (dimensionless ratio); ratios always to water at 4°C
Watch Out
Specific gravity has NO units. s = 0.85 means 85% as heavy as water. Always divide by water reference
When To Use
Compare fluid weight/density to water; always dimensionless
Formula
v_s = 1/ρ
Meaning
v_s = specific volume (m³/kg); volume per unit mass
Watch Out
Inverse of density; easy to confuse with kinematic viscosity ν
When To Use
Rarely in exams; mainly for gas compressibility calculations
Common Values
Value
1000 kg/m³
Symbol
ρ_w
Quantity
Water density
Value
9.81 kN/m³ (or 9810 N/m³)
Symbol
γ_w
Quantity
Water specific weight
Value
13.6
Symbol
s_Hg
Quantity
Mercury specific gravity
Value
0.85–0.95
Symbol
s_oil
Quantity
Oil specific gravity (typical)
Value
0.75
Symbol
s_gas
Quantity
Gasoline specific gravity
Value
9.81 m/s²
Symbol
g
Quantity
Standard gravity
Section Title
Density, Specific Weight & Specific Gravity
Important Facts
- Water at 4°C: ρ = 1000 kg/m³ is the reference standard for all s calculations
- γ_water = 9.81 kN/m³ (or 9.81 × 10³ N/m³); varies slightly with temperature
- Specific gravity is ALWAYS dimensionless and ALWAYS relative to water
- For liquids: ρ changes <1% with pressure; compressibility is negligible in most hydraulic problems
- Temperature affects density: water at 20°C ≈ 1000 kg/m³; at 0°C ≈ 999.8 kg/m³; use 1000 for exams unless specified
Key Definitions
Term
Density (ρ)
Example
Oil with s = 0.88 has ρ = 880 kg/m³
Definition
Mass per unit volume; fundamental property; water = 1000 kg/m³ at standard conditions
Term
Specific Weight (γ)
Example
A 1 m³ block of water weighs 9.81 kN
Definition
Weight per unit volume; γ = ρg; varies with location (g ≠ constant); water = 9.81 kN/m³
Term
Specific Gravity (s)
Example
Mercury s ≈ 13.6; oil s ≈ 0.85; gasoline s ≈ 0.75
Definition
Dimensionless ratio of fluid density (or weight) to water; s = ρ_fluid/1000 for kg/m³ input
Diagrams To Know
- Density vs temperature curve for water (increases 0–4°C, decreases 4°C–100°C)
- Specific gravity comparison chart for common fluids (mercury, oil, water, gasoline)
Formulas
Formula
τ = μ(dv/dy)
Meaning
τ = shear stress (Pa); μ = dynamic viscosity (Pa·s); dv/dy = velocity gradient (s⁻¹)
Watch Out
For LINEAR velocity profile: dv/dy = ΔV/Δy (total velocity change / total gap). If velocity is NOT linear, integrate. NEVER forget units: Pa = N/m²
When To Use
Whenever fluid shear stress is needed; pipe flow resistance, slider bearing, pumps
Formula
ν = μ/ρ
Meaning
ν = kinematic viscosity (m²/s); μ = dynamic viscosity (Pa·s); ρ = density (kg/m³)
Watch Out
ν in m²/s (NOT m/s or cm²/s). 1 Stoke = 10⁻⁴ m²/s. Forget to divide by ρ = common error
When To Use
In Reynolds number, Navier–Stokes, and all flow regime calculations; always in m²/s
Formula
μ = ρν
Meaning
Inverse form; solve for dynamic viscosity if kinematic is given
Watch Out
Dimensions: (kg/m³)(m²/s) = kg/(m·s) = Pa·s ✓
When To Use
When you have ν and need μ for shear stress calculation
Common Values
Value
0.001 Pa·s = 1 cP
Symbol
μ_w
Quantity
Water dynamic viscosity (20°C)
Value
1.0×10⁻⁶ m²/s = 1 cSt
Symbol
ν_w
Quantity
Water kinematic viscosity (20°C)
Value
1.8×10⁻⁵ Pa·s
Symbol
μ_air
Quantity
Air dynamic viscosity (15°C)
Value
~0.046 m²/s = 46 cSt
Symbol
ν_oil
Quantity
Standard oil viscosity (ISO VG 46)
Value
1 cP = 0.001 Pa·s
Symbol
Conversion
Quantity
Centipoise to Pa·s
Value
1 St = 10⁻⁴ m²/s
Symbol
Conversion
Quantity
Stoke to m²/s
Section Title
Viscosity (Dynamic & Kinematic)
Important Facts
- Water at 20°C: μ ≈ 0.001 Pa·s = 1 cP (centipoise); ν ≈ 1.0×10⁻⁶ m²/s = 1 cSt
- Viscosity DECREASES with temperature for liquids (opposite of gases); rule of thumb: μ halves every 20–30°C rise
- For Newtonian fluids: shear stress–velocity gradient relationship is LINEAR (straight-line plot)
