Hydraulics and Fluid Mechanics

Study lessons

1. 1

   Fluid Properties and Hydrostatics

   Learn how density, specific weight, and viscosity describe a fluid, then use the hydrostatic pressure equation, force on submerged plane and curved surfaces, and buoyancy to solve the largest single family of problems on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
2. 2

   Continuity, Energy, and Flow in Pipes and Channels

   Learn continuity (Q = A x V), the energy (Bernoulli) equation with head loss, orifice and weir flow measurement, Darcy-Weisbach pipe friction loss, and Manning's equation for open channels, the moving-fluid half of the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
3. 3

   Hydrology and Water Resources

   Follow water from rainfall to runoff to the aquifer: the hydrologic cycle, rainfall measurement, the rational method for peak runoff, return period and probability, infiltration, and Darcy's law for groundwater seepage, the water-resources core of the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
4. 4

   Momentum and Forces in Fluid Flow

   Apply the impulse-momentum equation, sum(F) = rho x Q x (V2 - V1), to find the dynamic force a moving fluid exerts on flat plates and curved vanes struck by a jet, on moving blades that produce power, and on nozzles and pipe bends where pressure and momentum combine into the anchoring force, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   16 min
5. 5

   Open Channel Flow

   Solve uniform open-channel flow with the Manning and Chezy equations and the most efficient sections, then read the specific-energy diagram to find critical depth, the Froude number, subcritical versus supercritical flow, and the depth and energy loss across a hydraulic jump, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
6. 6

   Pumps, Turbines, and Hydraulic Machines

   Master the total dynamic head a pump must supply, pump power P = gamma x Q x H and efficiency, the system head curve and operating point, net positive suction head and cavitation, the affinity laws, and turbine output power and specific speed, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
7. 7

   Groundwater and Well Hydraulics

   Track groundwater from Darcy's law and hydraulic conductivity through transmissivity, confined and unconfined aquifers, steady radial flow to a well by the Thiem and Dupuit equations, the drawdown cone of depression, and well interference, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
8. 8

   Flow Measurement Devices

   Measure pipe discharge with the venturi meter, orifice meter, and flow nozzle, read point velocity with the pitot tube, tie every reading together through the discharge, velocity, and contraction coefficients, and gauge open-channel flow with rectangular, V-notch, and Cipolletti weirs and critical-flow flumes, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
9. 9

   Unsteady Flow and Water Hammer

   Follow a pipeline transient from the idea of unsteady flow through the pressure-wave speed (celerity), the Joukowsky water hammer pressure rise, rapid versus slow valve closure, and the surge tank that tames it, on the Hydraulics and Geotechnical Engineering paper of the CELE.

   15 min
10. 10

    Dimensional Analysis and Hydraulic Similitude

    Reduce a messy hydraulics problem to dimensionless pi groups with the Buckingham pi theorem, read the Reynolds, Froude, Weber, and Mach numbers as ratios of forces, and scale a physical model to its prototype through geometric, kinematic, and dynamic similarity on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
11. 11

    Water Supply and Distribution Systems

    Size a municipal water system end to end, from per-capita demand and peak factors through service-reservoir storage, the Hardy Cross method for looped pipe networks, and the fire-flow and residual-pressure requirements that set the design floor, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
12. 12

    Pump and Turbine Selection and Performance

    Match a machine to its piping by crossing the pump head-capacity curve with the system head curve to fix the operating point, then apply specific speed to name the right pump or turbine, guard the suction side against cavitation with net positive suction head, stack pumps in series and parallel to reach a duty one pump cannot, and compute turbine shaft power, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
13. 13

    Sewer and Wastewater Hydraulics

    Size sanitary and storm sewers from their design flows and peak factors through the self-cleansing velocity, the Manning equation for a pipe flowing full, and the part-full hydraulic elements of a circular sewer, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
14. 14

    Flood Routing and Reservoir Operation

    Trace a flood wave through storage: the storage-continuity equation, level-pool reservoir routing by the storage-indication method, channel routing by the Muskingum method, and the attenuation and lag that every routed hydrograph shows, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
15. 15

