# Water level in connected tanks

I've got two water tanks on my rooftop(both tanks are of exactly same dimensions and are at exact same level) connected at the bottom. I fill them via an external pipe connected with a pump on the first floor. In order to fill the tanks, I open the lid of one tank (Tank 1) only so little as I can insert a pipe inside the tank.

After I've inserted the pipe I put some weight (a brick) on the lid so that the pipe does not come out of the tank due to water pressure. Please note that the lid on the other tank (Tank 2) remains closed. Tank 1 is also partially open (just a bit as there's a pipe inserted).

After some time of filling the water, I checked the water levels in both the tanks and I noticed a significant difference in the water levels(I opened the lid of both tanks to check the water level).

I'm confused because since the tanks are connected at the bottom, I was expecting both of them to have the same water level at all points of time. Why am I wrong? Can the rate with which the external pipe is filling Tank 1 be greater than the rate at which the water is going from Tank 1 to Tank 2 (via the connecting pipe)?

• What is the size of the connecting pipe? Does it have a valve in it? Is it fully open? What is the delivery rate?
– user207455
Jul 14, 2019 at 10:59
• Are the lids airtight when closed?
– Dale
Jul 14, 2019 at 11:35
• @SolarMike I don't know the exact dimensions of the pipes(connecting as well as the external one). It's fully open though. I don't have any figures for the delivery rate as well. But this is exactly what I wanted to understand. I thought that rate of delivery/size of connecting pipe shouldn't matter. Jul 14, 2019 at 12:02
• You can't expect the tanks to have the same level "at all points of time". You can only expect them to seek the same level after enough time has passed. The reason is that it takes time for water to flow through the connecting pipe. To understand this, suppose a large amount of water is suddenly added to the first tank. Will it suddenly appear in the second? Of course not. Aside: this, by the way, is the basic modeling structure used in pharmacokinetics. Drug is dumped into the gut. From there it leaks into the blood plasma. From there it leaks out of the system. There are other "tanks" too. Jul 14, 2019 at 13:29
• Yeah. I see now. It was stupid of me to assume that the water level will always be maintained no matter what the incoming delivery rate in Tank 1. I don't know why but I thought that the speed of water in the connecting pipe will increase accordingly to compensate so that the water level is maintained. But I understand now. Jul 14, 2019 at 13:38

1. If the lid on Tank2 is airtight, then the air pressure will build up in Tank 2 and prevent the water inflow into Tank 2 from the bottom (via Pipe 2).

2. If the lid on Tank2 is NOT airtight then:

• If the water flow through Pipe 1 is more than 2x greater, than the flow through Pipe 2, then Tank 1 will have a higher water level when the pump is ON. After the pump is turned OFF, the water levels will equalize eventually.
• If the water flow through Pipe 1 is NOT more than 2x greater, than the flow through Pipe 2, then the tanks will always have the same water level

The water flow depends on the pressure differential between the two pipe ends, divided by the resistance of the pipe to the water flow. For practical purposes, the resistance of the pipe to the water flow depends on the crossectional area of the pipe and the length of the pipe and its bends and kinks.

Note: The pressurized air in Tank 2 will affect the pressure differential between Pipe 2 ends and consequently will affect the water flow in that pipe. If that pressure differential falls down to zero, the water will stop flowing altogether.

• Why 2x? What if it's 1.5x? Jul 14, 2019 at 13:39
• The material and surface of the pipe can have a big effect on the flow especially with “ridged” pipes...
– user207455
Jul 14, 2019 at 15:04
• @Mike: Yes, the inner surface of the pipe and kinks and bends in it will affect the resistance of the pipe, too. Jul 15, 2019 at 8:30
• @Vishal: 2x because the tanks are equal, so when half of the water flow from Pipe1 ends up in Tank1 and the other half ends up in Tank2 (via Pipe2) then the water level in Tank2 will not lag behind the level in Tank1. The same in case of 1.5x, because 1/1.5=0.66, although Pipe2 will be "underutilized" in this case. Jul 15, 2019 at 8:35

As george mentioned the difference in level of water in both tanks depend on many factors like the pressure difference,pump capacity and the height of water level in tank 1. I assume that both lids 1 and 2 are not air sealed practically. Then the water flow will depend on the height of water level in tank 1.

Pressure difference given as P= (densitygh).

Now based on bernoulis equation this pressure head is converted into velocity head meaning p/(density*g) = v^2/(2*g).

Now we know that the mass flow rate Q = (density * v * A). Where v is velocity and A is cross sectional area of pipe.

Now generally when we consider a pipe many loses like frictional losses,bending losses,etc will all arise which eventually reduce the velocity by almost half of it.

Now if the pump capacity is greater than the flow rate from 1 to 2 then tank 2 takes a lot of time.

If you could know the exact specifications of your pump along with the specifications of pipes that you are using you can calulate all this.

Hope this helps you.

• This is all basics of fluid mechanics which you can calculate with ease.You can take this as general physics. Ya ofcouse I can understand that you might not encounter or deal with such issues daily.But we as mechanical engineers do such things regularly. Jul 14, 2019 at 13:47