![Fluid Matters](/img/default-banner.jpg)
- 137
- 1 431 468
Fluid Matters
Canada
เข้าร่วมเมื่อ 15 ต.ค. 2011
All Fluid Mechanics course videos at www.drdavidnaylor.net/
Dr. David Naylor, Professor of Mechanical Engineering in Toronto, Canada.
Dr. David Naylor, Professor of Mechanical Engineering in Toronto, Canada.
Solved Problem: Hydrostatic Calculation of the Mass of Earth's Atmosphere
MEC516/BME516 Fluid Mechanics, Chapter 2: A solved problem of calculating the mass of all the air in the Earth's atmosphere using basic hydrostatic principles: Pressure is caused by the weight of the air above the Earth's surface.
This problem has been reposted without a detailed discussion of the theory because many students are only seeking solved problems. This example was recently a midterm exam problem (for one of the other instructors) in this course.
All the videos in this course and hard copies (pdf) can be downloaded at: www.drdavidnaylor.net
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics
This problem has been reposted without a detailed discussion of the theory because many students are only seeking solved problems. This example was recently a midterm exam problem (for one of the other instructors) in this course.
All the videos in this course and hard copies (pdf) can be downloaded at: www.drdavidnaylor.net
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics
มุมมอง: 859
วีดีโอ
Solved Problem: Viscous Shear Stress using Newton's Law of Viscosity
มุมมอง 1.9K8 หลายเดือนก่อน
MEC516/BME516 Fluid Mechanics Chapter 1: This problem involves calculating the viscous shear stress in a thin oil layer using Newton's Law of Viscosity. This is a solved problem from a recent midterm exam. In Chapter 4, it is shown that velocity varies linearly in a thin layer of fluid with a moving boundary. This is called Couette flow: th-cam.com/video/ml2oiDORJmM/w-d-xo.html All the videos i...
The Reynolds Number and the Reynolds Apparatus
มุมมอง 1.4K9 หลายเดือนก่อน
MEC516/BME516 Fluid Mechanics: Osbourne Reynolds' famous experiment to characterize laminar to turbulent flow transition in a pipe is discussed. The Reynolds Apparatus is used to visualize laminar and turbulent flow in a round smooth pipe. The effect of the flow regime on pressure loss and pumping power is also discussed. This video is a supplement to MEC516/BME516 Lab 2. All the videos in this...
Watch This First! (Online Course Administration, Fall 2023)
มุมมอง 64111 หลายเดือนก่อน
An overview of the online course administration for Dr. Naylor's sections of Fluid Mechanics I for Fall 2023. I recommend that you start my course by watching this video. All the videos in this course and a copy (pdf) of the presentations can be downloaded at the course website: www.drdavidnaylor.net Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 20...
Lead climbing a 5.11+ at Joe Rockheads, Toronto
มุมมอง 130ปีที่แล้ว
Joe Rockheads, Toronto on June 19, 2023. It's an easy 5.11 after the second clip, but a new level on lead for me.
Quiz on the Saturation Temperature of Water
มุมมอง 675ปีที่แล้ว
MEC516/BME516 Fluid Mechanics Chapter 1: This is a Chapter 1 Quiz question about the boiling point of water. The key point is that the saturation temperature of water is a function of the absolute pressure. So, as the local atmospheric pressure changes (from day to day due to weather systems) the boiling temperature of water changes. All the videos in this course and a copy (pdf) of this presen...
Solved Exam Problem: Hydrostatic Forces on a Curved Gate
มุมมอง 6Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics: A solved exam problem of hydrostatic forces on a curved gate from a past midterm exam. This problem has been reposted without a detailed discussion of the theory because many students are only seeking solved problems. All the videos in this course and a copy (pdf) of this presentation can be downloaded at: www.drdavidnaylor.net Course Textbook: F.M. White and H. X...
Solved Buoyancy Problem: True Mass of Low Density Materials
มุมมอง 1.5Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics, Chapter 2: A short problem that demonstrates how to correct for buoyancy effects when weighing light materials with a weigh scale. This was a past Chapter 2 quiz problem. All the videos in this course and a copy (pdf) of this presentation can be downloaded at: www.drdavidnaylor.net Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, ...
Solved Problem: Linear Momentum Quiz
มุมมอง 7Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics, Chapter 3: A short quiz problem that demonstrates how to obtain an expression for the forces in a pipe elbow using the principle of conservation of linear momentum. A more detailed discussion of the general solution method (and the reason why gauge pressures must be used) is discussed in this video: th-cam.com/video/pk3nFNQRmFU/w-d-xo.html All the videos in this c...
