Pump Head & Suction (leaky closed system) PF Newbie

[halfgt2]

Hi physicists!

I am scratching my head to remember the most basic laws of fluid flow while I try to irrigate things from a barrel. Not exactly rocket science, I know ;-) But very exciting for me ...

The situation is simply a pump (cheap submersible one) put into a barrel (sitting on the bottom) where the barrel is placed at the beginning of a row of plants. The plants need to be watered. A main hose rises vertically inside the barrel from the pump goes along the line of plants and abruptly ends in a stopper, just beyond the last plant in the line.

Each plant gets a little individual sprayer connected to the main hose (looking like a drinking straw piercing the hose with its opening suspended in the center of the diameter of the hose). The sprayer tubes permits a relatively minor flow rate, like a leak, compared to what the hose is capable of delivering. For arguments' sake let's say each sprayer takes 1% of the potential flow in the area of interest, so the pump is always generating some pressure.

Now, this is sort of a closed system if I read this amazing thread right:

https://www.physicsforums.com/threads/pump-head-requirement-closed-vs-open-loop.753612/

Except mine is "leaky" since the whole purpose is to release water very slowly. So the small pump is placed in the barrel of barrel height H, call it a meter if you like. The hose is actually about 0.5 inches Inside diameter and the sprayer connectors 0.125" inner diameter just to get a good idea, but the restriction is in the sprayer connected on the far end of it where it is tied on to the plant.

The sprayers deliver the leaks :) at say they are at height h in each pot around 1 foot high. For poor gardeners who would like to grow vegetables for less than $10/pound, pumps and barrels can be expensive for just a few pots ... so how to best design this? The pressure drop is negligible from beginning to end of the hose (it is short, say 5 meters), but the spray heads deliver a volume and quality --and I'm guessing-- ~linearly increasing vs. pressure if that makes sense from observation. A certain pressure is necessary for a good spray and it is always more than the pump I buy can make. Questions:

1) If the hose runs vertically from the pump on the bottom of the barrel to height H, over the edge, and then drops to the ground of height = 0 where it runs along the ground, from which the sprayer connectors rise up to heights h and deliver in n sprayers (6 in a small example), how could we describe the pressure loss from running the hose out of the top of the barrel vs. perforating the barrel on the bottom and basically pumping at h=0?

2) How beneficial in terms of decreasing pressure loss, if much at all, would it be to raise the entire main hose to h' by say putting it on a track running along the plants, like an elevated train?

3) Is there a relationship of sort that would be useful for designing this employing P=pressure, h0, h, H?

I realize most of this deals with understanding "suction pressure" and differential pressure like siphons generate, but I still don't have a confident grasp of it. Looking for some help! I'd rather not perforate the barrel, but at some point higher pressure pumps become very expensive for the garden budget.
Thanks!
halfgt2

 

[Spinnor]

Does the water need to be delivered as a spray or can it just be a trickle?

 

[halfgt2]

Thanks Spinnor for coming by to help!

The water needs to be delivered as a spray, if that weren't the case, I could buy a low flow rate (very inexpensive) pump and deliver through rather small tubes. If it is dripped in, it will not sufficiently wet the area necessary for healthy root space (the cohesion of the water will drain to the bottom to waste like a blanket set to dry on a clothes line where the water quickly just finds the lowest point rather than distributing itself throughout the medium, and eventually result in dead plants and caked up soil in the pot wherever the water didn't reach. Soil has a certain capacity beyond which it drains in "free fall". Additionally there is a build up of fertilizer electrolytes (salts) that will concentrate like salt flats and become toxic. Those summarize the reason for having a spray with sufficient coverage and the motivation for this.

That's my main motivation, utilize most efficiently the pressure in the design. I can post a diagram if that is helpful, or even photos if that makes this interesting to you. One method to get a little more pressure is to put the barrel higher on a platform (on concrete blocks) like is done for water towers, and every little bit helps. That's not really part of the original question but it might come up. I know and verified that a 1.0 in^2 column of water 2.31 feet high weighs a pound, so that's an extra 1 psi I might also get, but don't see that I could lift the barrel much higher...and would prefer not to lift it at all if the net pressure saved is very negligible in this sort of basically closed system.

Speaking generally the sprayers need some unknown pressure between 5 -10 psi. My current pump delivers I estimate, ~1 psi and is a tiny trickle of 50 mL/min per sprayer, and has as much as 2 psi of loss due to my poor current design.

To get to 5 psi to 7 psi is where the cost of this type of pump takes off; over 7 PSI and I need to find a different class of pump. I only know for a fact that the manufacturer is happy with the spray quality at 10 psi but they know nothing further. At 10 PSI the sprayer is rated at 2.9 gallons per hour (183 mL/min). So the question is to explore the design to do the best I can applying pressure without loss, and that will determine in the pump I invest in. Keep in mind, it's just 6 plants in the garden ;-) If that works I'll scale it up to 15 plants, depending on the pump being available and lessons learned.

Sorry for all the details but I want to be clear and complete as I can. I'm just putting all the numbers to give an idea of the magnitudes involved, but the basic question is still more qualitative in estimating the effect of raising the main delivery hose to sit on a track and/or perforating the barrel on the bottom. Thanks again!

 

[Spinnor]

I guess you don't have access to pressurized running water from a home or barn?

How many gallons per day do your plants need?

 

[halfgt2]

Hi Spinnor,

Pressurized municipal tap water is available but won't meet the requirement. For the physics of the fluid, water closely approximates what is being pumped into the plants. The actual fluid I use is based on tap water which I first condition, and then dissolve varying ratios of soluble fertilizer into it. If I were a professional operation and not just someone having fun with this, one economical procedure is to connect to a tap and inject a carefully measured dosage continuously into the main tube as tap is introduced and flows through the inlet of the irrigation system, typically at a ratio of say 200:1. However most that have their own large scale operations including nurseries and greenhouses, have a quite large dedicated pump that monitors pressure and sometimes other variables like ionic strengths of drained effluents to keep the plants comfortable, temperature and pH.

Back to me, I am just having fun and modeling this sort of arrangement on a small scale in a batch process. I fill the barrel, treat the water, dissolving the component nutrients (soluble ionic salts) of the fertilizer,, shut the barrel and let the pump on a ~10-15 min/day timer, do the work until the barrel is nearly empty. Plant consumption depends on plant size and weather, but consider 2L/plant/day as typical (around 3 gal/day for the 6 pots).

The sprayers are very consistent at a given pressure, and since the pressure drop is negligible along the main from beginning to end, the concept is fine. The issue for small systems is cost, considering 6 pots are more a Sunday experiment than a cost effective garden. But it is a fun exercise as long as the hardware is cheap and relatively low power. Hope that helps ... please let me know if you have some ideas on the pressure optimization.
Thanks!
halfgt2