Caspar Hewett
Caspar Hewett
  • Видео 33
  • Просмотров 187 664
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.
Flow Measurement: Orifices
Просмотров 10 тыс.3 года назад
Flow Measurement: Orifices
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
1D Hydrodynamic Models
Просмотров 12 тыс.3 года назад
1D Hydrodynamic Models
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
Flow Measurement: Weirs
Просмотров 58 тыс.4 года назад
Flow Measurement: Weirs
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
Hydrostatic Pressure Distribution
Просмотров 2,7 тыс.4 года назад
Hydrostatic Pressure Distribution
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

Комментарии

  • @landrynoune2897
    @landrynoune2897 Месяц назад

    great job

  • @wooyoungsdoormat3853
    @wooyoungsdoormat3853 2 месяца назад

    i wish you would be my teacher. amazing

  • @kaursingh637
    @kaursingh637 3 месяца назад

    EXCELLENT-- WHICH UNIVERSITY ? -WHICH COUNTRY ?

  • @Daudweatherforcast
    @Daudweatherforcast 3 месяца назад

    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.

  • @musisipascal2370
    @musisipascal2370 3 месяца назад

    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.

  • @mohammadkhalili3247
    @mohammadkhalili3247 4 месяца назад

    👌👌👌

  • @WilliamRobert-od9vl
    @WilliamRobert-od9vl 5 месяцев назад

    Was this video inspired by a publication or academic resource? I would be interested in learning more about the stability analysis!

    • @CasparHewettFluids
      @CasparHewettFluids 5 месяцев назад

      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.

  • @ghbbllk4095
    @ghbbllk4095 5 месяцев назад

    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?🤔

    • @CasparHewettFluids
      @CasparHewettFluids 5 месяцев назад

      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

    • @CasparHewettFluids
      @CasparHewettFluids 5 месяцев назад

      The pressure forces are those acting on the control volume, which is why they are both inward

  • @DanTercelify
    @DanTercelify 5 месяцев назад

    Very good, detailed analysis. The figures and equations are beautifully rendered. Thanks!

  • @mrmagoo-i2l
    @mrmagoo-i2l 6 месяцев назад

    Perfect, just explained in 5 mins what took hours to be taught badly in university.

  • @HelloWorlds__JTS
    @HelloWorlds__JTS 7 месяцев назад

    Great video! But why can't I find anyone explaining 3-pt 1st-order FD?

  • @4_Gatitos
    @4_Gatitos 7 месяцев назад

    Hello! Is there a way we could send you an email?

    • @CasparHewettFluids
      @CasparHewettFluids 7 месяцев назад

      Do you have a question? I will do my best to answer it here!

  • @danielhakimzambri892
    @danielhakimzambri892 8 месяцев назад

    Hello, what is ubar in the bousinesque equation

  • @hhhberzerk5353
    @hhhberzerk5353 8 месяцев назад

    Well explained Keep up the good work 👍

  • @olooalfredo
    @olooalfredo 9 месяцев назад

    Shukran jidan!

  • @gopalashetty3592
    @gopalashetty3592 9 месяцев назад

    what is bournolis ?

  • @ernestjesly
    @ernestjesly 10 месяцев назад

    Is the beam warming scheme is implicit

  • @ernestjesly
    @ernestjesly 10 месяцев назад

    What basics should i study more to understand this?

  • @mohsen9828
    @mohsen9828 Год назад

    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?!

    • @CasparHewettFluids
      @CasparHewettFluids 3 месяца назад

      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.

  • @ayushsharma7044
    @ayushsharma7044 Год назад

    at 11:29 your wrote incorrect solution please review it. It should be (r - rho)*c(i+1),(j)

  • @nawaf8099
    @nawaf8099 Год назад

    What a wonderful video!!!!!!

  • @liambond3569
    @liambond3569 Год назад

    Would the vertical pressure force still be oriented downward if the curved pipe was facing down not up?

    • @CasparHewettFluids
      @CasparHewettFluids Год назад

      No, the pressure force always acts inwards towards the control volume so it would be acting upwards if the pipe were facing downward.

  • @pmt4297
    @pmt4297 Год назад

    excellent explanations! I wish I had such an articulate professor when I studied open channel hydraulics at university.

  • @adhimta3306
    @adhimta3306 Год назад

    this is amazing, thank you!

  • @JALAJDARPAN
    @JALAJDARPAN Год назад

    Thank you professor

  • @AJ-et3vf
    @AJ-et3vf Год назад

    Great video. Thank you

  • @miholju
    @miholju Год назад

    The last image looks just like B-Spline basis functions. Is my assumption right, or wrong?

  • @-HenguljyotiGayan
    @-HenguljyotiGayan Год назад

    Thanks a lot sir.

  • @jonathans.4046
    @jonathans.4046 Год назад

    Very well explained. Thanks a lot!

  • @nathancarpenter8895
    @nathancarpenter8895 Год назад

    Why is density not included in the Bernoulli equation?

  • @josephtraverso5355
    @josephtraverso5355 Год назад

    Well presented, thank you Caspar!

  • @mBilalAcademy
    @mBilalAcademy Год назад

    It helped me a lot. Can you tell me how did you define initial distribution?

  • @pippakolking1998
    @pippakolking1998 Год назад

    How do we determine the direction of pressure force?

    • @CasparHewettFluids
      @CasparHewettFluids Год назад

      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.

  • @elispot17
    @elispot17 Год назад

    such a nice video! well done!

  • @madalenamedeiros4371
    @madalenamedeiros4371 Год назад

    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?

  • @elispot17
    @elispot17 Год назад

    The best 1d hydrodinamic equation explanation video!!!

  • @marioforster5278
    @marioforster5278 2 года назад

    u da mvp!

  • @quangdang4884
    @quangdang4884 2 года назад

    Thank you. I learned a lot from this video

  • @freespirit5680
    @freespirit5680 2 года назад

    Very good explanation. Thank you (again), Caspar.

  • @freespirit5680
    @freespirit5680 2 года назад

    Thank you. Well explained.

  • @freespirit5680
    @freespirit5680 2 года назад

    Very neatly explained, Caspar; thank you.

  • @alejandroespino4773
    @alejandroespino4773 2 года назад

    Great video

  • @othmana2979
    @othmana2979 2 года назад

    This is priceless!! cant be explained in a better way. Thank you for your effort.

  • @othmana2979
    @othmana2979 2 года назад

    Thanks alot. This was very helpful.

  • @lightspd714
    @lightspd714 2 года назад

    Why isn’t there a Q1 and Q2? In other words why can we assume that A1u1=A2u2=Q ?

  • @marcusnobrega7526
    @marcusnobrega7526 2 года назад

    Absolutely fantastic. Great class, prof. Caspar.

  • @blessingamosmatunya8908
    @blessingamosmatunya8908 2 года назад

    On the summation of y direction forces, pQu is it not a negetive sir.

    • @CasparHewettFluids
      @CasparHewettFluids Год назад

      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).

    • @mpt2878
      @mpt2878 Год назад

      ​@@CasparHewettFluids omg true

  • @neranjanranaweera7411
    @neranjanranaweera7411 2 года назад

    It is a very clear explanation. Thanks a lot

  • @intanputridamarani976
    @intanputridamarani976 2 года назад

    Thank you prof

  • @sathyanov7552
    @sathyanov7552 2 года назад

    thank you and do you have matlab code for that?