Fluid Mechanics: Centrifugal Pump Characteristics (21 of 34)

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  • Опубліковано 12 січ 2025

КОМЕНТАРІ • 202

  • @mikeearls126
    @mikeearls126 6 років тому +25

    I am utterly amazed watching these videos...i am a 50 year old guy who was never good in math and science but have an overabundance of curiosity about how things work. I feel lucky to live in a time where i can look anything up on youtube and get some undestanding about how the physical world works around me. Also, i had no idea how involved pumps were...meaning the engineering behind the pump.

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому +4

      We feel lucky to live in a time where it is possible to leverage our efforts to help others well-beyond the classroom.

    • @craigbain1645
      @craigbain1645 5 років тому +1

      @@CPPMechEngTutorials thank you for your posts. I feel lost sometimes watching these things but rely on osmosis. Knowledge helps us all thanks

  • @celospiky329
    @celospiky329 6 місяців тому +2

    I have been working for more than 10 years as rotating engineer in water treatment plant and offshore oil n gas industry where the pump require either ANSI or API 610 type. But for me, this uncle has produced one of the best explanation in youtube and easy to be understood by our normal people in the world

  • @alouisiusprabowo3250
    @alouisiusprabowo3250 4 роки тому +23

    Am over 2 years in pump industry as engineer. Splendid, crystal clear sir. Thank you.

  • @jerrysmith9780
    @jerrysmith9780 3 роки тому +7

    Feel like this prof is more like a coach, you don't wanna let him down. I bet students work their tail off for him because he's engaged in the learning process.

  • @denwilden2748
    @denwilden2748 5 років тому +36

    Great lecture, remembering when I was in university. Now I work in small business servicing pump, and this lecture is realy helpfull. Thanks Prof

  • @eeoui0334
    @eeoui0334 5 років тому +13

    Excellent lecture, Dr. Biddle. My professor doesn't even try to explain and solve these problems. Thank you very much.

  • @primesonypaul7230
    @primesonypaul7230 Рік тому +2

    47:42, when Q=0, Hs=150. But how at increased flow rate Q=500, Hs is also increasing to 150.5? Because according to the curve at increased flow rate head decreases. Isn't it?

  • @TenkiKun24
    @TenkiKun24 5 років тому +5

    I left my class for this topic,but luckily i found this video,it's about 2 days bfr exam,,i watched it,,excellent lecture,,hope my final exam become good

  • @myokokoaung9857
    @myokokoaung9857 Рік тому +1

    It is crazy how I can watch those lessons for free. Thank you very much.

  • @wonkisbonita
    @wonkisbonita 3 роки тому +8

    If you try and do the math on minute 44:48, on the replacement of V, Q=AV, so you should have V=Q/A. Thus, V=4Q/(pi*D^2). V=4Q/pi with D=1.

  • @shibanishashin5993
    @shibanishashin5993 3 роки тому +1

    This is a beautiful culmination of my pumps course. the clarity of it brings tears to my eyes.

  • @pbpracticobienhecho3480
    @pbpracticobienhecho3480 4 роки тому +3

    Muchas gracias. Excelente explicación. I am an electrical engineer and these concepts are very useful for me. Thank you very much.

  • @jeezwheez4740
    @jeezwheez4740 9 місяців тому

    I haven't enjoyed a lecture as i have enjoyed this one!👏🏾👏🏾

  • @fa90lq
    @fa90lq 5 років тому +7

    Thanks for your effort. One tip though, unlike the case in the pump sketch you showed, for centrifugal pumps and compressors, the suction side is always one standard size larger than the discharge size. This is to minimize losses and, consequently, reduce cavitation possibilities.

  • @GenaEnSamIAm
    @GenaEnSamIAm 5 років тому +8

    All I can say is brilliant and thank you.
    Thank you for sharing!!

  • @GerardoSanchezZz
    @GerardoSanchezZz 6 років тому +4

    Thanks for including time stamps in these videos!

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому +4

      No problem. We are starting to add time stamps to the lecture series to make it easier for viewers to find exactly what they need. Hopefully the timestamps will save people a lot of time and frustration.

  • @AY-cj9kp
    @AY-cj9kp 3 роки тому

    What a great teacher! I am electrical engineer but just enjoy listening and understanding...

