Water Hammer Wave Reflection and Valve Closure Time

hello I'm Michael Crowley from fluid mechanics curved off UK I made hydraulics engineer and I specialized in transient flow and surge analysis modeling including this is my second video on the subject of water hammer in the previous video I explained the phenomenon of water and what pressures you generate during the water hammer event and the fact that you generate a pressure wave which in this second video I'm going to discuss what actually happens when the water hammer wave reaches the end of the pipe well there is a reflection and we'll discuss other wave is reflected in those wave reflections occurring we'll look pipeline vibration and how that's induced by these pressure waves going backwards and forwards up the pipeline I'll also discuss how fast the bow at the end of the pipe actually has to close or to and but briefly recap what we discussed reduce I mean we had a tank we then had an instantaneous closure at the end of the pipeline which induced a pressure wave which traveled up the pipe there is the pressure wave front and that there is at the pipeline at velocity C and the velocity in this section of the pipe was zero and the initial must field still in that section of the pipe I showed the jakku city equation which see the wave speed C and U which is the change in velocity and then went on to show how you actually calculate C the wave speed and it's basically Hookes law for a perfectly rigid pipe the wave speed is the bulk modulus over the density of the fluid for fluid such as water that would be equal to one thousand four hundred and eighty meters per second but that wave speed was significantly influenced by the pipeline that the material of the pipe the wall thickness of the pipe and there is a what if I took all blips take into account max which is which is basically this this part of the equation is the same as this bit up here but this is the diameter of the pipe the Youngs modulus of the material was made now in the previous video the wave speed would be in a 15 millimeter copper pipe and I showed that the pipe is actually very stiff but then we talked about other plastic to the pressure rise okay so we have the pressure wave which is traveling up the pipe and eventually what's happening first of all will meets define velocity in the pipe and the pressure varies in time see their position along the position of the pipe it up into three sections for the sake of this explanation position to position through the way we'll turn up the pipe during that speech see won't about or the end of the pipe is closed we're going to call that time t 0 when the way he jumped up the fight and it gets to this position 1 so where it is on the drawing there we'll call that T 1 when the way it gets to the next position we'll call that T 2 when we get to the end of the pipe we'll call that T 3 the pipe the wave will be reflected back up the pipe will discuss how that happens when it gets to the net go back T 4 etcetera etcetera before the value at the end of the pipe is closed the initial conditions where the velocity of the pipe is you you initial call back to mine what okay so let's start off two plots and the other will be pressure P project this is 0 at 0 bar gauge pressure here if this is go ahead of h-his pressure so actually it's the pressure at t minus 1/3 equals Rho G H so in other words it's the density times now in the previous video we discussed what sort of search pressures you could get with flow at 1 meter down a pipe so if we had a one meter flow and this was a copper pipe then the pressures that you would generate when you do an instantaneous valve closure would be 12 bar 12 and 1/2 bar now that's significantly more than these pressures here so in terms of where we have any other scale or pressure we are going to be slightly above zero at that point there but it's not much and zero the far end for clarity here I'm just going to shoot that it's the same so we now go to time T t0 and we close the end of the pipe so what happens this goes into the velocity at the very end of the point zero and we now get it was still the same pressure on the back except at the end where we get all of a sudden this change in pressure the surface pressure the wave that travel along and get to this position here so this is now we now go to time T t1 see what and what happened well the velocity has now stopped as far as that so actually the cost be zero zero from there and the pressure when that was this high pressure all the way up to that point C T one good thing going to t2 and Musti goes to their stop okay and then we finally get to the way pressure wave gets as far as the end of the pipe t3 she's 3 basically we did this for the that was with zero now going on to period what you have there just like that so now the pressure wave is going back in the opposite direction if we go to t5 right that that's to five and then when we get to t6 time to 6 to 6 now that's unsustainable because you've now got a limited blow at the end of the pipe is closed off so how come there is no verb so effectively what's going to happen now is instantaneously the blow that was going in there is no stop zero and the pressure wave is going to start traveling back in this direction the wave was going in that direction now it's coming back again in the other direction so if we now go on to 2 7 2 there okay 7 the velocity from there to there is stopped and from well what happened to the positives it's driven by the the jacuzzi equation so the jacuzzi equation tells you how much pressure is generated rate change velocity all you must remember is that most of you change this time is negative so actually the pressure change is Rho C minus u so if we took the previous example you 12.5 bar positive burger and if you go negative well that means we're going to have 