- Видео 33
- Просмотров 187 664
Caspar Hewett
Великобритания
Добавлен 11 сен 2012
Short videos covering various aspects of fluid mechanics, civil engineering hydraulics and computational hydraulics, including hydrostatics, derivations of the fundamental equations (conservation of mass, energy and momentum), flow measurement (weirs and orifices), finite difference methods for advection and diffusion.
Logarithms 1: What is a logarithm?
Definition of what is meant by a logarithm motivated by examining the behaviour of the exponential function to base 2.
Просмотров: 34
Видео
Numerical Integration - trapezium rule and Simpson's rule
Просмотров 755 месяцев назад
Derivation of two methods for performing numerical integration - the first, the trapezium or trapezoidal rule, is a first order method and the second, Simpson’s rule, is second order.
Definite Integration
Просмотров 476 месяцев назад
This video motivates the process of definite integration as a means of finding the area under a curve and examines how to use definite integration to calculate the average value of a function. For those unfamiliar with indefinite integration, which is the reverse of differentiation, then you should watch my video “What is Integration?” before this one.
Non-linear equations: The Newton-Raphson method
Просмотров 2948 месяцев назад
Derivation and example applications of the Newton-Raphson method, which is an iterative numerical procedure for finding the root of a non-linear equation.
Stability & Accuracy of Numerical Schemes (2024)
Просмотров 4568 месяцев назад
Definition of terms stability and accuracy and discussion of four features of numerical schemes that effect the stability and accuracy of their solutions: Numerical diffusion (which was discussed in depth in a previous video), bounded solutions, the Courant-Friedrichs-Lewy, or CFL, condition, & linear stability analysis. This video links with previous videos on Finite Difference Schemes for Adv...
Understanding Calculus: What Is Integration?
Просмотров 699 месяцев назад
Introduction to indefinite integration, which is the reverse of differentiation. This video discusses why there is a constant of integration in this procedure and what it means, and presents examples of indefinite integration of functions including powers of x, exponential functions, the natural logarithm and the primary trigonometric functions: sine, cosine and tangent.
Understanding Exponential Functions
Просмотров 459 месяцев назад
Introduction to exponential functions (functions of the form y = a to the power of x). This video covers the functions with base 2 (2 to the power of x), and base 3 and introduces the special case, usually called the exponential function, which has base e and has special properties under differentiation. The natural logarithm is introduced as the inverse of the exponential function and its diff...
The Chain Rule (Calculus 3)
Просмотров 649 месяцев назад
Derivation of the chain rule which is the method used to differentiate a function of a function.
Differentiating Trigonometric Functions (Calculus 2)
Просмотров 479 месяцев назад
The differentials of sine and cosine are derived from first principles. This video includes the definition of the radian and first order small angle approximations for sine and cosine.
What Is Differentiation? (Calculus 1) Differentiation from first principles.
Просмотров 147Год назад
Introduction to the notion of differentiation to describe the instantaneous rate of change of a function. A general expression for the differential or derivative is derived and an example of differentiation from first principles given using the function f(x) = x cubed.
Consistency and Numerical Diffusion
Просмотров 4,3 тыс.3 года назад
Consistency and Numerical Diffusion
Finite Difference Schemes for Advection and Diffusion
Просмотров 15 тыс.3 года назад
Derivation of first order explicit finite difference schemes for the advection-diffusion equation including discussion of boundary conditions.
Implicit Upwind Finite Difference Solution to the Advection Equation
Просмотров 4,1 тыс.3 года назад
Implicit Upwind Finite Difference Solution to the Advection Equation
Explicit Upwind Finite Difference Solution to the Advection Equation
Просмотров 12 тыс.3 года назад
Explicit Upwind Finite Difference Solution to the Advection Equation
Fluid Mechanics: The Continuity Equation
Просмотров 1,8 тыс.3 года назад
Fluid Mechanics: The Continuity Equation
Finite difference approximations to the first derivative
Просмотров 5 тыс.3 года назад
Finite difference approximations to the first derivative
Hydraulic River Modelling: Muskingum-Cunge
Просмотров 4 тыс.3 года назад
Hydraulic River Modelling: Muskingum-Cunge
Kinematic Wave Solution to 1D Shallow Water Equations
Просмотров 6 тыс.4 года назад
Kinematic Wave Solution to 1D Shallow Water Equations
Hydrostatics: Hydraulic Thrust Calculation Using Pressure Prisms
Просмотров 2,4 тыс.4 года назад
Hydrostatics: Hydraulic Thrust Calculation Using Pressure Prisms
Hydrostatics: Hydraulic Thrust On Plane Surfaces
Просмотров 1,8 тыс.4 года назад
Hydrostatics: Hydraulic Thrust On Plane Surfaces
Hydrostatics: Hydraulic Thrust on Curved Surfaces Part 2: Examples
Просмотров 4974 года назад
Hydrostatics: Hydraulic Thrust on Curved Surfaces Part 2: Examples
Hydrostatics: Hydraulic Thrust on Curved Surfaces Part 1
Просмотров 8414 года назад
Hydrostatics: Hydraulic Thrust on Curved Surfaces Part 1
Fluid Mechanics: Applications of the Fundamental Equations
Просмотров 6324 года назад
Fluid Mechanics: Applications of the Fundamental Equations
Fluid Mechanics: The Momentum Equation
Просмотров 43 тыс.4 года назад
Fluid Mechanics: The Momentum Equation
Fluid Mechanics: The Bernoulli Equation
Просмотров 6344 года назад
Fluid Mechanics: The Bernoulli Equation
Swale leaky barrier experiment 22/8/19
Просмотров 1514 года назад
Swale leaky barrier experiment 22/8/19
great job
i wish you would be my teacher. amazing
EXCELLENT-- WHICH UNIVERSITY ? -WHICH COUNTRY ?
