Fluid Mechanics & Hydraulics Chapter 1-3

Fluid Mechanics & Hydraulics Review Notes

• Chapter 1: Properties of Fluids

  • Unit Weight (γ) = ρg
  • Mass Density (ρ) = M/V
  • Specific Volume (Vs) = 1/ρ
  • Specific Gravity (S) = ρliquid/ρwater
  • Dynamic Viscosity (μ) = F/A (dV/dy)
  • Kinematic Viscosity (ν) = μ/ρ
  • Droplet Pressure (p) = 4σ/d
  • Capillarity (h) = 4σcosθ/ρgd
  • Compressibility (β) = -ΔV/V/Δρ
  • Bulk Modulus of Elasticity (Eb) = 1/β
  • Celerity (c) = √(E/ρ)
  • Gas Law (P₁V₁/T₁ = P₂V₂/T₂), Adiabatic/Isentropic (P₁V₁^k = P₂V₂^k)

• Chapter 2: Principles of Hydrostatics

  • Pressure (p) = F/A
  • Pascal's Law: Pressure on a fluid is equal in all directions
  • Gage Pressure = Pressure above atmospheric pressure
  • Atmospheric Pressure = 101.325 kPa = 14.7 psi
  • Absolute Pressure = Gage pressure + atmospheric pressure
  • Fluid Pressure (p) = yh
  • Pressure Below Layers of Fluids (p) = ∑(ynhn)

• Chapter 3: Total Hydrostatic Force on Surfaces

  • Force due to Pressure (F) = pA
  • Hydrostatic Force on Inclined Surfaces (F) = yhA or PcgA
  • Hydrostatic Force on Curved Surfaces (Fv) = yV
  • Archimedes' Principle: Upward force on a body immersed in a fluid = Weight of displaced fluid (BF = YVD)
  • Stability of Floating Bodies: Metacenter (M) determines stability (RM or OM = Wx = W(MGsine))

• Chapter 4: Relative Equilibrium of Liquids

  • Horizontal Rectilinear Translation: W = mg, REF = ma
  • Inclined Rectilinear Motion: W = mg, REF = ma
  • Vertical Rectilinear Motion: W = mg, REF = ma
  • Rotating Motion: tan θ = ω²x/g

• Chapter 5: Fundamentals of Fluid Flow

  • Discharge or Flow Rate (Q) = AV
  • Continuity Equation (Incompressible Fluids): A₁V₁ = A₂V₂
  • Bernoulli's Energy Theorem (E₁ = E₂),
  • Power and Efficiency (P = γQE),
  • Energy Head (v²/2g, P/γ, z),
  • Gains and Losses (Hp + hf loss + Ht loss = E₂)

• Chapter 6: Fluid Flow Measurement:

  • Device Coefficients (Cv, Cc),
  • Head Loss through Device (HL = (V₂² -V₁²)/2g),
  • Orifice Velocity (v = 2gH),
  • Weirs (Discharges)
  • Rectangular Weirs,Triangular Weirs,and Trapezoidal Weirs formula (Q = function of Head - H)

• Chapter 7: Fluid Flow in Pipes

  • Reynold's Number (Re) = (ρVD)/μ
  • Flow Type (Laminar, Turbulent, Critical)
  • Friction Factor (f)
  • Entrance Length (Le)
  • Velocity Distributions in Pipes (v = function of radius,avg velocity, max velocity)
  • Shearing Stress in Pipes (τo = function of V,p,L,f)
  • Major Head Losses (Darcy-Weisbach, Manning, Hazen Williams) – formula(hf= function of diameter,velocity,friction factor
  • Minor Head Losses (km)
  • Pipes in Series/Parallel (use head-loss formula to find total head losses)

• Chapter 8: Open Channel Flow

  • Specific Energy (E = v²/2g + d)
  • Chézy, Kutter, Ganguillet & Manning, Bazin, and Powell Formula (v=CR^1/2S^1/2, Q = AR^1/2S^1/2)
  • Uniform Flow (v=CR^1/2S^1/2),
  • Boundary Shear Stress [function of boundary roughness(S)]
  • Normal Depth (d= function of Q,R,S)
  • Most Efficient Cross Sections [proportions are given by formula
  • Velocity Distribution (v=function of hydraulic radius and depth),and flow rate(Q) are given]
  • Alternate Stages of Flow (plot d-Q)

• Chapter 9: Hydrodynamics

  • Reactions Against Flat Plates (R = pQv)
  • Forces Against Vanes (Fx = pQ(V₁x-V₂x),Fy=pQ(V₁y-V₂y))
  • Forces Developed in Pipes (R = Σ(Q₁V₁-(Q₂V₂)))

• Chapter 10: Deep Foundations (Cohesive Soil)

  • Ultimate Bearing Capacity of Pile(Qb = CNcAtip), and Ultimate Frictional Capacity of Pile (Qf = cLaP (method))
  • Ultimate Capacity of a Single Pile (Qult = Qb + Qf)
  • Ultimate Capacity of Group Piles (Qult = (Qb + QF) × n)

• Chapter 11: Slope Stability

  • Infinite Slope (Clay/Sandy Soil), Factor of Safety (FS), Equation(FS = function of angle of friction of soil,height of soil,unit weight,etc...)

• Geotechnical Engineering [Properties of Soil]:

  • Phase Diagram (V = Vv + Vs + ...).
  • Void Ratio (e = Vv/Vs)
  • Porosity (n = Vv/Vt)
  • Degree of Saturation (S = Vw/Vv)
  • Air Void Ratio (Avr = Va/Vt)
  • Moisture Content (W = Mw/Ms).
  • Specific Gravity (G = Yw/Yw)
  • Density (unit weight, Y). -Dry,Saturated,and Submerged unit weights (function of water weight and soil volume).
  • Hydraulic Gradient (i = Δh/Δl)
  • Basic Settlement Formulas (function of load, thickness of the soil layer, etc.)

• Chapter: 2: Classification of Soil -USCS and USDA classifications, and sieve analysis