Does water pressure ôgo to the endö of a pipe? 5

[gandytable]

Does water pressure go to the end of the pipe and lessen as you head back toward the pump? The application is a spray system with heavy flow. The water is pumped into pipes and dispersed by orifices in the pipes. The conventional wisdom here at work is that the greatest pressure and flow is near the end of the pipes, and that it therefore needs to be tapered toward the end to equalize the flow (or the orifices made smaller). It appears to me that the greatest pressure in a consistent ID pipe with equal size orifices would be nearest the pump. Can someone explain what the pressure does or direct me to something that explains simple rules of thumb for water flow.

 

[tr6]

Design velocity head is taken at the entrance, and the factor only applies to liquids.

In deriving this factor, it is assumed that the static head remains constant as the fluid travels down the pipe. Not quite true, but our design was based on relatively short pipes, maximum of 60".

 

[25362]

To bvi I feel I must disagree with the "simple" flow rule as stated by you.

The law of conservation of energy leads to seemingly odd observations of pressure increasing as the flow proceeds downstream. While this sounds impossible, it is thermodynamically correct, as pressure changes inversely to velocity to conserve energy (Bernoulli).

Although friction may affect the pressure developed in a gradual change of diameter, a sudden expansion in a pipe system may show downstream pressure gage readings being higher than upstream. As an example, for water flowing in a 4" pipe at 10.1 fps, then into an 8" pipe at 2.54 fps, the pressure rise would be:

[(10.1²)-(2.54²)](62.4)/[(2)(32.3)(2.3)]=40 psi !​

This is also a known effect in the diffusers of vacuum ejectors.

Another common example are centrifugal pumps which impart energy in the form of high velocity to fluids. A velocity which is then reduced by expanding the flow area both in the pump casing and frequently by expanding the pipe size on the pump outlet.

The word force, or better energy, would be indicated to replace the word pressure in your statement or, otherwise, the addition of: "in constant cross-section ducts or pipes" would be needed. Do you agree ?

 

[BRIS]

The total energy reduces towards the end of the pipe but if you have a consatnt diameter with orifice outlets along the pipe then the velocity reduces and the pressure can increase towards the end of the pipe. (similarly the water surface can rise and water flow uphill in an open channel.

It is a simple application of Bernoulli equation.



Brian

 

[hydrae]

Gandytable

As you see Bernuli rules here, but in your application you have one more factor to consider, the spray arm is spinning, with the spin comes centripedal acceleration, which will result in a higher head at the tip of the arm than at the center. With that you can run the numbers for flow, friction loss, pressure as a function of distance from the center, I can see this will be lots of number crunching.

One other item, since that arm is spinning, the lighter it can be at the end from both pipe mass and water mass, the signficantly less forces on the arm and support structure when in motion. I believe this is the primary reason for the preffered shape in common use.

Hydrae

 

[MikeHydroPhys]

The only manner in which force exerted on a conduit may be greater is that caused by a contraction in the flow cross section, or a deflection imposed by an intrusion, or on a bend, that is well covered in your statement and by your answers, this can cause localized stress but the possibility of it being greater than the pump head should be avoided by the design, or rupture will occur (this happens in soil piping where of course gravity prevails and pressures may be higher than some distant source, similar for groundwater conduits, however Newson 1975 has shown this usually leads to fracture and pipe burst, erosion being great), or the possibility of the pump head being lower in pressure would result in a back-up of the fluid and the pump would then come to equilibrium and probably burn out the motor as my wife did to the vaccum cleaner Tuesday, although it was a bit scrap before that. Any backwater pressure and aeration, water hammer will cause local pressure inconsistencies and flex in the pipe as described by your reply experts. This is not to be encouraged in oil pipelines and is a disaster in water mains, contractors washed out the entire side of a rhyne some years ago during a pile site house build under the show home intended zone while trying to permit half of Cadbury pressure tank to divert to the river by excavation error and the inestimable problem of foundering sands and silts of the North Somerset Levels. mdshydroplane

mdshydroplane

 

[BRIS]

hydrea - are you not creating energy?? The only energy being input into the system is the energy of the incoming flow. Spiining is caused by the change of momentum.

Brian

 

[hydrae]

BRIS

No, I am not creating energy. Look at the physics of the spray arm.
First lets consider the arm fixed. Water enters the pipe and travels to the first spray point, along the way the pressure is reduced by the friction loss of all the water moving though the pipe. a small portion of the water exits the pipe and the rest continues to the second spray point, if the pipe had a constant cross sectional area, the pressure drop per unit length is less than in the first section of pipe because there is less water flow though it. The response by designers has been to reduce the cross section area to reduce material costs, similar to HVAC designers reducing duct size. At each spray point pressure is converted to velocity to perform the work required in accordance to Bernulli.

Now let the arm spin,
It spins because the thrust of the last spray point is directed to the side imparting a torque on the arm. The arm will accelerate until the friction losses of the arm flowing through the air/water medium it is in and other friction losses equals the thrust created by the last spray point. (the other spray points also produce this thrust but they are counteracted by the bearing holding the spray arm and impart no movement to the arm).

Now consider that the arm has no spray points and is spun by an external mechanism. The water is pressurized by the supply pump to a pressure P1. If you measure the pressure at the end of the arm while it is spinning it will read a pressure greater than P1, just like a centrifuge imparts G forces on objects it will also impart a greater pressure on the water inside the pipe.
to quote Gandytable on March 24 "The conventional wisdom here at work is that the greatest pressure and flow is near the end of the pipes, and that it therefore needs to be tapered toward the end to equalize the flow?"

Now I agree to the 'conventional wisdom' but not the 'therefore'. With heavy objects on the end of a spinning device the forces are large when the items are heavy, if you can make it lighter the forces will be less.

Now to get back to your comment on creating energy, the only energy source is flow of water under pressure. All the energy supplied minus friction losses is converted to water having a high velocity under zero pressure. The energy used to spin the arm is converted from the last spray point imparting its velocity to the side, now this water has less absolute velocity because the spray arm is spinning away from the point of exit, reducing the energy in the water and putting it in the spray arm. ( a Pelton turbine works on this principle and when perfectly designed all the velocity is imparted to the arm (bucket) and none is left in the water) the energy added to the spray arm by the last spray point results in increased pressure inside the pipe but not so much pressure the total energy is increased.

As for water flowing uphill in an open channel, there head is coverted to velocity then back to head, minus the friction loss. In closed pipes, the same thing happens with reductions in cross sectional areas, pressure is converted to velocity then after the reduced area the pressure rises again when the velocity is conveted back to pressure (minus friction losses of course)

Hydrae

 

[BRIS]

Hydrea

An interesting problem - your explanation has me convinced - it is the "absolute" velocity that is the key.

Brian