# pub question

This is a water velocity thing.
Velocity of the water at the pipe exit will be closely connected to the 'head' of water ie Tank constant water surface height above the pipe exit.

For these purposes, neglecting flows of laminar and turbulent type, and neglecting frictional losses allowing 32 ft /sec² as approximation for 'g'

The velocity at exit will be C x sqrt ( 2g x head) ft / sec where C is the coefficient of velocity ( actual v / theoretical v ) this is an unknown in Breezer's case. and is comprised of all the restraints to the flow.

So theoretical velocity = sqrt ( 2 x 32 x 20 ) = 35.777 ft /sec
This is in an upward direction so 35.777 / 32 = 1.118 sec to lose all upward velocity.
And the height reached using v² = u² - 2 g s where u= initial vel v = final vel s = distance.
Rearranged to s = ( u² - v² ) / 2g leads to s = (35.777² - 0 ) / 64 and this gives an answer of 19.9999 ft ... being the original height.
So theoretically the two plumes reach the same height ie. the tank water surface level.
Obviously friction, type of orifice etc will have an effect and the theoretical height will not be reached... Which pipe generically provides most resistence to flow ? fIIK !!

I disagree, the 15mm pipe will spurt higher. As the volume decreases, the pressure increases. And you will have a venturi effect on the smaller pipe at the inlet on the tank. As they are both under the same head of water, pressure at the outlet will be different due to the inverse relationship between pressure and volume.
In real life, you try bunging a rad valve on microbore (carrot and tata in the header tank , I've had the bungs fail, and believe me the water hits the ceiling if you aren't quick enough with your rad valve change, or finger over the pipe. Its ok on paper, but I guess a lot of people talk a cracking job on paper.

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I reckon I am right, the significant influence in this case being the unknown co-efficient .. As I said all else being equal I think there is a relationship between pipe diameter and friction induced also bend radii will play a part.... inlet shapes have effect, but in this case would be of the same shape .. probably bell mouthed.

One could say, when a larger diam. pipe flows smoothly into a smaller diam via coned connection - venturi shape - and it is noted that the pipes remain full at all times, the mass flow rate is the same for both (what flows out must flow in to retain fullness), but the velocity would have increased in the smaller bore pipe because of the smaller csa.
The pipes above are not connected, and, with the data supplied therefore have no measurable influence upon each other.

Come on boys I am no expert .... Just some old memories of Fluid Mechanics .. and a bit of - perhaps misplaced - logic....

pipme said:
I reckon I am right, the significant influence in this case being the unknown co-efficient .. As I said all else being equal I think there is a relationship between pipe diameter and friction induced also bend radii will play a part.... inlet shapes have effect, but in this case would be of the same shape .. probably bell mouthed.

One could say, when a larger diam. pipe flows smoothly into a smaller diam via coned connection - venturi shape - and it is noted that the pipes remain full at all times, the mass flow rate is the same for both (what flows out must flow in to retain fullness), but the velocity would have increased in the smaller bore pipe because of the smaller csa.
The pipes above are not connected, and, with the data supplied therefore have no measurable influence upon each other.

Come on boys I am no expert .... Just some old memories of Fluid Mechanics .. and a bit of - perhaps misplaced - logic....
Have a paruse :-
http://uk.altavista.com/web/results?itag=ody&q=fluid+flow+in+pipes&kgs=1&kls=0&stq=10
Crikey .. a fair amount of stuff then !!

Posted: Tue May 17, 2005 5:14 am Post Subject:

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I reckon I am right, the significant influence in this case being the unknown co-efficient ..

So you're saying "it's the same but different". Not much to say then?

ANY plumber knows (some of us even have the formulae) that resistance is, relative to the amount of water, greater in a smaller pipe SO there's your answer. The water in the smaller pipe is slowed down more so it doesn't go as high.

NO there is NOT a venturi anywhere in this situation. There is (almost) NO movement of the bulk of water in the tank. This is NOT a case of water flowing in a pipe then having to go through a restriction.

the mass flow rate is the same for both
Nonsense.

