Fundamentals of Fluid Mechanics

Name: Fundamentals of Fluid Mechanics
Rating: 4.4 (156 reviews)

Master Fluid Mechanics Principles: In-Depth Concepts, Real-World Applications & 37 Solved Problems for Enhanced Learning

Created byProf. Samer

Last updated 9/2020

English

What you'll learn

Determine the variation of pressure in a fluid at rest
Calculate the forces and moments exerted by a fluid at rest on plane or curved submerged surfaces
Have a working knowledge of viscosity and the consequences of the frictional effects it causes in fluid flow
Calculate the capillary rise (or drop) in tubes due to the surface tension effect
Utilize Integral relations for a control volume and differential relations for fluid particles to analyze fluid flow problems.
Use control volume analysis to determine the forces associated with fluid flow

Course content

4 sections • 69 lectures • 8h 20m total length

The Concept of a Fluid5:21
Explore how solids deform elastically under shear and recover, while fluids continuously deform under shear, reaching a constant shear rate and illustrating the fundamental difference between fluids and solids.
Measures of Fluid Mass and Weight10:32
Define density as mass per unit volume, relate it to specific weight, the reciprocal of density (specific volume), and specific gravity, and note how temperature affects liquids and gases.
The Ideal Gas Law8:43
Derive and apply the ideal gas law to relate pressure, density, and temperature, and distinguish absolute versus gauge pressure with SI and English units.
Example 14:21
Apply the ideal gas law to compute density, specific gravity, and mass for a room using the given pressure, temperature, and volume. Derive density ≈ 1.17 kg/m3.
Viscosity13:26
Explore viscosity as the internal resistance to flow, the no-slip boundary condition between parallel plates, and newtonian fluids where shear stress is proportional to the velocity gradient via dynamic viscosity.
Non-Newtonian Fluids6:53
Explore Newtonian fluids with constant dynamic viscosity across shear rates, and non-Newtonian fluids where viscosity changes with shear rate, including shear thickening, shear thinning, and yield-stress behavior like Bingham plastics.
Viscosity vs Temperature5:31
Explore how viscosity decreases with temperature for liquids due to molecular collisions and weaker cohesive forces, while gas viscosity increases with temperature; learn correlations with constants to estimate viscosities.
Example 23:37
Example 37:24
Solve example 3 to determine fluid viscosity by relating torque to shear stress in a narrow gap between concentric cylinders, applying no-slip boundary conditions and a linear velocity profile.
Example 45:31
Explain how a block on a lubricated incline reaches terminal velocity as viscous shear from a thin oil film balances its weight component, using linear velocity distribution and non-slip boundaries.
Example 53:20
model the belt-driven oil contact with a linear velocity profile, showing how shear stress yields belt power P = mu V^2 B / H and a calculation around 73 W.
Compressibility of Fluids9:37
Define bulk modulus of elasticity as the pressure change over relative volume change and note that increased pressure decreases volume. Compare liquids and gases in compressibility and describe isothermal compression of a gas.
Speed of Sound and Mach Number17:26
Analyze the speed of sound and Mach number in a pressure wave, linking pressure, density, and enthalpy changes. Explain incompressible criteria and the isentropic ideal-gas relation for velocity of sound.
Example 63:53
Derive the speed of sound at 33,500 feet using gamma 1.4 and the gas constant, convert 550 mph to ft/s, and show subsonic flight.
Vapor Pressure10:19
Explain how evaporation and condensation reach equilibrium to create vapor pressure, and how boiling occurs when vapor pressure equals atmospheric pressure; highlight cavitation avoidance in pumps.
Example 72:10
Compute the torpedo cavitation velocity in freshwater at 10 degrees Celsius by equating the minimum pressure to the water vapor pressure, solving for v, giving about 18 m/s.
Surface Tension11:18
Explore surface tension from imbalanced surface forces, showing why surface molecules pull inward and droplets become spheres, and derive ΔP = 2σ/R for internal–external pressure difference.
Capillary Effect10:46
Example 82:30
This example analyzes capillary rise in a glass tube, using water properties at 20 degrees Celsius, surface tension, contact angle, and specific weight to determine the minimum diameter.
Example 92:14
Explore capillary rise in a tiny diameter tube by analyzing water in capillaries, given a 15-degree contact angle at 20 °C, with surface tension guiding the height.
Example 104:05
Explore how surface tension lets a steel ball float on water by balancing surface-tension force and weight, yielding the maximum diameter for density 7800 kg/m^3 at 10 C.
A-1: Physical Properties of Water (English Units)0:04
A-2: Physical Properties of Water (SI Units)0:04