  • @yashsherathia8349
    @yashsherathia8349 2 роки тому

    I got an exam tomorrow. My prof sucks. You are great. Thank you

  • @ericzenteno2531
    @ericzenteno2531 Рік тому +1

    This professor is a legend, I wish I had him as teacher at University 😮

  • @jonathanloorgarcia6961
    @jonathanloorgarcia6961 2 роки тому

    It´s such an amazing class, thank you so much for this video , I got a brief summary about centrifugal pumps which I learned through the university.

  • @mjvonstein
    @mjvonstein 5 років тому +2

    Appreciated the clear explanations and real-world practical focus.

  • @Fury-lg8vq
    @Fury-lg8vq День тому

    I have a quick question in minute 49:19 how did he get those operating points. Is there a way to calculate it?

  • @anthonyanderson1629
    @anthonyanderson1629 5 років тому +1

    This video is great, a lot of good information presented in a clear manner. Thanks!

  • @johnartgallery347
    @johnartgallery347 3 роки тому

    Great Teacher ,nice channel, improve my listening and English on engineering.

  • @miriam4428
    @miriam4428 4 роки тому

    Excellent Lecture. Pretty Understandable

  • @ebrahimamiritokaldany9179
    @ebrahimamiritokaldany9179 9 місяців тому

    The equation provided to calculate delta z based on NPSH is for the case that the water level at the supply reservoir is below the water level at the demand reservoir. So, for the case which is shown in the video, the water level at the downstream reservoir should be lower than that the water level at point 1 and for this case: delta z (minimum water level difference between two reservoirs)= (Pa-Pv)/gamma - NPSH (for available pump) -HL (all head losses) as shown in the video. It is not surprising that if the difference in water levels reduced to values less than delta Z, cavitation is expected to take place. For the other case if the water level at the demand or downstream reservoir is greater than the water level at supply reservoir (most cases), delta Z (Max different in water levels)= NPSH (of the available pump)- (Pa-Pv)/gamma +HL (all head losses) and in this case if the water level at supply reservoir or the well is dropped to lower depth, than the difference in the water levels increased to values more than computed delta Z and we expect cavitation will take place in this situation.

  • @5afbi
    @5afbi 3 роки тому +1

    This is very useful for engineering student thank you sir😍👍👍

  • @parsapirestani1421
    @parsapirestani1421 3 роки тому +1

    Thank Prof for the great lectures!

  • @JacksonMalcolm
    @JacksonMalcolm 4 роки тому +2

    this is great info, I'm studying for my next wastewater certification and notice a few differences. Total dynamic head and Head in general is always referd to as the verticle distance the water has to be pumed (measured in feet). But it sounds like head is just any force acting to restrict flow?
    Also Cavitaion is described only happening at the impeller near the inlet or outlet and not in the pipe itself. this is due to the pressure difference across the impeller. the bubbles are formed by rapid pressure loss and on implotion they take part of the impeller with them and they sound like BBs in the pump.
    again, great video. i enjoyed getting away from the text book for a bit.

  • @serrarbrahim
    @serrarbrahim 5 років тому +3

    Thanks a lot Dr Biddle for sharing this is a really helpfull !

  • @freedomcompany3428
    @freedomcompany3428 4 роки тому +1

    Check me out but at 25:10 the 101kpa makes it 101,0000 Pa which is NPSH is 7.4 METERS then that makes sense with the whole equation to make the units workout.
    But he wrote that vapor pressure is 1666 kPa and then out it in the equation as that value so there's a mistake on that one way or the other. Either it was incorrectly labeled with the kPa units initially or he should've left the Patm in 101 kPa form and converted later.
    Can someone confirm?

    • @dawidpietrucha5333
      @dawidpietrucha5333 3 роки тому

      Yeah exactly. Patm is 101 kPa and the Pv at 15C according to the steam tables is equal to 1.7 kPa.

    • @freedomcompany3428
      @freedomcompany3428 3 роки тому

      @@dawidpietrucha5333 lol too long ago I can't tell if you're agreeing or disagreeing

    • @aj_david
      @aj_david 10 місяців тому

      He's agreeing....

  • @sagarpuri7838
    @sagarpuri7838 Рік тому

    Thank you very much . Very helpful lecture videos.