There's an surprising lack of engineering nouse on this site, which probably represents a brighter than average selection of plumbers!
If in doubt always consider the extremes. Think of a similar pipe of really small diameter. The resistance would be so overwhelming the water would dribble out of the end.

Misread , and condemned out of hand, unfair I'd say.

pipme said:
I reckon I am right, the significant influence in this case being the unknown co-efficient .. As I said all else being equal I think there is a relationship between pipe diameter and friction induced also bend radii will play a part.... inlet shapes have effect, but in this case would be of the same shape .. probably bell mouthed.
The unknown CoEfficient for each pipe are the figures which would reduce the flow differently for each diameter pipe... That means I think they would have different velocities hence plume to different heights .. true !!

pipme said:
One could say, when a larger diam. pipe flows smoothly into a smaller diam via coned connection - venturi shape - and it is noted that the pipes remain full at all times, the mass flow rate is the same for both (what flows out must flow in to retain fullness), but the velocity would have increased in the smaller bore pipe because of the smaller csa.

The pipes above (in breezer's problem) are not connected, and, with the data supplied therefore have no measurable influence upon each other.

I was then in a different paragraph pointing out to someone who had mentioned placing their finger over an orifice, thus restricting it and promoting a lengthy 'squirt' -- what happens when a pipe reduces from a large to small bore in a smooth transition .. It is true that the mass flow remains the same in this particular type of pipe, if it remains filled... under constant head that is why the velocity increases in the smaller bore portion, to maintain the mass flow... v x csa
This of course has no relevance to Breezer's problem, but was an aside.

For these purposes, neglecting flows of laminar and turbulent type, and neglecting frictional losses
That stated the situation at the start ... Quite fair I thought.

Which pipe generically provides most resistence to flow ? fIIK !!
And that stated honestly that I had no idea which pipe would be expected to have the greater restrction to flow from pure friction alone.

ChrisR's extremely small example had water trickling out the end.
Take the other extreme - a pipe the size of the base of the tank suddenly opening. I reckon the water would crash down the pipe and rush madly over the edge at the end of the upward bit - more of an ungainly splash than getting to any great height It's not like a ball rolling down a hill and up the other side. The dispersal of the water in the air needs to be taken into account.
So my suggestion is that a very big pipe won't get the water very high and neither will a small pipe.
So, somewhere between very big and very small there is a size of pipe that will result in the maximum height. And smart people could draw a graph relating height to pipe diameter - and then answer the original question.

Breezer asked “which” & “why”. It stands to reason that the pressure at the terminal end of the two pipes will determine the resulting height of the water flow. Whether the pipes are vertical or horizontal, it is the pressure of the water at the exit of the pipe that determines the exit force of the water. Remember pressure and force are not the same, ( i.e. P=F/A ) . Basically, the factors that affect pressure loss through a straight length pipe are:-
1. Length of pipe. ----------------------------------------------Both pipes same length.
2. Density of fluid being conveyed. -------------------- ----Same water from tank.
3. Volume of fluid being conveyed over a given time.----Volume not asked for.*
4. Coefficient of friction of pipe wall material.------------Same material(Cu/Fe etc.,)
5. Cross-sectional area of the pipe conveying the fluid---This is very important, because as the cross sectional area of the pipe increases so does the ratio of pipe area to pipe wall increases, there is less pipe wall in contact with the fluid per unit volume of flow. Simply, there is less frictional resistance per unit volume of fluid flow in a larger pipe, as every-one on this forum knows quite well.
*Note :- In this case, volume flow rate is dependant on pressure loss.
From the above, it will be seen that the predominant pressure drop across the two identical run pipes is dependant upon the cross sectional area of the two pipes, therefore the smaller of the two pipes has the greatest pressure loss, hence the lowest terminal pressure at the exit, thus less force to overcome gravity. The larger bore pipe as ChrisR and others stated, will rise the highest. The above, answers why!
The reason why the hosepipe “squirts “ further, is that pressure energy is converted to velocity energy at the point of restriction i.e. the hosepipe exit, as in a venturi.
I hope to have shed some light on this in my own small way.

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