Pressure Variation in a Fluid at Rest8:10
In a fluid at rest, pressure is the same at all points on a horizontal plane and varies with vertical position according to dp/dz = -gamma.
Hydrostatic Pressure in Gases8:19
Explore hydrostatic pressure in liquids and gases using incompressible density and the ideal gas law; relate P2 to P1 via isothermal and lapse-rate models.
The Mercury Barometer4:50
Demonstrates the mercury barometer, a simple hydrostatic formula that links atmospheric pressure to mercury height in a tube; mercury's high density keeps the height small.
Example 17:16
This lecture shows how a hydraulic jack uses a small and a large piston to lift a car by transmitting pressure through oil, with equal pressures determining the holding force.
Example 24:55
Compare exact atmospheric pressure calculations with isothermal assumptions, applying lapse rate and standard temperature to estimate pressure at 5000 meters and assess error.
Application to Manometry8:17
Calculate the chamber pressure relative to atmosphere using a manometer and hydrostatic relations across fluid levels while considering fluid densities and level changes.
A Complicated Manometer3:27
Explore a complicated multi-fluid manometer used to determine the pressure difference Pa minus Pb between chamber a and chamber b by tracing pressure changes through fluids of varying densities.
Example 33:10
Explore how to compute pressure differences between two horizontal points using a manometer, accounting for height changes, density, and distance traveled to relate pA and pB.
Example 43:06
Relate pressures between points A and B in a fluid layer (water, mercury, oil) using hydrostatics and an 87 kPa gauge to estimate pressure at point A, about 96.35 kPa.
Example 52:53
Compute the interface height H in a two-layer oil-water system by balancing hydrostatic pressures with densities 898 and 909 under atmospheric conditions, yielding H = 0.08 m.
Example 62:56
Examine hydrostatics in open-tank and open-tube setups, relating atmospheric pressure and vertical distances to water height, calculated via specific gravity in example 6.
Hydrostatic Forces on Plane Surfaces6:49
Compute hydrostatic force on a submerged plane surface by evaluating the pressure at the surface's center of gravity, P_cg = P_atm + gamma h_cg, and multiplying by the area A.
The Center of Pressure17:09
Explore how the center of pressure, determined from hydrostatic moments and the product moment of inertia Ixy, lies below the center of gravity for plane surfaces.
Example 710:43
Example 810:32
Compute the weight of a 180 kg gate and the hydrostatic force from the water at depth h, then use a free-body diagram to determine reactions at A and B.
Hydrostatic Forces on Curved Surfaces4:45
Examine hydrostatic forces on curved surfaces by decomposing the resultant into horizontal and vertical components, using projection onto a vertical plane and the plane surface formula.
Example 918:13
Compute hydrostatic forces on a parabolic dam surface, decompose into horizontal and vertical components, and locate the center of pressure where the resultant intersects the curved surface.
Example 107:30
Compute the resultant hydrostatic force on a benzene-filled tank with an air gap, combining weight and pressure distribution to locate the equivalent force and its line of action.
Buoyancy8:59
Example 111:39
Example 126:07
an underwater cylindrical rod with a 2 kg lead mass is analyzed via a free-body diagram and static equilibrium to determine the rod’s specific gravity, balancing buoyancy and weight.
A-3 Moments of Inertia for Various Cross Sections0:02