  • @syedemaadrizwan6259
    @syedemaadrizwan6259 4 роки тому +3

    LEGEND Dr. Biddle

  • @chitramypower4344
    @chitramypower4344 5 років тому +4

    Thank you for your lacture.. I learnt a lot and but why the H vs Q curve by manufacturer is decreasing while system head curve is increasing..However, I know, at 0 flow, head will be maximum and if flow will increase, head will be go down because pressure will be reduced but please make me clear on what basis or data manufacturer plot H vs Q.

  • @teslaheavyelectricals5957
    @teslaheavyelectricals5957 4 роки тому +3

    Very much interesting and informative lecture. Thank you Professor.

  • @hussainshaheed4502
    @hussainshaheed4502 3 роки тому

    Best lecturer. Thanks

  • @andresjanz
    @andresjanz 3 роки тому +2

    Great class, what's the professor's name?, he mentions 'his book' and I'd like to check it out....thanks CPPMechEngTutorials guys !

  • @zoazali7484
    @zoazali7484 5 років тому +11

    dear DR.
    AT 45 MIN there is a little error Q=VA so V=Q/A SO it well be V=Q 4/ π D^2
    thanks lot ...

  • @brettruss3359
    @brettruss3359 4 роки тому +2

    Hey it would be great if the handout was posted for this video.

  • @ajaynavale9739
    @ajaynavale9739 Рік тому +1

    Thank you very much sir... really appreciate it 🙏...

  • @shoaibahmed5561
    @shoaibahmed5561 4 роки тому +1

    my supervisor recommend this video i was in search of topic for research.

  • @jha8539
    @jha8539 4 роки тому +1

    Excellent lecture

  • @gouthamraghavan6467
    @gouthamraghavan6467 2 роки тому +1

    Thank you sir for the explannation, it helped understand the fundamentals better. Also, I would like to add a note on vapor pressure. Vapor pressure of Water @ 15degC unit shall be read in Pa (i.e 1666 Pa)

  • @mojtabaabdjbarh3436
    @mojtabaabdjbarh3436 2 роки тому

    Hi teacher
    I would like to thank you for your wonderful explanation
    and I want to know why in the pump efficiency chart, when the height increases, the discharge decreases,please

  • @celospiky329
    @celospiky329 5 місяців тому

    Just to confirm that Axial flow Pump is also one of the types of the Centrifugal Pump, for Example of Between Bearing BB1 API 610 Centrifugal Pump

  • @shrikantmnit
    @shrikantmnit 4 роки тому

    Great lecture, Thanks Professor.

  • @isaachaynes6935
    @isaachaynes6935 2 роки тому

    Would cavitation also occur if boiling coolant (car's cooling system) is flowing through the pump? Pump would be at the lowest point in the system. I'm really curious about this

  • @jhonmoncaleanotorres1975
    @jhonmoncaleanotorres1975 5 місяців тому

    Great explanation, thanks, what is the textbook used?

  • @osamashamil4941
    @osamashamil4941 3 роки тому

    Thank you sir for sharing this valuable informations !

  • @sandilendlela6531
    @sandilendlela6531 2 роки тому

    Great lecture indeed but I'm confused where did the professor get 175 and 140ft to generate the pump head curve?

  • @hydraulictestrig
    @hydraulictestrig 3 роки тому

    Beautiful Class Thanks Prof

  • @133wavi
    @133wavi 4 роки тому +2

    Thank you for the great video. I have a question about the effect of temperature on the characteristics curve of the pump.
    How does the characteris curve of a centrifugal pump change with the decrease in temperature provided that the pump power is constant.
    A reference material to read would of great help.
    Thank you

    • @benmoussayoucef4699
      @benmoussayoucef4699 2 роки тому

      I can tell you that increasing tempreture will increase the risque of cavitation; unfortunantlly i don't know really it's effect on HQ curve.

  • @avika88
    @avika88 Рік тому

    Thanks for some great videos! This is probably a shot in the dark, but could anyone help me reference to the book he is using. I’m in the middle of a thesis but I cant seem to find alot of good theoretical references on the subject.

  • @blessingmajongwe2076
    @blessingmajongwe2076 5 років тому

    Excellent explanation

  • @lazer2405
    @lazer2405 6 років тому +5

    When you run the pump at a constant speed, how do you increase the flowrate through the pump?