Does Average Fluid Velocity Increase Along an Inclined Pipe?
มุมมอง 3.7Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics, Chapter 3: This short problem concerns the variation in the average velocity for incompressible flow in a pipe. Does the average flow velocity increase in an inclined pipe? The answer is NO! This problem is from a past Chapter 3 quiz. It demonstrates (and hopefully corrects) a very common misconception. This is an important concept for solving pipe flow problems i...
Navier-Stokes Final Exam Question (Liquid Film)
มุมมอง 23Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics I: A Fluid Mechanics Final Exam question on solving the Navier-Stokes equations (Chapter 4). The velocity and pressure fields are calculated for a gravity-driven liquid film on an inclined plate. This unique aspect of this problem is the no shear stress boundary condition at the top of the liquid film. All the videos in this course and a copy (pdf) of this presenta...
Fluid Mechanics: Solved Manometer Problem
มุมมอง 6Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics: A solved manometer problem from a previous Fluid Mechanics midterm exam. The problem involves calculating a pressure difference using fluid levels in a manometer. The pressure difference in the air-filled section is neglected because the density of gases is two orders of magnitude less than liquids. All the videos in this course and a copy (pdf) of this solution c...
Solved Problem: Dimensional Analysis of the Drag Force on a Plate
มุมมอง 1.9Kปีที่แล้ว
Dimensional analysis of the drag force on a bluff body using the Buckingham Pi Theorem and the Method of Repeating Variables. Sorry about the sibilance (s-sound). I had a microphone issue. A copy (pdf) of this solution can be downloaded at www.drdavidnaylor.net Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021. #archimedesprinciple #fluidmechanics...
Demonstration: Buoyancy Stability of Floating Objects
มุมมอง 5Kปีที่แล้ว
MEC516/BME516 Fluid Mechanics: A physical demonstration of the stability of floating objects. The model boat is stable when the center of mass is below the metacenter. When the center of mass is above the metacenter the model boat is unstable and overturns. The demonstration video has been adapted from the supplemental video materials of the textbook Young, D.F., Munson, B.R., Okiishi, T.H., an...
Solved Buoyancy Problem: Floating Objects
มุมมอง 4.3Kปีที่แล้ว
Solved Buoyancy Problem: Floating Objects
Solved Example: Hydrostatic Forces on a Vertical Gate
มุมมอง 53Kปีที่แล้ว
Solved Example: Hydrostatic Forces on a Vertical Gate
The Thermodynamics (and Math) of Compression Ignition
มุมมอง 4.2Kปีที่แล้ว
The Thermodynamics (and Math) of Compression Ignition
Solved Exam Problem: Hydrostatic Forces on a Curved Gate
มุมมอง 43Kปีที่แล้ว
Solved Exam Problem: Hydrostatic Forces on a Curved Gate
The Reynolds Experiment: Visualization of Flow Transition in a Pipe
มุมมอง 6Kปีที่แล้ว
The Reynolds Experiment: Visualization of Flow Transition in a Pipe
Demonstration: No Slip Condition in Fluid Mechanics
มุมมอง 3.6Kปีที่แล้ว
Demonstration: No Slip Condition in Fluid Mechanics
Joe Rockheads (5.10a), Toronto, June 27, 2022
มุมมอง 8782 ปีที่แล้ว
Joe Rockheads (5.10a), Toronto, June 27, 2022
Dimensional Analysis in Fluid Mechanics: Buckingham Pi Theorem
มุมมอง 8K2 ปีที่แล้ว
Dimensional Analysis in Fluid Mechanics: Buckingham Pi Theorem
Visualization of Opposing Mixed Convection from a Vertical Plate
มุมมอง 5012 ปีที่แล้ว
Visualization of Opposing Mixed Convection from a Vertical Plate
Derivation of the Continuity Equation for Fluid Flow
มุมมอง 32K3 ปีที่แล้ว
Derivation of the Continuity Equation for Fluid Flow
Fluid Mechanics Exam Problem: Hydrostatic Forces on a Plane Gate
มุมมอง 17K3 ปีที่แล้ว
Fluid Mechanics Exam Problem: Hydrostatic Forces on a Plane Gate
Introduction to Fluid Mechanics: Surface Tension
มุมมอง 12K3 ปีที่แล้ว
Introduction to Fluid Mechanics: Surface Tension
Odd Behavior of a Super-hydrophobic Razor Blade
มุมมอง 3623 ปีที่แล้ว
Odd Behavior of a Super-hydrophobic Razor Blade
Introduction to Fluid Mechanics: Vapor Pressure and Cavitation
มุมมอง 11K3 ปีที่แล้ว
Introduction to Fluid Mechanics: Vapor Pressure and Cavitation
Hi, when finding F_bc, since it is a vertical force, wouldn't the formula be F_bc = pgV ?
no. F_BC is the a fluid weight. F_BC is the upward pressure force on plane surface BC. The entire surface BC is a depth R. The pressure at this depth is rho*g*R, which gets multiplied by the surface area. I hope that helps.