- Non-Newtonian fluids (blood, paint, concrete) have μ that depends on shear rate; NOT in scope of most basic exams
- Typical values: air ≈ 1.8×10⁻⁵ Pa·s; SAE 10W oil ≈ 0.1 Pa·s; SAE 40 oil ≈ 0.5 Pa·s
Key Definitions
Term
Dynamic Viscosity (μ)
Example
Water at 20°C: μ ≈ 0.001 Pa·s; honey: μ ≈ 10 Pa·s
Definition
Fluid's resistance to shear flow; units Pa·s or N·s/m²; independent of shear rate for Newtonian fluids
Term
Kinematic Viscosity (ν)
Example
Water at 20°C: ν ≈ 1×10⁻⁶ m²/s = 1 cSt (centistoke)
Definition
Dynamic viscosity divided by density; ν = μ/ρ; units m²/s; used in dimensionless groups
Term
Newtonian Fluid
Example
Water, glycerin, most common hydraulic fluids; τ vs dv/dy is linear
Definition
Fluid with constant μ at fixed temperature, independent of shear rate; includes water, air, light oils
Diagrams To Know
- Velocity profile in a narrow gap (linear v vs y for steady shear)
- Viscosity vs temperature plot (logarithmic scale; straight line for most oils)
- Newtonian vs non-Newtonian fluid behavior (shear stress vs velocity gradient)
Reactions Or Equations
Note
If plate moves at V and gap is h: gradient = V/h; shear stress = μV/h
Equation
τ = μ(dv/dy); Linear profile: τ = μ(ΔV/Δy) = μ(V/h)
Conditions
Velocity varies linearly from 0 to V over distance h; constant μ (Newtonian)
Formulas
Formula
h = (4σcosθ)/(γd)
Meaning
h = capillary rise/depression (m); σ = surface tension (N/m); θ = contact angle (°); γ = specific weight (N/m³); d = tube diameter (m)
Watch Out
CRITICAL: Use DIAMETER d, not radius r. If given radius: h = (2σcosθ)/(γr). θ = 0° for water on clean glass (rise); θ > 90° for mercury (depression). UNITS: σ in N/m (NOT N/m²)
When To Use
When fluid rises or falls in a small-diameter tube (diameter <5 mm); account for capillary effects in manometers
Formula
h = (2σcosθ)/(γr)
Meaning
Alternative form using radius r instead of diameter d
Watch Out
Mixing d and r is the #1 error. 4σ/(γd) = 2σ/(γr) are equivalent
When To Use
Same as above but when radius is given instead of diameter; d = 2r
Common Values
Value
0.0728 N/m
Symbol
σ_w
Quantity
Water surface tension (20°C)
Value
0.486 N/m
Symbol
σ_Hg
Quantity
Mercury surface tension (20°C)
Value
0°
Symbol
θ_water
Quantity
Water contact angle on clean glass
Value
~140°
Symbol
θ_mercury
Quantity
Mercury contact angle on glass
Value
~15 mm
Symbol
h_1mm
Quantity
Capillary rise of water in 1 mm tube
Section Title
Surface Tension & Capillarity
Important Facts
- Surface tension is a property of the liquid–air interface; depends on temperature and purity
- Capillary effects are SIGNIFICANT only in small tubes (d < 5 mm); negligible in large pipes
- Water on clean glass: θ ≈ 0°, so cosθ ≈ 1 → maximum rise; mercury: θ ≈ 140°, cosθ ≈ −0.77 → depression
- For small tubes in manometers: if h > 1–2 mm, MUST correct reading for capillarity (common exam trap)
- Surface tension decreases with temperature; water at 80°C has σ ≈ 0.063 N/m vs 0.0728 at 20°C
Key Definitions
Term
Surface Tension (σ)
Example
Water at 20°C: σ ≈ 0.0728 N/m; mercury: σ ≈ 0.486 N/m
Definition
Energy per unit area (N/m) at a liquid–air interface; caused by unequal intermolecular forces; high for water, low for oils
Term
Contact Angle (θ)
Example
Water on clean glass: θ ≈ 0°; mercury on glass: θ ≈ 140°
Definition
Angle between liquid meniscus and solid wall; θ < 90° = wetting (rise); θ > 90° = non-wetting (depression)
Term
Capillary Rise/Depression
Example
Water in 1 mm glass tube: h ≈ 15 mm; mercury in same: h ≈ −5 mm (falls)
Definition
Vertical displacement of meniscus in small-diameter tube due to surface tension; rise if water (wetting), depression if mercury (non-wetting)
Diagrams To Know
- Capillary rise in narrow tube (water meniscus curved upward; force diagram)