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому +5

      Open the flow control valve downstream from the pump.

    • @jeffreystroman2811
      @jeffreystroman2811 4 роки тому

      Raise the fluid temperature to change viscosity, density? (Not practical but I'm an electronic guy working at a farm and my boss keeps trying to make me do things that are not correct. My solution, learn about fluid dynamics on my own, not to be right but to respect energy and knowledge). Thank you professor, much respect for your life's work, reminding me as always I am standing on the shoulders of giants

    • @MichaelATH
      @MichaelATH 4 роки тому +1

      Change the impeller size as per manufacturers impeller data

    • @abdelfattahkhyralla2203
      @abdelfattahkhyralla2203 3 роки тому

      @@CPPMechEngTutorials
      Awesome

  • @imky08111
    @imky08111 4 роки тому

    great tutorial for a EE....At 25.00 regarding NPSH, visually the water tank is below the pump, the Z is the height between the two. How would the analysis change, if the pump was below and the water tank was above? I would think the ABS | Patm -Pv | may be a more general solution to avoid an answer with a -Z value.

  • @dheyaalgallaf6060
    @dheyaalgallaf6060 5 років тому +3

    How to find his lectures about Turbine & compressor

  • @PracticeMakePerfectMuslim93
    @PracticeMakePerfectMuslim93 Рік тому +1

    love this subject 😊

  • @imky08111
    @imky08111 4 роки тому +1

    Is NPSH used for the single purpose of determining the maximum elevation which the liquid can be raised?

    • @dawidpietrucha5333
      @dawidpietrucha5333 3 роки тому

      No, because NPSH changes with the change of Q. The higher is the flow rate, the higher is the pressure drop at the suction side. Therefore it's rather used to get to know the maximum flow rate available.
      Also the temperature plays the key role, since it influences the vapor pressure.

  • @pnekanayaka4650
    @pnekanayaka4650 3 роки тому

    Great professor. Thank you

  • @AKK105
    @AKK105 3 роки тому

    How can we calculate the flow rate of a split type centrifugal pump if we know the refrigerant flow rate through the chiller's evaporator?

  • @ALNasserSaladin
    @ALNasserSaladin 3 роки тому

    Hello Sir,
    Can you drive the specific speed formoula?
    How we have got the range for every type?

  • @AKK105
    @AKK105 3 роки тому

    Dr. Biddle, Good day to you. Which textbook are you using?

  • @satriobp9
    @satriobp9 3 роки тому +1

    on NPSH example problem, Patm defined by value of 101000 kPa. Should it be valued 101 kPa if Pv also in kPa? CMIIW

    • @dawidpietrucha5333
      @dawidpietrucha5333 3 роки тому

      Yes you're right. He denoted it with the coma. However the value of Pv at 15C according to my steam table is equal to 1,7 kPa.

    • @bhradramazani
      @bhradramazani 3 роки тому

      @@dawidpietrucha5333 Same, from Table A.5 in the class textbook, interpolating you'd get 1.782 kPa for vapor pressure.

  • @rahulmore6274
    @rahulmore6274 5 років тому

    Informative and pretty good.

  • @brendangolledge8312
    @brendangolledge8312 2 роки тому

    Is there a theoretical derivation for the shape of a pump curve?
    I guessed maybe a centrifugal pump imparts constant energy per unit mass to whatever fluid passes through it. Then you'd get E = constant (for any given fluid density) = P + (1/2)dv^2 (d is density), or h = E/(dg) - Q^2/(2gA^2). This has the shape of an upside down parabola (right basic shape), but when I try to compare it to real pump curves, the real curves turn downwards something on the order of 100 times faster than my theoretical model. Do you know why this might be? Am I making some unit conversion error, or is the whole thought process just wrong?
    If the real pump curves turned down something like 10-50% faster than the theoretical one, I'd be happy, because I guess the pump doesn't conserve energy perfectly and it doesn't have the same efficiency at all operating ranges. But getting a result 10,000% different than the theory is unsatisfying.