❤ beautiful
I've got a question: in the example of discharge flow from a tank, if I put my finger at the discharge point, I see the speed of the discharging fluid is increasing, but Bernulli equation shows the discharge speed is not function of discharge diameter. Is there any explanation for that?
Interesting question. I haven't tried it, but I suspect your intuition is not correct. Try drilling a small hole and a larger hole at the same depth near the bottom of large plastic water bottle. My bet is that both water streams follow the same arc and extend the same distance from the bottle i.e., they have the same exit velocity. It would make a nice short video. I'm completely open to be proven wrong! Thanks for the question.
This channel is helpful for my research project.
Glad it helps. What's the project?
I wouldn't say that the rest of the analysis is easy (at 14:34). Firstly, because the term (r+dr)[dθdz] is missing in the formulation of the mass outflow on the infinitesimal area; if you follow this video only you can't arrive at the correct answer. Secondly, when you isolate the inflows and outflows across this face, you have to use the curious mathematical fact that dr^2 = 0 to get rid of one of the terms. Then, you have to see the odd step of multiplying some terms by r/r so you can factor a 1/r term out. Then, after more simplification, you're left with a term like (1/r)[ρVr+∂(ρVr)/∂r], and you have to recognize that the term in brackets is the same as ∂(rρVr)/∂r by virtue of the product rule of derivatives.
Hello Professor, may i know why F(AB) is not considered in the moment ?
FAB=FH. So, this force is considered, indirectly. When you take moments on the gates, you have to consider the forces of the water on the gate. I hope that helps.
This video is absolutely GOLD for someone like me struggling with fluid mechanics. Glad to find this on TH-cam!!
how is there a moment because of Fbc? not sure how that causes rotation
I suggest doing a review of basic statics. Fbc has a moment arm that will cause the gate to rotate CCW. It will act to open the gate.
I was wondering if, rather than taking the control volume such that V2 is perpendicular to the normal area vector, we took a rectangular box with no θ inclined edge. We would have a dot product of V2 . A = cosθ and hence a Rx = ρV²A (cos²θ -1). Which would mean the reaction force is dependent on the chosen control surface. What am I missing? :( Thanks for the video, it really helps me out!
The force is independent of the control volume you select. You are missing that the mass flow rate must to be calculated using the velocity normal to the control surface. See the explanation of mass flow rate here: th-cam.com/video/iffMXHFueSo/w-d-xo.htmlsi=RAaBqj6FX4djHgfM&t=321
@@FluidMatters Uhm, it makes sense then. Thanks a lot for the response!
Btw, that we an insightful question. I bet this will help other students with the same issue.
Can you explain why (at 1:05) the pressure forces act inwards as opposed to in the direction of flow / where in Chapter 2 specifically should I look to find out why?
p. 61 of the White text: "Pressure creates a force due to the molecules bombarding the surface, and it is normal to the surface." Fluid molecules bouncing off a surface push on the surface. So, the pressure force acts inward and normal to the surface. Also, see the proof of that pressure is a point property in Chapter 2, Fig. 2.1. Equilibrium on a small wedge of fluid. Think also about your experience. A balloon of air submerged in deep in water will get compressed by the water pressure, because the static pressure acts inward. If pressure acted outward, it would expand, which it certainly does not. I hope that helps.
@@FluidMattersthank you! That makes complete sense for the inlet… however, at the outlet, aren’t the molecules moving away from the surface (in the direction of flow) as opposed to pushing against the surface? maybe I am missing something?
@@arundhati.parikh The bulk motion of fluid is not the root cause of static pressure. Maybe this will help: Do you expect the outflow side of elbow to be held onto the pipe at the flange by suction? That's what you are thinking, which I hope you can sense is clearly not what happens.
Does this mean the Bernoulli Equation / Venturi effect can be applied to non ideal fluids as well? (approximately of course)
Yes. In real (viscous) fluids there are some energy losses. But "Bernoulli" is often still a good approximation for air and water, which both have low viscosity.
