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.
Density, Specific Weight & Specific Gravity
Formulas
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
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)
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
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
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
Density (ρ)
Example
Oil with s = 0.88 has ρ = 880 kg/m³
Mass per unit volume; fundamental property; water = 1000 kg/m³ at standard conditions
Specific Weight (γ)
Example
A 1 m³ block of water weighs 9.81 kN
Weight per unit volume; γ = ρg; varies with location (g ≠ constant); water = 9.81 kN/m³
Specific Gravity (s)
Example
Mercury s ≈ 13.6; oil s ≈ 0.85; gasoline s ≈ 0.75
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)
Viscosity (Dynamic & Kinematic)
Formulas
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
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
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
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
Dynamic Viscosity (μ)
Example
Water at 20°C: μ ≈ 0.001 Pa·s; honey: μ ≈ 10 Pa·s
Fluid's resistance to shear flow; units Pa·s or N·s/m²; independent of shear rate for Newtonian fluids
Kinematic Viscosity (ν)
Example
Water at 20°C: ν ≈ 1×10⁻⁶ m²/s = 1 cSt (centistoke)
Dynamic viscosity divided by density; ν = μ/ρ; units m²/s; used in dimensionless groups
Newtonian Fluid
Example
Water, glycerin, most common hydraulic fluids; τ vs dv/dy is linear
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
τ = μ(dv/dy); Linear profile: τ = μ(ΔV/Δy) = μ(V/h)
Note
If plate moves at V and gap is h: gradient = V/h; shear stress = μV/h
Conditions
Velocity varies linearly from 0 to V over distance h; constant μ (Newtonian)
Surface Tension & Capillarity
Formulas
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
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
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
Surface Tension (σ)
Example
Water at 20°C: σ ≈ 0.0728 N/m; mercury: σ ≈ 0.486 N/m
Energy per unit area (N/m) at a liquid–air interface; caused by unequal intermolecular forces; high for water, low for oils
Contact Angle (θ)
Example
Water on clean glass: θ ≈ 0°; mercury on glass: θ ≈ 140°
Angle between liquid meniscus and solid wall; θ < 90° = wetting (rise); θ > 90° = non-wetting (depression)
Capillary Rise/Depression
Example
Water in 1 mm glass tube: h ≈ 15 mm; mercury in same: h ≈ −5 mm (falls)
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)
Compressibility & Bulk Modulus
Formulas
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
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
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
Bulk Modulus (E_B)
Example
Water: E_B ≈ 2.2 GPa (nearly incompressible); air at 1 atm: E_B ≈ 0.1 MPa (very compressible)
Measure of fluid's resistance to volume change under pressure; large E_B = incompressible; Pa or GPa
Compressibility (β)
Example
Water: β ≈ 4.5×10⁻¹⁰ Pa⁻¹
Inverse of bulk modulus; β = 1/E_B; fractional volume change per unit pressure; less common in exams
Incompressible Fluid
Example
Water in open-channel flow, gravity flow; assumption breaks for high-pressure (>10 MPa) pump discharge
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
For isothermal process: pV^n = constant; for adiabatic: pV^k = constant (gases only)
Note
Liquids use incompressible assumption; gases must account for pressure–volume relationship
Conditions
n ≈ 1 for liquids (incompressible); k = C_p/C_v for gases (≈ 1.4 for air)
Vapor Pressure & Cavitation
Formulas
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)
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
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)
Absolute pressure at which a liquid boils at a given temperature; independent of total pressure; read from saturated fluid tables
Cavitation
Example
Pump impeller inlet: low pressure zone → bubbles form → collapse near blade → damage
Formation and collapse of vapor bubbles in liquid when local absolute pressure drops below vapor pressure; causes noise, erosion, efficiency loss
Cavitation Number (σ_c)
Example
Pump cavitation coefficient ~0.5; turbine inlet ~2–5 depending on design
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
NPSH_available = (p_atm − p_v − h_f − h_z)/γ
Note
NPSH is a pressure head in meters; NPSH_available must exceed NPSH_required per pump specification
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
Fluid Property Variation & Temperature Effects
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
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
Thermal Expansion Coefficient (α)
Example
Water: α ≈ 0.0002 K⁻¹ (very small; density change ~0.02% per °C)
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
Density vs Specific Weight vs Specific Gravity
| Property | Symbol | Units | Definition | Example (Water) |
|---|---|---|---|---|
| Density | ρ | kg/m³ | Mass per unit volume | 1000 kg/m³ |
| Specific Weight | γ | N/m³ or kN/m³ | Weight per unit volume = ρg | 9.81 kN/m³ or 9810 N/m³ |
| Specific Gravity | s | Dimensionless | Ratio to water; always reference to ρ_water = 1000 kg/m³ | 1.0 (by definition) |
Dynamic vs Kinematic Viscosity
| Property | Symbol | Units | Formula | When Used |
|---|---|---|---|---|
| Dynamic (Absolute) | μ | Pa·s or cP | τ = μ(dv/dy) | Shear stress, force, momentum; direct fluid property |
| Kinematic | ν | m²/s or cSt | ν = μ/ρ | Reynolds number, Navier–Stokes, flow regime classification |
| Conversion | — | 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 |
Capillary Rise vs Depression
| Fluid | Contact Angle θ | Behavior | cos θ | h Formula Result | |
|---|---|---|---|---|---|
| Water on clean glass | ~0° | Wetting (adhesive > cohesive) | Rise (positive h) | ~+1.0 | h = +15 mm (in 1 mm tube) |
| Mercury on glass | ~140° | Non-wetting (cohesive > adhesive) | Depression (negative h) | ~−0.77 | h = −5 mm (in 1 mm tube) |
| General rule | 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 |
Compressibility: Liquids vs Gases
| Fluid Type | Bulk Modulus E_B | Compressibility | Assumption in Hydraulics | Example |
|---|---|---|---|---|
| Liquid (Water) | ~2.2 GPa (very large) | Very low; β ≈ 4.5×10⁻¹⁰ Pa⁻¹ | Incompressible; ρ = constant | Valid for most flows; pressure < 20 MPa |
| Gas (Air, 1 atm) | ~0.1 MPa (very small) | Very high; easily compressible | MUST account for compressibility | Use ideal gas law or pV^k = const |
| Check validity | 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 |
Vapor Pressure & Cavitation Conditions
| Location / Scenario | Pressure Status | Cavitation Risk | Prevention |
|---|---|---|---|
| Pump inlet (suction side) | Low (sub-atmospheric if hot water) | HIGH if p < p_v | Increase inlet head; reduce flow velocity; cool fluid; larger suction line |
| Turbine runner exit | Expansion & low static pressure | Risk if p_static < p_v | Avoid negative gauge pressures; increase tail-water elevation; limit velocity |
| Sharp pipe bend or constriction | Pressure drop due to Bernoulli effect | If p < p_v at contraction vena contracta | Smooth bends, avoid sharp elbows, increase inlet pressure |
| High-temperature fluid (50–80°C) | 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 |
Diagrams
Properties of Fluids – Concept Map
Mind map showing how all five major fluid properties interconnect. Central node branches into density, viscosity, surface tension, compressibility, and vapor pressure, each with key sub-concepts. Use as quick mental model before exam.
Fluid Property Problem-Solving Decision Tree
Decision tree for selecting and applying the correct fluid property formula. Follow the path based on what is given and what is asked. Avoids common errors of formula selection.