The Reynolds Transport Theorem24:48
The Reynolds transport theorem links the time rate of change of a property for a system to its rate within a control volume, accounting for influx and outflux across boundaries.
Conservation of Mass10:42
Apply mass conservation for fixed-mass systems with Reynolds transport theorem, linking mass flux across control volumes and surfaces in steady incompressible flow where Q equals A V.
Example 19:45
Example 24:47
Apply mass conservation to a tank using a control volume to relate inflows Q1, Q2, and Q3 and water level change; in steady state, Q2 = Q1 + Q3.
Example 35:45
Explore one-dimensional compressible flow through a converging and diverging nozzle, computing mass flow and exit velocity using ideal gas law, revealing a supersonic flow with Mach 3.41.
Example 45:05
The Linear Momentum Equation15:21
Example 55:01
Assess a nozzle’s pressure forces using a nonuniform surface distribution; derive 25 psi on section one and conclude a net 177 pound force to the right.
Example 62:41
Apply the linear momentum equation to a steady, one-dimensional tube flow with uniform inlets and outlets, deriving the net force on the control volume from mass conservation and momentum.
Example 79:04
Example 85:15
Compute the gate force in steady incompressible flow by a control-volume approach, neglecting friction and atmospheric pressure, and relate inlet/outlet velocities and areas via mass conservation.
The Bernoulli Equation24:12
Explore the Bernoulli equation in steady, incompressible, frictionless flow, applying along a streamline to relate pressure, velocity, and potential energy while deriving energy conservation insights.
Static, Dynamic, and Stagnation Pressures10:46
Investigate static, dynamic, and stagnation pressures and measure flow velocity with a pitot-static tube, linking total pressure to pressure components along streamlines.
The Energy Line and the Hydraulic Grade Line12:18
Example 93:05
Apply Bernoulli's equation to a garden hose jet to relate velocity, pressure, and height; show the ideal maximum height is 40.8 m, reduced by friction in reality.
Example 102:57
Apply Bernoulli's equation to an open tank 5 meters above the outlet, assuming atmospheric pressure and negligible surface velocity, yielding v2 approximately 9.9 m/s; real flow is lower.
Example 114:05
Using a pitot tube tapped into a horizontal pipe, apply Bernoulli to relate stagnation and static pressures to the velocity via the height difference of the water column.
Example 126:22
Apply Bernoulli and continuity to a venturi meter example, linking area change to velocity increase and pressure drop, and explain discharge coefficient accounting for frictional losses.
Example 136:03
Apply a control-volume momentum approach to determine the force exerted by the bolts to hold the nozzle and hose, using Bernoulli and incompressible flow relations for nozzle and exit conditions.
The Energy Equation11:25
Explore the energy equation for a control volume, linking energy per unit mass to internal, kinetic, and potential energy, heat transfer, and work, culminating in enthalpy concepts.
Energy Analysis of Steady Flows13:42
Apply the steady-state, one-dimensional energy equation to a control volume between inlet and outlet, balancing pressure head, velocity head, and elevation with heat transfer and pump or turbine losses.
Example 143:17
Compute the hydroelectric turbine output for example 14 using a 30 m^3/s flow, head 89.8 m, density 1000 kg/m^3, g 9.81 m/s^2, and 80% efficiency to obtain about 21.14 megawatts.
Example 154:42
Apply the energy equation to pump water from lower to upper elevation, accounting for elevation gain and friction head; determine velocity, flow rate, and horsepower with pump efficiency.

Requirements

Physics and Calculus

Description

Discover Fluid Mechanics Fundamentals: In-Depth Concepts, Practical Applications & Problem Solving with 37 Solved Examples

Dive into the fascinating world of fluid mechanics with this comprehensive course, designed to introduce you to the essential fluid properties, viscosity, surface tension, and pressure distribution in fluids. Gain a deep understanding of hydrostatic forces on plane and curved surfaces, buoyancy, and pressure measurement techniques using manometers and barometers.

This course covers integral relations for a control volume, including mass conservation, linear momentum equation, energy, and Bernoulli equations, providing you with a solid foundation in fluid mechanics principles. To ensure a thorough understanding and bridge the gap between knowledge and application, we have incorporated 37 solved problems throughout the course, helping you grasp the concepts with real-world examples.

Key Topics Covered:

Fluid properties: Explore the fundamentals of fluid mechanics, including fluid properties and their significance in various applications.
Viscosity and surface tension: Understand the critical role of viscosity and surface tension in fluid dynamics and their impact on fluid behavior.
Pressure distribution: Learn about pressure distribution in fluids and how it influences fluid flow and interactions with various surfaces.
Hydrostatic forces: Examine the hydrostatic forces acting on plane and curved surfaces and their implications in practical scenarios.
Buoyancy and pressure measurement: Discover the principles of buoyancy and pressure measurement techniques using manometers and barometers, essential tools in fluid mechanics.
Integral relations for a control volume: Master the integral relations for a control volume, including mass conservation, linear momentum equation, energy, and Bernoulli equations.
Problem-solving: Strengthen your understanding of fluid mechanics concepts through 37 solved problems, connecting theory with real-world applications.

Embark on your fluid mechanics journey and enhance your knowledge and problem-solving skills in this critical field. Enroll now for a comprehensive learning experience!

Who this course is for:

Engineering Students

Fundamentals of Fluid Mechanics

What you'll learn

Explore related topics

Course content

Introduction23 lectures • 2hr 29min

Pressure and Fluid Statics22 lectures • 2hr 30min

Integral Relations for a Control Volume23 lectures • 3hr 21min

Bonus Section: Coupons for all courses1 lecture • 1min

Requirements

Description

Who this course is for: