Water Pressure Calculation (Limited Information)

In summary: I'd think would have laminar flow up until its ejection through the nozzle which then would of course turn the flow into laminar spray.The piping in which I'd be using ideally will be clear vinyl tubing, which I'd assume has a much lower surface roughness than something like iron tubing which may have a rougher surface due to machining processes. But I will take into account what you have stated in the future, thank you mate.
  • #1
Sirsh
267
10
Is it possible to find the pressure of water that leaves a pipe of certain area/diameter given only the flow rate of the water itself? OR the requires piping diameter/area given the pressure that I desire.

I'm trying to design a system that requires relatively high pressure (for spraying) however, I do not want to invest money in pumps, piping, gear etc. I'd rather try find a way to figure out a combination of criteria before I do this.

For this, I'm assuming that the flow regime is laminar. I have found an equation that I think may give me what I need, however I am unsure how I can apply it in this situation.

Hagen-Poiseuille equation:

Flow rate = πr4(P−P0)/8ηl

where r is the radius of the pipe or tube, P0 is the fluid pressure at one end of the pipe, P is the fluid pressure at the other end of the pipe, η is the fluid's viscosity, and l is the length of the pipe or tube.

I am unsure what pressure I should set the input (pump end) of the equation, P0?

Any help would be appreciated, thanks.
 
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  • #2
Hagen-Poiseuille equation is theory result for laminar flow with very fine tube surface.
Meassures on real old iron tubes shows that flow rate related to ##r^{2.63}\left(\frac{dp}{dx}\right)^{0.54}##.
I think you must take these results as limits between them is the real behaviour.
https://www.uio.no/studier/emner/matnat/math/MEK4450/h11/undervisningsmateriale/modul-5/Pipeflow_intro.pdf
 
Last edited:
  • #3
Sirsh said:
Is it possible to find the pressure of water that leaves a pipe of certain area/diameter given only the flow rate of the water itself? OR the requires piping diameter/area given the pressure that I desire.

I'm trying to design a system that requires relatively high pressure (for spraying) however, I do not want to invest money in pumps, piping, gear etc. I'd rather try find a way to figure out a combination of criteria before I do this.

For this, I'm assuming that the flow regime is laminar. I have found an equation that I think may give me what I need, however I am unsure how I can apply it in this situation.

Hagen-Poiseuille equation:

Flow rate = πr4(P−P0)/8ηl

where r is the radius of the pipe or tube, P0 is the fluid pressure at one end of the pipe, P is the fluid pressure at the other end of the pipe, η is the fluid's viscosity, and l is the length of the pipe or tube.

I am unsure what pressure I should set the input (pump end) of the equation, P0?

Any help would be appreciated, thanks.
In the Hagen-Poiseuille equation, P0 is the outlet pressure, not the inlet pressure.

For flow coming out of a pipe into the air, the pressure at the outlet of the pipe is atmospheric pressure, ~100 kPa.

For the relationship between pressure drop and flow rate in turbulent flow of water in a pipe, see Transport Phenomena by Bird, Stewart, and Lightfoot.

Chet
 
  • #4
theodoros.mihos said:
Hagen-Poiseuille equation is theory result for laminar flow with very fine tube surface.
Meassures on real old iron tubes shows that flow rate related to ##r^{2.63}\left(\frac{dp}{dx}\right)^{0.54}##.
I think you must take these results as limits between them is the real behaviour.
https://www.uio.no/studier/emner/matnat/math/MEK4450/h11/undervisningsmateriale/modul-5/Pipeflow_intro.pdf

The piping in which I'd be using ideally will be clear vinyl tubing, which I'd assume has a much lower surface roughness than something like iron tubing which may have a rougher surface due to machining processes. But I will take into account what you have stated in the future, thank you mate.

Chestermiller said:
In the Hagen-Poiseuille equation, P0 is the outlet pressure, not the inlet pressure.

