Does a higher water volume increase pressure?

I am constructing a gravity flow water system. I have 100ft point where I can put my tank. My question is does the size of my tank matter? I am using a 1" pipe. Will I get more pressure if I use a bigger tank? For example what is the difference in pressure if I use a 10 gallon tank or a 50 gallon tank?

The static pressure $p$ depends solely on the height $h$. If $p_0$ is the atmospheric pressure, then:

$$p=p_0+\rho gh$$

Where $\rho$ is the liquid's density and $g\approx10\:\mathrm{ms^{-2}}$.

So for the left hand side tank the pressure would be slightly higher because the tank is taller (not because it has higher or lower capacity).

Flow through the pipe always causes some viscous pressure loss though.

Do I need a tank and secondly as far as I can gather from you guys it is the pressure that the water leaves the bottom of the tank is the pressure at the end of the pipe?

If you have easy access to the stream, a tank is not required.

The pressure discussed in my answer is called hydrostatic pressure and for good reason: if one blocks the end of the pipe, the pressure $p$ at that point would be exactly as indicated above ($p=p_0+\rho gh$, where $h$ is the height difference between the water's open surface and the pipe's end).

But when flow is allowed a certain amount of pressure is lost due to friction in the pipe. In that case the corrected pressure can be noted as:

$$p'=p_0+\rho gh-\Delta p$$ Without going into full details of pipe flow theory we can say with certainty that $\Delta p$:

1. increases with pipe length,
2. decreases with pipe diameter,
3. increases with volumetric throughput (flow speed),
4. increases with pipe inside roughness: smooth, uncorroded, new pipes reduce pressure less,
5. increases in the presence of local resistances like bends, kinks, valves, sudden diameter changes and such like.

A short, wide, smooth, straight pipe operated at low flow speed will deliver pressure almost identical to the hydrostatic pressure $p$.

But using a long, narrow (etc) pipe can lead to almost all of the hydrostatic pressure being lost to friction ($\Delta p \approx p_0+\rho gh$).

• Good pictures always help. Commented Aug 19, 2016 at 1:27
• No doubt. I post few answers w/o them.
– Gert
Commented Aug 19, 2016 at 1:34
• Thank you so much for your answers. It has helped me a bit but still trying to get my head around the physics, was daydreaming in school. I have a stream, my highest point is 100ft, I initially just put my 1" water pipe into the stream and hoped it would flow neatly through the pipe and out 100ft below with great pressure. This is not happening. So I thought I need a tank to create the pressure. Firstly, is this the case? Do I need a tank and secondly as far as I can gather from you guys it is the pressure that the water leaves the bottom of the tank is the pressure at the end of the pipe? Commented Aug 19, 2016 at 20:18
• Will answer as an edit. Ta.
– Gert
Commented Aug 19, 2016 at 20:40
• Done. See what you think.
– Gert
Commented Aug 19, 2016 at 21:12

The pressure experienced at the bottom of the pipe depends on the diameter of the pipe, the flow rate, the total height difference between the surface of the water and the point where you measure the pressure, and the density of the liquid.

When the flow rate is zero (no liquid flows: before you open the valve) the only thing left is the density and the height difference, and the pressure at the bottom will be higher than atmospheric pressure according to

$$\Delta P = \rho g \Delta h$$

Where $\rho$ is the density of water (1000 kg/m$^3$), $g$ is the gravitational acceleration (9.8 m/s$^2$), and $\Delta h$ is the height difference (100 ft).

Now if you have a small container at the top, then when water starts to flow the water level is likely to drop quickly - and this will give a small drop in pressure (small, because with 100 ft initial height there just isn't a lot of height to drop in a 10 gallon container). But otherwise there will be no difference between the two containers.

