Fundamentals of Fluid Mechanics

Explain the no-slip condition at solid boundaries, where fluid velocity is zero, forming a velocity gradient in the boundary layer and near-wall flow shaped by viscosity.

Explain how shear stress in moving fluids relates to strain rate via viscosity, showing a velocity gradient in a parallel-plate setup and the no-slip condition.

Explore viscosity as internal resistance to motion and distinguish newtonian from non-newtonian fluids. Identify shear thinning, shear thickening, and Bingham plastic behaviors, and units of dynamic and kinematic viscosity.

Explore how to apply Newton's law of viscosity to compute shear stress from velocity distributions of Newtonian fluids between plates, using no-slip boundaries and velocity gradients.

Compute Reynolds number to predict laminar, transitional, or turbulent pipe flow and understand parabolic laminar vs uniform turbulent velocity profiles.

Explore fluid pressure and hydrostatic pressure, using density, gravity, and height. Learn to relate pressure to specific weight and specific gravity, including gauge and atmospheric pressures in multi-fluid systems.

Explore how piezometer, u-tube, and differential manometers measure fluid pressure, use equilibrium heights, and convert readings to gauge or absolute pressure.

Master buoyancy concepts, solve buoyancy problems using free body diagrams and vertical equilibrium, and analyze floating, submerged, and neutral buoyancy scenarios.

Explore buoyancy in fundamentals of fluid mechanics by solving a partial-submersion problem for a cone-shaped instrument on a buoy, computing displaced volume and weight to yield 287 pounds.

Explore moving fluids through pipes using the continuity equation to relate volume flow rate, area, velocity, and apply Bernoulli’s principle to design and analyze pump piping systems.

Explore commercially available pipe and tubing, learn to read appendices with nominal size, outside/inside diameters, wall thickness, and floor area, and apply ISO, ASTM, and other international standards for selection.

Calculate volume flow rate from area and velocity using a standard steel tube’s outer diameter and wall thickness, then select a schedule 40 pipe size to meet the flow limits.

Explain how conservation of energy in pipe flow yields Bernoulli’s equation from elevation, velocity, and pressure energies, with restrictions for no energy additions or losses and for compressible fluids.

Use Bernoulli's equation and continuity to analyze water flow between 25 mm and 50 mm sections with a 2 m elevation change, solving pressure at section two under no-loss conditions.

Calculate the volumetric flow rate through a 2-inch nozzle attached to a 3-inch pipe, using Bernoulli's equation, continuity, and unit conversions to gallons per minute.

apply bernoulli's equation to open tanks, reservoirs, and nozzles, canceling atmospheric pressure and velocity heads to compute flow rate and nozzle pressures along a siphon.

Apply continuity and Bernoulli equations to calculate velocity and volumetric flow rate in a Venturi meter, using a manometer to relate pressure differences and illustrate Torricelli’s theorem.

Explore calculating nozzle velocity and volumetric flow rates using Torricelli’s theorem for open tanks and applying Bernoulli’s equation for sealed tanks, with practical unit conversions.

Apply Bernoulli’s equation and continuity to compute nozzle volumetric flow rate and the pressures at points A and B for an oil system.

Learn the general energy equation as a practical extension of Bernoulli's equation, accounting for energy additions by pumps, losses from friction, valves, and fittings, and the nomenclature of energy heads.

Apply the modified Bernoulli energy equation to analyze energy losses from valves, elbows, pipe friction, and pumps, solving practical pump and minor loss problems.

Define power as the rate of energy transfer, relate pump input to fluid delivery, and present mechanical efficiency as output over input with unit conversions and a numerical example.

Compute the pump's mechanical efficiency by relating output power to input power via the energy equation, using volumetric flow and oil and mercury specific weights to determine head and pressure.

Use the energy equation to compute power delivered by fluid motors and assess mechanical efficiency from losses. Example: water motor delivers 1.08 kW, 0.95 kW output at 85% efficiency.

Explore Reynolds number for circular and non circular cross sections, distinguish laminar and turbulent regimes, and compute friction losses using hydraulic radius and its fourfold form for non circular pipes.

Apply Moody’s chart to calculate friction factor, head loss, and pump power in a fire protection piping system using energy equations and Reynolds number analysis.

Derive velocity and hydraulic radius from the non-circular duct cross-section, then compute Reynolds number using Re = ρ v (4 R_h)/μ.

Learn to compute friction loss in non-circular cross sections by replacing diameter with four times hydraulic radius, using Darcy's equation, Reynolds number, and Moody's chart to determine pressure drop.

Compute energy losses due to friction in pipe flow using Darcy's equation for laminar and turbulent regimes, including the friction factor, Renault's number, and relative roughness.

Explore minor losses in fluid systems, especially sudden enlargements, and learn to compute energy losses using the resistance coefficient k and velocity head.

Calculate the pressure difference P1–P2 across a sudden enlargement by applying the energy equation with velocity heads and the minor loss HL, using continuity to find V1 and V2.

Explain exit loss as energy dissipated when flow leaves pipe into reservoir, using Bernoulli and velocity head, and show gradual enlargement reduces loss with cone angle and diameter ratio.

Analyze energy loss from sudden contraction as flow moves from a large to a smaller pipe; relate velocity change, contraction geometry, streamlines, and turbulence to the loss.

Analyze energy loss from gradual contraction, showing how cone angle and diameter ratio affect resistance and velocity head, and how invert projecting and rounded inlets reduce loss.

Explore minor losses from valves and fittings, using resistance coefficients and Le/D to estimate head losses, supported by Moody diagrams and manufacturer data.

Apply the energy balance to compute head difference between reservoirs by summing friction losses and losses from valves, fittings, and sudden enlargements, using Moody's chart to determine the friction factor.

Compute head losses in pipes of different diameters, including elbows, using Darcy's equation and Moody's chart, then apply Reynolds number and roughness to determine energy loss.

Explore flow measurement using Venturi, flow nozzle, and orifice meters, and learn how range, accuracy, calibration, and discharge coefficient influence meter selection.

Describe variable area meters (rotameters) as simple flow meters that give a direct readout of flow rate by balancing drag and weight on a float in a tapered transparent tube.

Explore open channel flow measurement using weirs and notches—rectangular, contracted, and triangle (v-notch)—where head above crest and notch geometry determine discharge Q via formulas.

Explore the performance of positive displacement pumps, including reciprocating and rotary pumps, with fixed flow per revolution, pulsating output, and efficiency changes under varying pressure and speed.

Explore centrifugal pump operation, including priming and self priming methods, performance curves, and affinity laws, with head, capacity, efficiency, and brake horsepower to match systems and select pumps.

Apply affinity laws to predict how capacity, head, and power of centrifugal pumps vary with speed and impeller diameter, and read manufacturer data and designations.

Explore how impeller diameter and speed affect pump head and flow, and examine power, efficiency, cavitation risk, vapor pressure, and net positive suction head margin.