A submerged ball when released does not “rocket out of the water”. It rockets up when in the water, but only to reach the surface.
www.tiktok.com/@thelahayfamily/video/6846123958639578374?lang=en
Great video and explanation
Thanks. Glad to hear it was helpful.
Is it the no slip condition that causes the velocity gradient, professor or the internal shear stresses?
I'm not sure which part of this video you are specifically referring to. Here is a general answer. The fluid "sticks" to the surface i.e., the no slip condition. If the fluid above a stationary surface is moving (because of a pump or fan, for example), the fluid's viscosity will decrease (to zero) as you approach the surface. It's the internal viscous shear forces in the fluid, which opposes fluid motion, that slows the fluid in the near wall region. So, to answer your question, it is both effects. I hope that helps.
So, hypothetically speaking, even if there doesn't exist 'no-slip' at the bottom surface ( but the fluid sticks to the top surface) there would be a velocity gradient in the fluid, solely because of the internal friction between them. Am I right, professor?
I meant internal resistance between the fluid layers, alone, sir.
when you have losses, you add them to get to EGL?
Yes. The EGL remains constant only in the ideal friction case. But in the real world you always have energy losses in the flow direction. So, the EGL decreases because of energy losses (due to turbulence, wall viscous friction & pressure losses across a valve.) I hope that helps.
Thanks for this lecture Dr Neylor i have a question though at 11:42 is the height difference not supposed to be (Z3 - Z2) or it doesnt matter
Note that z is measured upward, i.e. Z2>Z3. You need that term to be positive, since you are moving downward into zone of higher pressure. So it must be Z2-Z3 to get a positive number. You might find it easier to work in terms of DeltaZ, where DeltaZ is always a positive value.
Thank you sir.
THIS VIDEO IS SO GOOD
All your videos helped a lot. Thank you so much!
I like this series
Is that a plaquette on a hinge?
🌹🌹
At 13:29, shouldn’t it be C1 = -1/(2*mu*b)*dp/dx - U/b and not C1 = -b/(2*mu)*dp/dx - U/b ? Doing the algebra, I feel the b should be in the bottom of the fraction and not the top. Can someone explain please?
Before simplification, we have b^2 in the numerator (from y^2 in the original expression applied at b). So, when you divide by b to isolate C1, you end up with b in the numerator. I hope that helps.
@@FluidMattersThanks! I didn’t see that
great stuff
Great stuff, for the last problem i see we have our origin placed midway between the plates, I would therefore expect the y at the bottom to be y = -h
Agree. The axis in the graphic (that I stole from the book publisher) is in the wrong place. But I think it's totally clear in the presentation that y=0 is at the bottom. At some point, a long time ago, I fixed it in the pdf download.
He saved my final exam😭😭😭
Point of Confusion for me - The cube as 6 faces with viscous stresses on each face. Therefore, there are 6 x 3 = 18 stresses on the differential element. Are we somehow saying that the stresses on opposite faces are the same, so that it is really only one? Then, all stresses are referred to a central point? What happens to the extra nine stresses?
OK, so you are not claiming that the nine stresses cover the entire differential volume. You are simply positing the stresses on three faces, and then using taylor series to get the stresses on the opposite face. The posited stress plus the Taylor-derived stress provide the stress on the entire cube.
best instructor
Thanks for the kind words. Best of luck with your studies.
thank you you are a great teacher
Hi professor, many thanks for the excellent lectures. I tried the derivation of the equation in cylindrical co-ordinates and I couldn't quite get there so ended up looking at another reference. Should the dA in the outlet term you show at 14:30 actually be (r+dr)dΘdz (rather than rdΘdz) to account for the slightly larger area at the outer radius? This is what the derivation I saw suggested.
Good point. Yes, I think you are correct.
thank you for your great explanation
from 3:40 on, why didn't we use the fluid for W and the wood for Fb?
As shown in the free body diagram, W is the weight of the WOOD and Fb is the buoyancy force. Thus, Fb is the weight of the WATER displaced by the wood (Archimedes principle). That is why I used the specific gravity of wood for W, and the specific gravity of water for Fb. I hope that helps.
@@FluidMatters Thank you!
I came just to check for a concept, then proceed to finish the whole series.
Glad to be able to help. Best of luck with your studies.
what da dog doing
Where is the vertical force acting on the top of the free body in no 2 prblm 7:55
If I'm understanding your question: There is no vertical force on "the top of the free body". The vertical force acts upward and equals the weight of the water, which acts downward.
@@FluidMatters if we considered only the upper left quarter of the circle instead of the semi circle then there would have been vertical force acting on the upper part of the quarter circle then why not for the semi circle?