• Thank you Floris. But the tank is the key isn't it? Initially, I just had my 1" pipe in the stream hoping the height would give me great pressure but I think I need a tank to create the pressure, dont I Commented Aug 19, 2016 at 20:38
• You need the tank to maintain the pressure. If you look at the diagram in Gert's answer, you can see that you will get the same pressure as long as the surface of the water is at the same height. Now if you are catching water from a stream you may be trapping bubbles (lowering the apparent density) and a tank will allow the bubbles to go to the surface (water flows slowly in the tank, giving the bubbles time to "float upstream".) If you try to trap water from a stream straight in a tank you may be sucking in air - that would lower the density and thus pressure. Commented Aug 19, 2016 at 20:44
• Thanks Floris, I have to use a pipe to fill my tank. I will cut a hole near the top and another hole near the bottom to continue bringing my pipe downstream.So I hope that any bubbles will float to the top of the tank? My tank will be as near as I can get to my 100ft height. This is a practical water system that I am trying to create that needs physics done correctly to get a good outcome. I propose to use a 50gallon tank about 4ft tall. Thank you again so much for your input and I hope I get a successful outcome. :-) Commented Aug 19, 2016 at 20:56
• The 'tank/not tank' question is a little subjective. If you can tap into the stream at sufficient depth air bubbles should not be an issue. Building a tank however is a complication best avoided where possible.
– Gert
Commented Aug 19, 2016 at 21:26

If you have a tank with an outlet at the bottom then the pressure in the outlet is the same as the pressure in the water at the bottom of the tank.

The pressure $P$ at the bottom of the tank is $P=\rho g h$ where $\rho$ is the constant density of water, $g$ is the acceleration due to gravity, and $h$ is the height of your tank.

This shows that for your tank the pressure at the outlet depends only on the height of your tank.

If you swim to the bottom of a 2m deep pool you can feel some pressure. If you're in a small back-yard pool it feels like the same pressure as an olympic sized swimming pool. The volume of the pool isn't affecting the pressure 2 metres down.

• So a tall narrow tank where the water is high is better than a shallow wide tank with the same volume of water? It creates more pressure? And will the pressure be the same at 50ft as it will be at ground level? What will give me most pressure? A bigger tank? Commented Aug 19, 2016 at 20:30
• @RichardJ referring to Gert's diagram, the height between the top of the water level and the point of the pipe outlet is the height that determines the pressure. If you have many pipe outlets over several storeys of a building then the ground floor will have the highest pressure and upper floors will have lower pressure.
– Hugh
Commented Aug 20, 2016 at 10:24
• Continuing from my last comment... A tall narrow tank will add to the height and therefore the pressure. If your building is 50ft tall then ground floor won't notice a big difference if you make the tank tall and narrow but for the top floor of the building the tall narrow tank could noticeably increase their water pressure (again look at Gert's diagram)
– Hugh
Commented Aug 20, 2016 at 10:26

Gravity flow pressure can be figured, or measured, simply by two methods:

1) divide the drop in elevation (in feet) by 2.31 OR........2.31 feet of drop = 1# of pressure

2) if you have a system already established, screw an inexpensive water pressure gauge on a hydrant, or hose bibb and read the pressure

NOTE: the volume of water in a tank does not increase the water pressure. Height, or amount of drop, is what creates water pressure. CAVEAT: I am a lay person, not an engineer, so can only explain this in simple terms. And, being a lay person, I have found that it is difficult to wrap your head around the fact that the volume of a tank does not impact water pressure. Only the height of the tank plays into the amount of water pressure you'll have.

Friction will reduce water pressure. The more elbows and the distance/length of the pipe will change the pressure.

• Thank you so much Larry, I too am a lay person and you have explained it very well. Yes, I have discovered that volume does not increase water pressure. I am adding more distance and elbows as we speak and pressure seems to be holding well. With 100ft height I am getting great pressure but distance will reduce it I expect but I must have 2km pipe laid at this stage and I am still happy with it. Commented Jun 21, 2018 at 22:07
• Your idea of an inexpensive water pressure gauge is a great idea. I must look into it. Commented Jun 21, 2018 at 22:11