Hydraulics & Principles in Geotechnical Engineering - Flashcards

This set of flashcards covers key concepts from the lecture notes on fluids, buoyancy, flow in pipes and channels, soil mechanics, and related hydraulic principles.

What is the definition of unit weight (γ) of a fluid and its formula?

Unit weight is the weight of a unit volume of fluid; γ = W/V = ρ g.

What is mass density (ρ) of a fluid and its formula?

Mass per unit volume; ρ = m/V (kg/m^3).

What does Specific Gravity (SG) represent for a substance?

The ratio of its density to the density of water at 4°C: SG = ρ/ρw = γ/γw.

What are the standard unit weight and density of water at 4°C?

γw = 9.81 kN/m^3; ρw = 1000 kg/m^3.

What is Specific Volume (V) and its relation to density?

The reciprocal of density: V = 1/ρ; volume per unit mass.

What is Bulk Modulus of Elasticity (EB) and its formula?

EB expresses compressibility: EB = ΔP/(ΔV/V).

What does compressibility (β) measure?

The fractional change in volume per unit change in pressure in a constant-temperature process.

What is hydrostatic pressure and its formula?

Pressure due to fluid weight: P = γ h.

What is capillarity height in a capillary tube?

h = 4 σ cos θ / (γ d).

What is the capillary diameter relation involving d, σ, θ, γ, and r?

d = 2 σ cos θ /(γ r).

What is the capillary pressure inside a droplet of liquid?

P = 4 σ / d (gage pressure).

What is the wave speed c in a liquid in terms of bulk modulus and density?

c = sqrt( EB / ρ ).

What is water hammer in pipelines?

A shock (pressure rise) in a pipeline caused by sudden decrease or stoppage of fluid motion.

What is instantaneous closure pressure for water hammer?

P_h = ρ v c for tc = 0.

What is the wave speed constant for rigid pipes?

C = sqrt( EB / ρ ).

What is time of travel (T) for pressure waves in a pipe?

T = 2L / c.

How is rapid closure defined in water hammer and its pressure expression?

Rapid closure: tc < T; P_h = ρ v c.

How is slow closure defined in water hammer and its pressure expression?

Slow closure: tc > T; Ph = 2 L ρ v / tc.

What is viscosity and its dynamic form?

Viscosity is resistance to shear; τ = μ dv/dy; μ is dynamic viscosity.

What is kinematic viscosity and its relation to dynamic viscosity?

ν = μ / ρ; kinematic viscosity is dynamic viscosity divided by density.

What is pressure (P) in fluids?

Force per unit area: P = F / A.

What is differential pressure and its relation to head?

dP = γ d h; changes in pressure relate to changes in head.

What is atmospheric pressure at sea level and its common equivalents?

1 atm = 101.325 kPa = 760 mmHg.

What is absolute pressure P_abs?

Pabs = Pgage + P_atm.

What does Pascal's Law state?

A pressure change at a point in a confined incompressible fluid is transmitted undiminished throughout the fluid.

How do you compute the total hydrostatic force on a plane surface with uniform pressure?

F = p A; for inclined planes, F can be taken as F = pcg A where pcg is the pressure at the centroid.

What is Archimedes’ principle?

The buoyant force equals the weight of the fluid displaced.

What factors affect buoyancy?

Fluid density, displaced volume, and local gravity.

Does buoyancy depend on the mass or density of the immersed object?

No; buoyancy depends on the displaced fluid and gravity, not on the object's mass or density.

What is metacentric height (GM)?

The distance between the center of gravity and the metacenter; positive GM indicates stable equilibrium, negative indicates instability.

What is a flow net in groundwater hydraulics?

A network of flow lines (paths of water) and equipotential lines (constant head) describing seepage.

What does Darcy’s law express in terms of discharge velocity?

v = k i, where v is discharge velocity, k is hydraulic conductivity, and i is hydraulic gradient.

What is seepage velocity and its relation to porosity?

The actual velocity of water through the pore space; seepage velocity is related to Darcy velocity and porosity.

What is a constant-head permeability test?

A test where head is held constant and discharge is measured to determine hydraulic properties.

What is a falling-head permeability test?

A test where head falls with time and discharge is measured to determine permeability.

What is transmissivity (T) of an aquifer?

T = k b; the ability of the aquifer to transmit water per unit width.

What is equivalent hydraulic conductivity in stratified soils?

Horizontal and vertical equivalents: kh and kv, representing conductivity in layered media.

What are flow nets used for in geotechnical engineering?

To represent seepage paths and head loss in soils and to estimate discharge.

What are the Boussinesq and Westergaard formulas used for?

They provide stresses in soils due to point loads or line loads on foundations.

What is effective stress in soils?

Total stress minus pore water pressure: σ' = σ - u.

What does OCR stand for in soil consolidation?

Overconsolidation ratio; OCR > 1 indicates overconsolidated soil, OCR = 1 normally consolidated.

What are D10, Cu, Cc, So in USCS soil classification?

D10 is the effective size (10% finer); Cu is the uniformity coefficient; Cc is the coefficient of gradation; So is the sorting coefficient.

What are Atterberg limits in soil testing?

Liquid limit (LL), Plastic limit (PL), and Plasticity index (PI = LL − PL).

What is the practical meaning of residual soils?

Soils formed by weathering in place with little movement from the original location.

What is the significance of a V-notch weir?

A triangular weir used to measure discharge in open-channel flow.

What is a Cipolletti weir?

A trapezoidal weir with side slopes of 1 horizontal to 4 vertical to offset side contractions.

Which formula relates discharge to area and velocity in uniform open-channel flow?

Q = A v; relates flow rate to cross-sectional area and mean velocity.

What is Chezy’s formula used for in open-channel flow?

A formula for average velocity: v = C √(R S) or similar depending on form with Chezy coefficient C.

What is Manning’s formula used for?

A roughness-based method to relate flow velocity to hydraulic radius and slope: v = (1/n) R^(2/3) S^(1/2).

What is the purpose of a Bernoulli’s energy theorem in fluid flow?

Relates energy forms (kinetic, potential, pressure head) along a streamline and accounts for head losses.

What is the hydraulic jump?

An abrupt increase in depth of rapidly flowing water, transitioning from supercritical to subcritical with energy loss.

What is the critical depth in open-channel flow?

Depth at which flow transitions between subcritical and supercritical for a given discharge.