For flow coming out of a pipe into the air, the pressure at the outlet of the pipe is atmospheric pressure, ~100 kPa.

For the relationship between pressure drop and flow rate in turbulent flow of water in a pipe, see Transport Phenomena by Bird, Stewart, and Lightfoot.

Chet

Thanks for the book reference Chet, I'll be sure to go find it at my university. Though, if we are talking about not extremely high pressured water which passes through a very smooth surfaced pipe, would it be correct to classify it as laminar? my project is based upon the premise of a weed sprayer which I'd think would have laminar flow up until its ejection through the nozzle which then would of course turn the flow into laminar spray.
 
  • #5
Sirsh said:
The piping in which I'd be using ideally will be clear vinyl tubing, which I'd assume has a much lower surface roughness than something like iron tubing which may have a rougher surface due to machining processes. But I will take into account what you have stated in the future, thank you mate.
Thanks for the book reference Chet, I'll be sure to go find it at my university. Though, if we are talking about not extremely high pressured water which passes through a very smooth surfaced pipe, would it be correct to classify it as laminar? my project is based upon the premise of a weed sprayer which I'd think would have laminar flow up until its ejection through the nozzle which then would of course turn the flow into laminar spray.
I doubt if it will be laminar, but you will be calculating the Reynolds number, which will tell you for sure.
 
  • #6
I do not want to invest money in pumps, piping, gear etc. I'd rather try find a way to figure out a combination of criteria before I do this.

I made my own small spraying system for weedkiller some years ago. As I recall the company that sold me the spray nozzles had charts for the flow rate at a given pressure. Just had to ensure the pump could manage the combined flow rate of several nozzles at the required pressure. The nozzles had colour coded replaceable inserts so it's quite easy and cheap to change the flow rate if I got it slightly wrong. The flow rate was modest so I could ignore any pressure losses in the hose pipes etc.
 
  • #7
Reconsider your assumptions. This will not be laminar flow in the tubing. Use the following equation for flow out the nozzle:

Flow rate (Volume/unit time) = Cd*A*sqrt(2*P/density)

For Cd (nozzle coefficient, no units) use 0.89, an approximation for most nozzles.

A is area of nozzles in length squared.

P is pressure force/area, pressure in the tubing just before the nozzle.

Density is the liquid density

If proper units & conversions are selected, the sqrt items end up being length/unit time, so when multiplied by A & Cd, flow rate is Volume/ unit time.

My. Reference book doesn't give provide the name of this equation, but I have used it many times.

V,
 

Related to Water Pressure Calculation (Limited Information)

1. How is water pressure calculated?

Water pressure is calculated by dividing the force exerted by the water on a surface by the area of that surface. This is known as the formula for pressure: P = F/A. The units of measurement for water pressure are typically pounds per square inch (psi) or kilopascals (kPa).

2. What information is needed to calculate water pressure?

The three main pieces of information needed to calculate water pressure are the force of the water, the area over which the force is acting, and the units of measurement being used. In order to calculate water pressure accurately, it is important to have precise measurements of these factors.

3. How does water pressure affect plumbing systems?

Water pressure plays a crucial role in the functioning of plumbing systems. If the water pressure is too high, it can cause damage to pipes and fixtures, leading to leaks and potential flooding. On the other hand, if the water pressure is too low, it can result in poor water flow and difficulty in using appliances and fixtures.

4. What factors can affect water pressure?

Several factors can affect water pressure, including the elevation of the water source, the distance from the source to the point of use, friction within the pipes, and the number of fixtures using water at the same time. Changes in these factors can impact the overall water pressure in a system.

5. How can water pressure be increased or decreased?

Water pressure can be increased by installing a booster pump or adjusting the pressure regulator on the main water supply line. Alternatively, it can be decreased by installing a pressure reducing valve or adjusting the pressure regulator. It is important to consult a professional plumber before making any changes to the water pressure in a plumbing system.

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