- Contact angle: wetting (θ < 90°) vs non-wetting (θ > 90°)
- Mercury depression in tube vs water rise (side-by-side comparison)
Formulas
Formula
E_B = −dp/(dV/V) = dp/(dρ/ρ)
Meaning
E_B = bulk modulus of elasticity (Pa); dp = pressure change; dV/V = fractional volume change; dρ/ρ = fractional density change
Watch Out
Negative sign in first form accounts for pressure increasing (dp > 0) while volume decreases (dV < 0). Use SECOND form (with density) to avoid sign confusion. UNITS: Pa or GPa
When To Use
Determine how much a fluid compresses under pressure; assess incompressibility assumption validity
Formula
dρ/ρ = dp/E_B
Meaning
Rearranged: fractional density change equals pressure change divided by bulk modulus
Watch Out
If dp = 2 MPa and E_B = 2.2 GPa, then dρ/ρ = 2/2200 ≈ 0.001 or 0.1% (negligible)
When To Use
Calculate density increase under pressure; verify incompressibility (dρ/ρ ≈ 0 if E_B >> dp)
Common Values
Value
2.2 GPa (2200 MPa)
Symbol
E_B,w
Quantity
Water bulk modulus
Value
1.6 GPa
Symbol
E_B,oil
Quantity
Oil bulk modulus (typical)
Value
0.1 MPa
Symbol
E_B,air
Quantity
Air bulk modulus (1 atm, isothermal)
Value
4.5×10⁻¹⁰ Pa⁻¹
Symbol
β_w
Quantity
Compressibility of water
Section Title
Compressibility & Bulk Modulus
Important Facts
- Liquids (water, oil) have E_B ~ 1–2 GPa; assumption ρ = constant is valid for most hydraulic engineering
- Gases have E_B ~ 0.1 MPa at atmospheric pressure; MUST account for compressibility (use ideal gas law)
- For water: a 2 MPa pressure increase causes only 0.1% density change; usually ignored in calculations
- Pressure waves (sound) travel faster in fluids with higher E_B; speed of sound in water ≈ 1480 m/s vs air ≈ 340 m/s
- Cavitation occurs when local pressure drops; at bubble formation, liquid cannot sustain further expansion (E_B limit)
Key Definitions
Term
Bulk Modulus (E_B)
Example
Water: E_B ≈ 2.2 GPa (nearly incompressible); air at 1 atm: E_B ≈ 0.1 MPa (very compressible)
Definition
Measure of fluid's resistance to volume change under pressure; large E_B = incompressible; Pa or GPa
Term
Compressibility (β)
Example
Water: β ≈ 4.5×10⁻¹⁰ Pa⁻¹
Definition
Inverse of bulk modulus; β = 1/E_B; fractional volume change per unit pressure; less common in exams
Term
Incompressible Fluid
Example
Water in open-channel flow, gravity flow; assumption breaks for high-pressure (>10 MPa) pump discharge
Definition
Fluid with E_B → ∞ (or pressure effect negligible); density constant; valid assumption for liquids in low-speed flow
Diagrams To Know
- Pressure vs density change curve for water and air (non-linear for gas, nearly flat for water)
- Bulk modulus comparison bar chart: water, oil, air
Reactions Or Equations
Note
Liquids use incompressible assumption; gases must account for pressure–volume relationship
Equation
For isothermal process: pV^n = constant; for adiabatic: pV^k = constant (gases only)
Conditions
n ≈ 1 for liquids (incompressible); k = C_p/C_v for gases (≈ 1.4 for air)
Formulas
Formula
p_v = saturation pressure at fluid temperature T
Meaning
p_v = vapor pressure (Pa or kPa); absolute, not gauge; varies with T; read from steam/fluid tables
Watch Out
p_v is ALWAYS an absolute pressure. If local gauge pressure = −5 kPa and atmospheric = 101.3 kPa, absolute = 96.3 kPa. If p_v_water at 20°C = 2.34 kPa (absolute), cavitation risk exists. NEVER confuse with vapor pressure in atm
When To Use
Identify cavitation risk; compare local static pressure to vapor pressure; pump inlet/suction, turbine runner
Common Values
Value
1.23 kPa (abs)
Symbol
p_v,10
Quantity
Water vapor pressure at 10°C
Value
2.34 kPa (abs)
Symbol
p_v,20
Quantity
Water vapor pressure at 20°C
Value
12.3 kPa (abs)
Symbol
p_v,50
Quantity
