Fluid Mechanics

Define fluid, fluid mechanics, from statics to dynamics, and highlight civil engineering applications like water pipelines, dams, and water supply systems. Explain SI, French, and British units and conversions.

Apply unit conversions in fluid mechanics by converting cubic feet per minute to liter per second and pounds per square inch to gram per square centimeter, using standard factors.

Explore density and specific weight in fluids. Apply rho = m/v and gamma = W/v, noting water at 4 C is 1000 kg/m^3 and heating lowers density and specific weight; oil example yields rho around 852 kg/m^3.

Learn how specific gravity and relative density compare a liquid to water using SG = gamma liquid / gamma water and rho liquid / rho water.

Explore surface tension, the liquid's resistance to tension measured in newton per meter, and how cohesion and adhesion govern interfacial behavior and capillary rise in small tubes.

Examine viscosity as the sixth liquid property, its measurement by dynamic (absolute) viscosity, and Newton's law of viscosity, distinguishing Newton and non-Newton fluids with plate-flow examples.

Understand kinematic viscosity v = mu / rho, its unit conversions from poise to kg s per m^2, and discuss liquid compressibility beta = 1/k with small water compressibility.

Explore hydrostatic pressure by deriving p = gamma h from weight and area. In static liquids, pressure is the same on a horizontal plane and depends on height.

Examine atmospheric pressure, gauge pressure, and absolute pressure, showing how p absolute equals p atmosphere plus gamma h and p gage equals p absolute minus p atmosphere, with vacuum pressure.

explains how pressure head and piezometric head relate to elevation, showing that p plus gamma z is constant and that pressure head difference equals elevation difference.

Balance forces on a tiny static-fluid element to get the basic equations: rho phi_x = delta p / delta x, and analogous in y and z.

Derive Pascal's law from static fluid equations and show that pressure depends only on depth. Let p equal gamma h plus p0, with gamma the specific weight.

Apply Pascal's law to calculate the pressure at point a in a static two-liquid setup, using p = p_surface + gamma h, with water and mercury.

Explore Pascal's principle through a hydraulic jack, showing how a small force on a small piston creates a larger force on a bigger piston while equalizing pressure, with practical calculations.

Explore how barometers measure atmospheric pressure with a mercury column. Apply the relation P atmosphere equals rho g h, the 760 mm standard, and altitude effects.

Explore how a U-tube manometer uses liquids of known specific gravity to relate pressure differences to height, applying Pascal's law to compute absolute gas pressure.

Use a differential manometer to measure pressure drop across a flow section by applying Pascal's law; derive p1 minus p2 equals (rho2 minus rho1) g h with a water-mercury example.

Study a three-fluid manometer with water, oil, and mercury, applying p1 = p_atm + ρm g h3 − ρo g h2 − ρw g h1 to compute about 130 kPa.

Explore differential and inverted u-tube manometers to measure pressure differences between vessels, derive delta p = h(gamma m − gamma w), and apply this to example calculations.

Explain how hydrostatic force on submerged plane surface forms a resultant through the center of pressure, from pressure p = gamma h and Pascal's law, with dam and water-tower applications.

Determine the center of pressure and resultant hydrostatic force on a completely submerged plane surface in a homogeneous fluid, using the centroid, area, and eccentricity e = I_g / A.

Determine the hydrostatic force and action-line depth for a submerged semicircular plane surface, using diameter eight feet, area 25.1 ft², and y' dash 8.77 ft, yielding Yp about 8.9 ft.

Compute the hydrostatic resultant on an elliptical gate at the end of a four-meter pipe, using centroid pressure, to determine the opening force at the center of pressure.

Compute center of pressure for a submerged elliptical plate, using y_dash, y_p, and moment of inertia, to determine the opening force required at the hinge via equilibrium.

Compute hydrostatic forces on submerged curved surfaces by decomposing into horizontal and vertical components, then derive the resultant and its center of pressure for a practical gate example.

Apply Archimedes principle to buoyancy, linking the buoyant force to the weight of displaced fluid; determine submerged volume and density ratio to predict sinking, floating, or complete submersion.

Explore fluid kinematics, distinguishing open channel flow from closed channel flow (pipe) flow, driven by gravity or pressure gradient. Learn steady, unsteady, uniform, nonuniform, and laminar, turbulent, and transitional flows.

Apply Reynolds number, rho v D over mu, to distinguish laminar, transitional, and turbulent pipe flow; compare inertial and viscous forces with thresholds under 2000 and over 4000.

Learn how volume flow rate and discharge relate to cross section area and mean velocity through the continuity equation, with practical pipe and arterial flow examples.

Derive Bernoulli equation from energy conservation for incompressible, no-viscosity flow, balancing kinetic energy, pressure head, and elevation head between two sections. Note friction losses and the total energy line TEL.

Derives the Bernoulli energy equation between two flow sections by equating kinetic, pressure, and elevation heads, and accounts for energy losses and unit potential energy concepts.

Apply the Bernoulli equation to a Venturi meter to measure velocity and flow, using continuity and height difference to relate diameters to v2.

Apply Bernoulli to a venturi meter to relate throat velocity and pipe flow using Q = A2 V2 and the venturi constant k, with Cd correcting for hydraulic losses.

Apply Bernoulli's equation to tank emptying, derive v2 = sqrt(2 g h) and flow q = A2 v2, with atmospheric end pressures and negligible v1.

Derive tank emptying time using Bernoulli and continuity, with q = a sqrt(2gz) and T = 2A sqrt(H)/(a sqrt(2g)); illustrate with a numerical example.

The siphon uses the Bernoulli equation to empty tanks through a pipe above the liquid surface, deriving v3 equals sqrt(2 g H) and showing p2 < p atmosphere drives emptying.