    Sediment Transport and Scour

    Predict when a channel bed starts to move using the boundary shear stress, the threshold of motion, and the Shields parameter, separate the load into bed load and suspended load, size grains by their Stokes settling velocity, and estimate local scour depth at bridge piers, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
16. 16

    Hydraulic Jump and Energy Dissipation

    Master the hydraulic jump on the CELE Hydraulics and Geotechnical Engineering paper, working from specific energy and the Froude number to sequent depths from the momentum equation, the head loss and efficiency of a jump, the classification of jumps by Froude number, and the stilling basins that put a jump to work dissipating energy below spillways and chutes.

    15 min
17. 17

    Reservoir and Dam Hydraulics

    Compute the hydrostatic thrust on a dam face, add uplift at the base, then check a gravity dam section for overturning and sliding with proper factors of safety, size a spillway with the weir equation, and route a flood through reservoir storage, all board-standard skills on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
18. 18

    Stormwater and Drainage Design

    Design urban drainage with the rational method Q = C i A, choose the runoff coefficient, read intensity from an IDF curve at the time of concentration, size the storm sewer with the Manning equation, and check inlet capacity, for the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
19. 19

    Coastal and Tidal Hydraulics

    Read ocean surface waves through their height, period, wavelength, and celerity, separate deep-water from shallow-water behavior with the dispersion relation, size wave energy and power, work with tides and tidal range, estimate wave run-up on a slope, and follow the basics of littoral transport, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
20. 20

    Pipe Network Analysis

    Solve looped pipe networks with junction continuity, loop head balance, and the Hardy Cross method, then collapse pipes in series and parallel into a single equivalent pipe or equivalent length, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
21. 21

    Cavitation and Pump Performance

    Read the pump head-capacity, efficiency, power, and NPSH-required curves, cross the pump curve with the system head curve to fix the operating point, guard the suction side against cavitation using net positive suction head available versus required, scale performance with the affinity laws, and rank a machine by its specific speed and suction specific speed, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
22. 22

    Surge Tanks and Transient Flow

    Trace a pipeline transient from wave celerity through the Joukowsky water hammer pressure rise, rapid versus slow valve closure, and the surge tank that converts a violent hammer into a slow mass oscillation, for the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
23. 23

    Irrigation and Drainage Hydraulics

    Size irrigation canals and drains for the CELE by turning crop water demand into a discharge, linking duty, delta, and the base period, running the Manning equation on a trapezoidal canal within a permissible velocity, and fixing the drainage coefficient and subsurface drain spacing for the Hydraulics and Geotechnical Engineering paper.

    15 min
24. 24

    Viscous and Laminar Flow

    Master Newton law of viscosity and the shear stress tau = mu du/dy, the parabolic laminar velocity profile between plates and inside pipes, the Hagen-Poiseuille discharge Q = pi delta_p D^4 / (128 mu L), the Reynolds number that separates laminar from turbulent flow, and the laminar friction factor f = 64 / Re for the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
25. 25

    Boundary Layer and Drag

    Build the boundary layer from the no-slip wall outward, separate laminar from turbulent growth and estimate the boundary layer thickness, compute drag and lift from the drag and lift coefficients and the dynamic pressure, read flow separation and streamlining, and find the terminal velocity of a settling sphere on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
26. 26

    Culvert and Bridge Hydraulics

    Analyze culverts under inlet control and outlet control, relate headwater to tailwater and barrel capacity, size a bridge waterway opening from the design discharge and a permissible velocity, estimate afflux and backwater at a constriction, and check scour at piers, for the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min
27. 27

    Water Quality and Environmental Hydraulics

    Track dissolved oxygen and BOD through a polluted stream using first-order decay, the mass-balance mixing of a waste flow with a river, the self-purification oxygen sag, and the settling velocity that sizes a sedimentation basin, on the Hydraulics and Geotechnical Engineering paper of the CELE.

    15 min

Section practice test

35 test sets covering the whole Hydraulics and Fluid Mechanics section, 1050 original questions with explanations. After you finish the lessons above, prove it here. Randomized every run.