Water vapor pressure at 50°C
Value
101.3 kPa (abs)
Symbol
p_v,100
Quantity
Water vapor pressure at 100°C
Value
101.3 kPa (abs) = 0 kPa (gauge)
Symbol
p_atm
Quantity
Atmospheric pressure (sea level)
Section Title
Vapor Pressure & Cavitation
Important Facts
- Vapor pressure increases with temperature (exponential trend); water: 2.34 kPa @ 20°C → 101.3 kPa @ 100°C
- Cavitation occurs at pump inlet (low pressure), turbine runner exit, sharp bends in pipelines, or wherever p_local < p_v
- Once bubbles form, collapse generates shock waves → pitting, erosion, loss of head, vibration, noise
- Prevention: increase inlet pressure (higher elevation, larger pipe), reduce flow velocity, lower fluid temperature
- Net Positive Suction Head (NPSH) available must exceed NPSH required for pump to avoid cavitation
Key Definitions
Term
Vapor Pressure (p_v)
Example
Water at 20°C: p_v ≈ 2.34 kPa (abs); at 50°C: p_v ≈ 12.3 kPa (abs); at 100°C: p_v = 101.3 kPa (1 atm)
Definition
Absolute pressure at which a liquid boils at a given temperature; independent of total pressure; read from saturated fluid tables
Term
Cavitation
Example
Pump impeller inlet: low pressure zone → bubbles form → collapse near blade → damage
Definition
Formation and collapse of vapor bubbles in liquid when local absolute pressure drops below vapor pressure; causes noise, erosion, efficiency loss
Term
Cavitation Number (σ_c)
Example
Pump cavitation coefficient ~0.5; turbine inlet ~2–5 depending on design
Definition
Dimensionless index: σ_c = (p−p_v)/(½ρV²); σ_c < critical value → cavitation risk
Diagrams To Know
- Vapor pressure vs temperature curve for water (exponential; log scale)
- Pressure profile in pump suction line showing cavitation zone
- NPSH available vs required diagram (pump operating envelope)
Reactions Or Equations
Note
NPSH is a pressure head in meters; NPSH_available must exceed NPSH_required per pump specification
Equation
NPSH_available = (p_atm − p_v − h_f − h_z)/γ
Conditions
p_atm = atmospheric (101.3 kPa abs); p_v = vapor pressure at T; h_f = friction losses in suction line; h_z = elevation difference
Common Values
Value
999.9 kg/m³
Symbol
ρ_0C
Quantity
Water density at 0°C
Value
1000.0 kg/m³
Symbol
ρ_4C
Quantity
Water density at 4°C (maximum)
Value
998.2 kg/m³ (use 1000 for exams)
Symbol
ρ_20C
Quantity
Water density at 20°C
Value
0.00131 Pa·s
Symbol
μ_10C
Quantity
Water viscosity at 10°C
Value
0.001002 Pa·s
Symbol
μ_20C
Quantity
Water viscosity at 20°C
Value
0.000653 Pa·s
Symbol
μ_40C
Quantity
Water viscosity at 40°C
Section Title
Fluid Property Variation & Temperature Effects
Important Facts
- Viscosity decreases with temperature; rule: μ roughly HALVES every 20–30°C for oils; use viscosity–temperature charts
- Density of water decreases with temperature above 4°C (anomaly below 4°C); at 20°C ≈ 998 kg/m³, use 1000 for exams
- Surface tension decreases ~0.1–0.2% per °C; water: 0.0728 N/m @ 20°C → 0.0594 N/m @ 80°C
- Vapor pressure increases dramatically with temperature (exponential); watch risk of cavitation in hot fluid systems
- Bulk modulus is nearly constant with pressure; decreases slightly with temperature for liquids
Key Definitions
Term
Thermal Expansion Coefficient (α)
Example
Water: α ≈ 0.0002 K⁻¹ (very small; density change ~0.02% per °C)
Definition
Fractional volume change per degree temperature; ρ decreases (slightly) with T for most liquids; rarely tested in basic exams
Diagrams To Know
- Viscosity vs temperature (log–log plot; straight line for Newtonian fluids)
- Density vs temperature for water (shows anomaly at 4°C)
- Combined effect chart: how μ, ρ, σ, p_v change with T
Must Remember
- Water reference: ρ = 1000 kg/m³, γ = 9.81 kN/m³, s = 1.0 by definition. ANY OTHER FLUID: express as ratio or product.