  • @ibrahimhajjaj8155
    @ibrahimhajjaj8155 4 роки тому +1

    Thank you sir.. I like ur way

  • @nadonadia2521
    @nadonadia2521 Рік тому

    What a great teacher, where do you teach, i want to join one of your classes

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  Рік тому

      Sorry. Only Cal Poly Pomona students are supposed to be in the classroom.

  • @Henry-yw8bl
    @Henry-yw8bl 3 роки тому

    may i know which textbook you guys used? and where can i get the copy?

  • @panoskb9405
    @panoskb9405 3 роки тому

    How do you arrive to the equation which include the term Hp?

  • @arifabdurrahman2599
    @arifabdurrahman2599 4 роки тому

    I just want to know that shouldn't the peak of efficiency be below the horsepower curve?

  • @bashamsk1288
    @bashamsk1288 6 років тому +2

    how can we increase Q at constant V ? Area? I mean with velocity diagrams we can calculate everything then why we need graphs for?

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому

      Since Q = VA, we cannot increase Q at constant V (assuming the fluid is incompressible).

    • @fa90lq
      @fa90lq 5 років тому

      For centrifugal pumps and compressors, the suction side is always one standard size larger than the discharge size. So yes, area will be a factor.

  • @Abhijeetsingh-ql5il
    @Abhijeetsingh-ql5il 3 роки тому

    Sir what will happen if pump is run at very low head than rated head... There will be low efficiency i know. What other practical problems will occur.

  • @siriuselectrical9986
    @siriuselectrical9986 8 місяців тому

    Which textbook does he use?

  • @un7745
    @un7745 2 роки тому

    I have a question,
    If a centrifugal pump flow limit is from 60 LPM to 535 LPM at 3500 rpm, does the low flow limit of 60 LPM changes with running the pump at lower rpm? Does this limit changes goes down when we run the pump at lower rpm?

    • @mattstevenson5849
      @mattstevenson5849 2 роки тому

      Surely changing the flow rate from 60 LPM to 535 LPM would mean a change of impeller, assuming constant rpm.
      If you have a 60 LPM impeller, on a 3500 rpm motor, and you reduce the speed of the motor - the flow rate will reduce.

  • @Rtqd721
    @Rtqd721 5 років тому +1

    thank you very much professor!!!

  • @samanvaziri8195
    @samanvaziri8195 Рік тому +1

    It was great👍 thank you so much, but I should say the teacher made a tiny mistake, at the end of the video he wrote Q=V/A, actually it is wrong and the correct formula is Q=A.V

  • @NithinNayak-dm2ii
    @NithinNayak-dm2ii Рік тому

    Which Text book he is referring to?

  • @vijaybhatawdekar6213
    @vijaybhatawdekar6213 2 роки тому +1

    Actually V=Q/A (Cross sectional area of pipe)

  • @rantogunawan4178
    @rantogunawan4178 4 роки тому

    Well explained...thanks a lot

  • @ghij7530
    @ghij7530 Рік тому

    Where i can find the explaination of chapter 10 ?

  • @ahmedabdelkader31
    @ahmedabdelkader31 4 роки тому

    Hello,
    could anyone tell me how pump curve is determined at a certain speed however the input power = ( torque x angular velocity).
    so, to get more discharge we need more input power by increasing velocity
    and then by applying the efficiency formula (output power / input power) we can draw an efficiency curve.
    so, how this curve could be at a certain velocity?

  • @chemicalengineer1985
    @chemicalengineer1985 2 роки тому

    Great explains 👍

  • @moazsalem3488
    @moazsalem3488 5 років тому

    please Sir If the inlet fluid is subcold ( at low temperature ) but the liquid is entering the pump at low pressure and the impeller will start swirling the liquid and create bubbles just as when you move your hand quickly on water surface you will create water bubbles though the inlet pressure is above the vapor pressure is that possible

  • @seydou432
    @seydou432 5 років тому +4

    Thank you so much for the excellent lecture prof. I have one question: why the efficiency form on previous graph is different from those of pump performance map?

    • @piyushgupta4769
      @piyushgupta4769 2 роки тому +1

      Yeahh, the same question crossed to my mind !!! Even I'm confused for it

    • @seydou432
      @seydou432 2 роки тому

      Dear Prof! speaking about elevation of the pump above reservoir surface you said:
      Well, as you get the pump higher and higher in the flow rate, that pressure is going to start drop.
      I think that could be:
      Well, as you get the pump higher and higher in the elevation, that pressure is going to start drop.
      What do you think about that? Thank you very much.