Newcastle University, UK
@@CasparHewettFluids thank u sir
Please someone help me out, I have a tube well with 3 inches delivery and water is pulled by a 7.5 hp submersible pump system. What I am planning to do is to reuse the water force which falls out and to produce electricity or mechanical power. What output can be obtained and which system is more efficient, micro hydro turbine or a propeller.
Hi, Thank you for the good explanation. I'm personally interested in how you can use it to solve a nonlinear reaction diffusion equation. How would you go about analysis its stability in relation to the Von Neumann Stability condition? Thank you in advance.
👌👌👌
Was this video inspired by a publication or academic resource? I would be interested in learning more about the stability analysis!
No, I wrote the material myself for a course. I will be publishing a book on Computational Hydraulics later this year, though, which will expand on this material.
Why is the momentum force in the opposite direction as the pressure force? Seems like they would both be acting in the same direction, no?🤔
There are two elements of the momentum. The momentum into the control volume, which acts in the same direction as the pressure and the momentum out of the control volume which is in the opposite direction to the pressure
The pressure forces are those acting on the control volume, which is why they are both inward
Very good, detailed analysis. The figures and equations are beautifully rendered. Thanks!
Perfect, just explained in 5 mins what took hours to be taught badly in university.
Great video! But why can't I find anyone explaining 3-pt 1st-order FD?
Hello! Is there a way we could send you an email?
Do you have a question? I will do my best to answer it here!
Hello, what is ubar in the bousinesque equation
Is it like the average velocity or what?
@@danielhakimzambri892 yes, it is the average velocity 😉
@@CasparHewettFluids thanks
Well explained Keep up the good work 👍
Shukran jidan!
what is bournolis ?
Is the beam warming scheme is implicit
What basics should i study more to understand this?
if we consider a 90-degree bend pipe, with initial conditions as follows: inlet velocity 15 m/s, no change in cross-section area (let's say radius of 0.2 m), and we only know outlet pressure is equal to atmospheric pressure. Is Bernoulli's equation satisfied? does it mean outlet and inlet pressure are the same? in that case, there's no flow?!
Bernoulli equation is satisfied within the pipe so pressure will be constant if the pipe is horizontal, resulting in a jet at the outlet. The pressure in the pipe can't be atmospheric pressure if the water has a velocity! Conditions are different once water reaches the outlet. Thus, the problem you pose can't be solved. There is insufficient information. You would need to know the pressure in the pipe.
at 11:29 your wrote incorrect solution please review it. It should be (r - rho)*c(i+1),(j)
What a wonderful video!!!!!!
Would the vertical pressure force still be oriented downward if the curved pipe was facing down not up?
No, the pressure force always acts inwards towards the control volume so it would be acting upwards if the pipe were facing downward.
excellent explanations! I wish I had such an articulate professor when I studied open channel hydraulics at university.
this is amazing, thank you!
Thank you professor
Great video. Thank you
The last image looks just like B-Spline basis functions. Is my assumption right, or wrong?
Thanks a lot sir.
Very well explained. Thanks a lot!
Why is density not included in the Bernoulli equation?
P/dg=H-z1
Well presented, thank you Caspar!
It helped me a lot. Can you tell me how did you define initial distribution?
How do we determine the direction of pressure force?
We are considering the forces on the control volume, so the pressure force is acting inwards on that control volume (there is an equal and opposite pressure force outward, but that isn't relevant to the calculation) thus it is acting to the right on the left hand side and to the left on the right hand side.
such a nice video! well done!
hello, i stumbled upon a exercise that was similar to the last example but the curve was divided in half by two fluids. Would the resultant vertical force be the same?
The best 1d hydrodinamic equation explanation video!!!
u da mvp!
Thank you. I learned a lot from this video
Very good explanation. Thank you (again), Caspar.
Thank you. Well explained.
Very neatly explained, Caspar; thank you.
Great video
This is priceless!! cant be explained in a better way. Thank you for your effort.
Thanks alot. This was very helpful.
Why isn’t there a Q1 and Q2? In other words why can we assume that A1u1=A2u2=Q ?
law of continuity, Q1 = Q2 = Q
@@abdulkabiraduragba5240 Thanks!
Absolutely fantastic. Great class, prof. Caspar.
On the summation of y direction forces, pQu is it not a negetive sir.
If you mean in the example of the vertical bend you are correct, the outward momentum (not force) is in positive y direction, but you need to remember that for the momentum equation in the y-direction it is momentum out (i.e. is on the right hand side of the equation).
@@CasparHewettFluids omg true
It is a very clear explanation. Thanks a lot
Thank you prof
P/dg=H-z1
thank you and do you have matlab code for that?