- Viscosity dual identity: μ (Pa·s, dynamic) is in force equations; ν = μ/ρ (m²/s, kinematic) is in dimensionless groups (Reynolds, Froude). Forget to divide by ρ = instant wrong answer.
- Capillary formula h = (4σcosθ)/(γd) uses DIAMETER d, not radius. If problem gives radius r: use h = (2σcosθ)/(γr). One misplaced digit = entire answer wrong.
- Specific gravity is ALWAYS dimensionless and ALWAYS relative to water at 4°C (ρ_w = 1000 kg/m³). s has no units; γ = s × 9.81 kN/m³.
- Bulk modulus E_B for water ≈ 2.2 GPa; fractional density change = Δp/E_B. If Δp = 2 MPa, then Δρ/ρ ≈ 0.001 (0.1%) — negligible, so ASSUME ρ constant for liquids unless pressure > 10 MPa.
- Vapor pressure p_v is ABSOLUTE pressure (not gauge); varies with temperature only. Cavitation occurs when local absolute pressure < p_v. At 20°C: p_v,water ≈ 2.34 kPa (abs).
- Shear stress τ = μ(dv/dy); for LINEAR velocity profile across gap h with max velocity V: dv/dy = V/h, so τ = μV/h. Non-linear velocity? Integrate dv/dy from velocity profile equation.
- Newtonian fluid definition: μ independent of shear rate (dv/dy). τ vs dv/dy is LINEAR plot. Water, air, light oils → Newtonian. Blood, paint, concrete → non-Newtonian (mostly outside exam scope).
- Contact angle θ: water on clean glass θ ≈ 0° (cosθ = 1) → RISE; mercury on glass θ ≈ 140° (cosθ ≈ −0.77) → DEPRESSION. Same formula h = (4σcosθ)/(γd); sign of cosθ determines rise or fall.
- Board exam trap: confusing specific gravity (dimensionless s) with specific weight (γ in N/m³ or kN/m³). Example: s = 0.85 → γ = 0.85 × 9.81 = 8.34 kN/m³, NOT γ = 850 kN/m³. Read problem carefully.
Last Minute Tips
- Units, units, units: Density in kg/m³, not g/cm³. Specific weight in kN/m³ or N/m³, not kg/m³. Viscosity in Pa·s, not g/(cm·s). Surface tension in N/m, not dyne/cm (1 dyne/cm = 0.001 N/m). Check your units before final answer.
- Water benchmark: ρ_w = 1000 kg/m³, γ_w = 9.81 kN/m³. Everything else is a ratio (specific gravity s) or multiple of this. If you get a huge number (e.g., γ = 8500 kN/m³), you've made an order-of-magnitude error—backtrack immediately.
- Capillary in exams: Small-diameter tubes (< 5 mm) in manometers or microscale problems often include capillary correction. Check if d is explicitly small; if so, calculate h. If h > 1 mm, it affects reading significantly. Don't ignore it.
- Cavitation red flags: Pump inlet, turbine exit, hot-fluid systems (high p_v), low-pressure regions (bends, constrictions). If a problem mentions 'cavitation risk' or NPSH, compare local absolute pressure to p_v. NPSH_available must exceed NPSH_required.