  • @benmoussayoucef4699
    @benmoussayoucef4699 2 роки тому

    please can you tell us the effects of no flow rate (valve closed on runing pump).

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  2 роки тому +1

      The pump may overheat since it is dumping lots of kinetic energy into water that is not flowing.

    • @benmoussayoucef4699
      @benmoussayoucef4699 2 роки тому

      @@CPPMechEngTutorials thank you very much

  • @leonardogomes6361
    @leonardogomes6361 2 роки тому +1

    Very good vid

  • @nooruddindalvi591
    @nooruddindalvi591 6 років тому +2

    The professor writes Q=V/A at 44:52, shouldn't it be Q=V*A?

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому +5

      Whoops! Great catch. I will put this in the video notes.

    • @HarisKhan-df8tr
      @HarisKhan-df8tr 6 років тому

      @@CPPMechEngTutorials CAN WE GET VIDEO NOTES PLEASE ??????

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  6 років тому

      By "video notes" I mean the comments just underneath the video.

  • @masihtukhi6356
    @masihtukhi6356 4 роки тому

    Professor: why is the velocity difference between point 1 and 2 very small? Shouldn’t the velocity at point 2 be very high because impeller blade is pushing the liquid and velocity should increase significantly.

    • @piyushgupta4769
      @piyushgupta4769 2 роки тому +1

      The pump definitely provides Kinetic energy to the water which intutively make us think the increase in velocity of flow at outlet, but because of volute casing of pump that kinetic energy of fluid gets converted into pressure energy. Thus the velocity remains same. Moreover velocity is governed by the pipe diameter. Since pipe diameter at inlet and outlet of pump is assumed to be same and flow rate also going to be same to maintain steady state ( because whatever amount of water is entering , the same amount of water will move out of pump). Hope it will help!!

  • @planetdeepak
    @planetdeepak 4 роки тому +1

    Thank you very much

  • @alipacheco8149
    @alipacheco8149 4 роки тому

    Great class. One would intuitively think that the velocity of the fluid at the discharge of the pump is higher than the suction velocity. Apparently, this is not true, because the professor is neglecting that difference. I would like to understand better the reason behind it. Any advice?

    • @laxmikantpuranik3967
      @laxmikantpuranik3967 3 роки тому

      Usually, suction pipe is one size higher than the discharge pipe size, hence the velocity in discharge pipe is higher than that of the suction pipe

  • @htwang4228
    @htwang4228 4 роки тому

    Near 31st minute:
    It seems, we put g instead of 9.81 [m/s^2] in the N's formula JUST TO MAKE THE FORMULA VALID ON THE MOON.
    On the moon, g is small, the pump head H is big, hence g*H is the same as on earth.

  • @MunirLoyed
    @MunirLoyed Рік тому

    do you have videos for closed loop system.

    • @CPPMechEngTutorials
      @CPPMechEngTutorials  Рік тому

      Some of the earlier videos in the lecture series involve the energy equation for pipes.

  • @halasimov1362
    @halasimov1362 3 роки тому

    But what is the water horse power in Shark Power?

  • @panosnik4662
    @panosnik4662 5 років тому

    ΦΙΛΙΕ ΣΕ ΕΥΧΑΡΙΣΤΩ, ΔΕΣ ΠΩΣ ΚΑΝΟΥΝΕ ΜΑΘΗΜΑ ΣΕ ΠΑΡΑΚΑΛΩ. Do you know If I could find the document that was given to the students? Thank you

  • @NuclearSavety
    @NuclearSavety 5 років тому +3

    Love this defining of all abbreviations .... thats unfotunately not standart any more...

  • @ahmednaji4375
    @ahmednaji4375 5 років тому

    what is the textbook title which you kindly are using please?

  • @eduardotorressierra1387
    @eduardotorressierra1387 6 років тому

    Excelent explanation

  • @operasisngr115
    @operasisngr115 3 роки тому

    Thank you for sharing

  • @MohammadAtaeinejad
    @MohammadAtaeinejad Рік тому

    Hi.tanks for this class. one mistake in calculating ouccer is Q=AV