At 6:57 inclined forces at the upper portion should have vertical components ..isn't it? Can u pls clarify?
Continue the videos sir ..... following your videos ... ..waiting to learn from you sir.....
Glad to hear you find them helpful. Good luck with your studies.
Just wanted to extend my thanks for putting together a great TH-cam series on Fluid Mechanics. Been a couple years since I've taken the class, the series has been a great refresher on the theory, in addition to tying it to some very informative experiments that visually cement the concepts 🙂
Thanks. Great to hear!
Why isn't d^2u/dy^2 not 0?
d2u/dy2=0 means that the velocity profile must be linear i.e. no curvature. There is no basis for this requirement, as you can see from the solution.
Nice job... Related to the FBD, do you need to include a Moment, M, along with the Fx & Fy? (assume a direction...?)
This analysis is based on conservation of LINEAR momentum. So the are the forces needed to redirect the jet. No moment.
THANKS A LOT SIR!!!!
Glad to hear it was helpful. Best of luck with your studies.
To estimate the impact force of a 5-meter fall from a 90 kg person, we can use the work-energy principle which states that the work done by the impact force is equal to the change in kinetic energy. When a person falls from a height, they gain kinetic energy, which is then absorbed by the impact. The kinetic energy (KE) just before impact is given by: $$ KE = \frac{1}{2} m v^2 $$ Where: - \( m \) is the mass (90 kg in this case), - \( v \) is the velocity at impact. The velocity at impact can be found using the equation for velocity of an object in free fall: $$ v = \sqrt{2gh} $$ Where: - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)), - \( h \) is the height of the fall (5 meters). Substituting the values, we get: $$ v = \sqrt{2 \times 9.81 \, m/s^2 \times 5 \, m} $$ $$ v = \sqrt{98.1 \, m^2/s^2} $$ $$ v \approx 9.9 \, m/s $$ Now we can calculate the kinetic energy: $$ KE = \frac{1}{2} \times 90 \, kg \times (9.9 \, m/s)^2 $$ $$ KE = \frac{1}{2} \times 90 \, kg \times 98.01 \, m^2/s^2 $$ $$ KE = 4410.45 \, J $$ The impact force (F) can then be estimated if we know the distance over which the impact force acts (d), which is the distance over which the person's momentum is brought to zero. This distance will depend on many factors, including how the person lands and the nature of the surface they land on. Assuming a certain stopping distance, we can use the formula: $$ F = \frac{KE}{d} $$ For example, if the person comes to a stop over a distance of 0.5 meters, the impact force would be: $$ F = \frac{4410.45 \, J}{0.5 \, m} $$ $$ F = 8820.9 \, N $$ So the impact force would be approximately **8820.9 Newtons**. Please note that this is a simplified calculation and the actual impact force can vary. For accurate results, especially for safety considerations or engineering applications, a detailed analysis considering all relevant factors would be necessary. Source: Conversation with Bing, 4/30/2024 (1) Impact Force Calculator - Calculate the impact force in a collision. www.gigacalculator.com/calculators/impact-force-calculator.php. (2) Impact Force - The Engineering ToolBox. www.engineeringtoolbox.com/impact-force-d_1780.html. (3) Free Fall Force Calculator Online. calculatorshub.net/physics-calculators/free-fall-force-calculator/. (4) Impact Force Calculator | Calculate Impact Force in Collision .... physicscalc.com/physics/impact-force-calculator/. (5) Impact Energy Calculator | Impact Force. www.omnicalculator.com/physics/impact-energy.
ok
Cool video!
Greetings from Turkey, this material helped me a lot. Thanks professor.
hi professor, why are there no videos for content past chapter 5?
That's where the intro fluid mechanics course ends at my university. I don't teach "Fluids II", at least for now.
Impressive profound experiment and explanation. Additionally, I encountered numerous novel ideas in the comments section here.
Thanks for the kind words. A colleague and I ended up writing a paper on this effect.
These interesting videos make your tutorial more and more attractive. These formulas jump out of the screen and appear in our lives. Thank you for your amazing idea!
Nice! Chapter 2 completed!!Next is the two ptional videos haha.
I can’t stop learning, so take a break, click the like button, and then continue!
why do I have a course called wave physics and fluid mechanics? I think both are hard enough on their own 🥲
Must be a different Dr. Naylor for the wave physics....
Sir where can i get its theory part...
Here's the theory lecture for hydrostatic forces on curved surfaces: th-cam.com/video/LdbEpRXUpOQ/w-d-xo.htmlsi=DoySt3zv_nYTipHn You can find all the lectures as www.drdavidnaylor.net