- Formula card sanity check: Before plugging numbers, ask 'Does the result make sense?' Example: capillary rise in 0.5 mm water tube ~30 mm? Yes, plausible (inversely proportional to d). Water compresses 2% under 2 GPa? No—should be ~0.1%. Recheck calculation.
Comparison Tables
Rows
Values
- ρ
- kg/m³
- Mass per unit volume
- 1000 kg/m³
Property
Density
Values
- γ
- N/m³ or kN/m³
- Weight per unit volume = ρg
- 9.81 kN/m³ or 9810 N/m³
Property
Specific Weight
Values
- s
- Dimensionless
- Ratio to water; always reference to ρ_water = 1000 kg/m³
- 1.0 (by definition)
Property
Specific Gravity
Columns
- Property
- Symbol
- Units
- Definition
- Example (Water)
Table Title
Density vs Specific Weight vs Specific Gravity
Rows
Values
- μ
- Pa·s or cP
- τ = μ(dv/dy)
- Shear stress, force, momentum; direct fluid property
Property
Dynamic (Absolute)
Values
- ν
- m²/s or cSt
- ν = μ/ρ
- Reynolds number, Navier–Stokes, flow regime classification
Property
Kinematic
Values
- —
- 1 cP = 0.001 Pa·s; 1 cSt = 10⁻⁶ m²/s
- Multiply by ρ (kg/m³) to convert ν to μ
- 1 cSt water = 10⁻⁶ m²/s
Property
Conversion
Columns
- Property
- Symbol
- Units
- Formula
- When Used
Table Title
Dynamic vs Kinematic Viscosity
Rows
Values
- ~0°
- Wetting (adhesive > cohesive)
- Rise (positive h)
- ~+1.0
- h = +15 mm (in 1 mm tube)
Property
Water on clean glass
Values
- ~140°
- Non-wetting (cohesive > adhesive)
- Depression (negative h)
- ~−0.77
- h = −5 mm (in 1 mm tube)
Property
Mercury on glass
Values
- θ < 90°: rise; θ > 90°: depression
- h ∝ cosθ; h ∝ 1/d
- Smaller d → larger |h|
- cos(0°) = 1; cos(90°) = 0; cos(140°) = −0.766
- In 5 mm tube: rise ~3 mm; in 0.5 mm tube: rise ~30 mm
Property
General rule
Columns
- Fluid
- Contact Angle θ
- Behavior
- cos θ
- h Formula Result
Table Title
Capillary Rise vs Depression
Rows
Values
- ~2.2 GPa (very large)
- Very low; β ≈ 4.5×10⁻¹⁰ Pa⁻¹
- Incompressible; ρ = constant
- Valid for most flows; pressure < 20 MPa
Property
Liquid (Water)
Values
- ~0.1 MPa (very small)
- Very high; easily compressible
- MUST account for compressibility
- Use ideal gas law or pV^k = const
Property
Gas (Air, 1 atm)
Values
- If Δp/E_B << 1 (e.g., 2/2200 ≈ 0.001)
- Then Δρ/ρ is negligible
- Incompressible assumption OK
- If Δp/E_B > 0.05, account for density change
Property
Check validity
Columns
- Fluid Type
- Bulk Modulus E_B
- Compressibility
- Assumption in Hydraulics
- Example
Table Title
Compressibility: Liquids vs Gases
Rows
Values
- Low (sub-atmospheric if hot water)
- HIGH if p < p_v
- Increase inlet head; reduce flow velocity; cool fluid; larger suction line
Property
Pump inlet (suction side)
Values
- Expansion & low static pressure
- Risk if p_static < p_v
- Avoid negative gauge pressures; increase tail-water elevation; limit velocity
Property
Turbine runner exit
Values
- Pressure drop due to Bernoulli effect
- If p < p_v at contraction vena contracta
- Smooth bends, avoid sharp elbows, increase inlet pressure
Property
Sharp pipe bend or constriction
Values
- p_v rises (e.g., water at 50°C: p_v = 12.3 kPa)
- MUCH higher risk than cold water
- Lower fluid temperature; increase system pressure
Property
High-temperature fluid (50–80°C)
Columns
- Location / Scenario
- Pressure Status
- Cavitation Risk
- Prevention
Table Title
Vapor Pressure & Cavitation Conditions
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