12.5 bar negative pressure but that's not possible you cannot get negative pressures you can only get pressures down to absolute zero absent we are talking about 0 bar gauge which is 1 bar so so effectively you can only get pressure of minus 1 bar so that's as far so actually the pressure is not going to be minus 12 it's going to be effectively coming back in this direction it's going to be well it's not only minus 1 it's going to be down to the cavitation pressure or the vapor pressure of the water you probably also got air in there which will come out so that this equation makes sense because I previously showed that's what see thank you the the pressure what's actually happening here is that this the velocity is not the same either so basically we go back to Hookes law it's the square root of K when I worked out to originally the velocity receivers for solid water we've now got a mixture of vapor possibly air in the water coming back so effectively yes the velocity changes its minus 1 but actually the speed and so therefore when you do the calculation the pressure so then let's go along to time T 8 and it goes to that and then T going back the other way that's t9 so we've now brought to the situation where the flow in the pipeline a stopped and the pipeline under vacuum pressure - wah-wah now that is unsustainable so what's going to happen because the pressure there we know is this broke eh is that the glow is actually going to make trouble back in the opposite direction into the slab so we're now going to get a negative sorry positive flow back into the pot and so if we go up to time period tank the wave we've got two there and then push it in the pipe and then we get to 12 so we're now at position time to time interval 12 and if you look at this we've basically got no pressure on zero pressure in the pipe and we have got the initial velocity in the pipe that comes back to the same as what we had initially just now that was close so we get the same effect stops the pressure surge yes so they're getting with four cycles then actually is the frequency of the system so if we go back to the previous video when we were talking about on a domestic plumbing situation and we wanted to work out the natural frequency the pipe would vibrator or the frequency would be forced to by break that may or may not be we can say that the time period is four times the length of the pipe over see the velocity in the pipe now that C is a bit complicated because as I explained in the video earlier when the wave is coming back this seed may change due to cavitation but it gives you an approximation to the sort of frequencies just using that sort of base using a constant C so if we had same pipes of about 20 metres or never for bite by 20 and if we one two five four three four point six six three five seconds which is equivalent to 15 Hertz I think that might be something similar to what you might experienced if you deceive us into the pipe vibrating in your homes on the mother now the next thing we need to think about is how quickly does about how to close for it to be considered water hammer or to induce a wall down so we have the initial situation flowing down and then we instantaneously we start blue instantaneously close the pelvis now look gradually close the valve so we're going to gradually close the valve and as we close the valve it will send up away a way of going up the pipe okay now this is not the same as the the original case where you've got a complete jacuzzi this is going to be a gradual increasing so basically what happened is that on this side of the way the losses will be the initial velocity and on this side lost it will gradually decrease to the minimum velocity there and the pressure will gradually increase today now saving range the system so that just as the pipe closed the way today well actually what working to find is actually that well actually as long as the valve is closed by the time you will get this form to Kooskia that but if that if it was the truth I would be very would only nice for a much shorter length of time so in other words the time at which the black line will be pressurized would be less but from a pipeline design point of view but that doesn't make any difference it's just the fact you get up to the pressure that's the thing that equation to be true basically the time that it takes to close is going to be faster than to one thing okay so it's two times the length on C so if you went back to the previous example of the water the 28 meters of pipe copper pipe come out at a time of three seconds something about that that's pretty quick so it'd be quite hard actually close about this boy in sort of domestics plumbing you don't often get very however let's take another example so you have a 10 millimeter 10 kimeta long black line okay which was an oil pipeline or water pipeline times 2 and the wave speed was say a thousand meters per second okay that could be a significant problem and when you've got long pipes water hammer and your couscous becomes much more efficient now in my next video on this subject I'm going to look at what happens when there is a branch so and there's a branch coming off there and that's a quite interesting so I'd like to discuss that thank you for watching please if you want to find a little bit more about me have a look at my website at fluid mechanics code or UK I'll be very grateful if you could like this video on youtube thank you

Channel: Mike Crowley

Views: 30,662

Keywords: Water hammer, wave reflection, wave period, cavitation, valve closure time, pipe vibration, Joukowsky equation, wave speed, surge, transient flow, surge analysis, Valve closure, waterhamer, water hammer, water hammer calculation, elastic water column theory, water, hydraulics

Id: lrt7oY5DFRQ

Length: 26min 29sec (1589 seconds)

Published: Mon Aug 03 2015