# Pressure required for water discharge

• praveenncyr
In summary, you will need a little more than atmospheric pressure to push liquid out of a tank when it is full and when it is empty. The relationship between pressure and flow is linear.
praveenncyr
Hello everyone,

I am very interested in knowing the relation to determine the pressure required to push the water upstream.

In the attached picture, water is filled inside a tank of volume V and air is constantly flowing inside the tank through an inlet with constant flow rate M. Water should be discharged with a flow rate of W through the outlet. The outlet is maintained at a pressure of P2. Now, considering the fact that air is compressible and temperature dependent, how could I calculate the pressure required by air at the top of water to push the water out through the outlet?

I am sorry for not being so specific about the dimensions. I just want to relate it somehow! Your comments are highly appreciated!

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In US/imperial units, pressure is often expressed in height of a water column. That's your minimum required pressure here, plus your outlet pressure.

Chestermiller
russ_watters said:
In US/imperial units, pressure is often expressed in height of a water column. That's your minimum required pressure here, plus your outlet pressure.
Hey, that's a coincidence ! In normal units too !

BvU said:
Hey, that's a coincidence ! In normal units too !
What are "normal" units?

I've seen atmospheric pressure in mm of mercury of course, but I'm not sure I've ever done an SI pump sizing. For airflow, I always see inches of water converted to Pascals.

BvU
russ_watters said:
What are "normal" units?
After some research, I concluded the physics is independent of the system of units used to express the relationships! So, in that respect, even us/Imperial units could be considered to be somewhat normal !

But let's lure @praveenncyr to reveal to us helpers what he/she actually wants! (as opposed to discussing what we consider decent versus backward systems of units )

russ_watters
praveenncyr said:
I am sorry for not being so specific about the dimensions. I just want to relate it somehow! Your comments are highly appreciated!
Welcome!
As dimensions of the tank grow, the ability to supply enough flow of air becomes more important, if certain amount of water flow is needed.
You will also need to consider resistance to the flow of water imposed by the pipe system to which the tank could be connected to.

Thanks everyone for your showing interest.

Lets discuss it with an example...The tank has a capacity of 70 litres and the water should be rised just above the tank. Let's say that the height of tank is 0.6 m and the radius of tank is 0.2 m. The diameter of air inlet and water outlet pipes are both 0.013 m. Air flows inside the tank with constant flow rate at 20°c. Now, I would like to know the pressure at inlet and outlet, considering 8E-5 m^3/s of water is being discharged.

I am in need of a relation to calculate it!

praveenncyr said:
I am in need of a relation to calculate it!
Several relations !
First you have the already mentioned ##\Delta p = \rho g\; \Delta h## for the water.
For the air, use ##pV = nRT##, the ideal gas law.
And you can't fix all variables you mention: for a given flow of water, the flow of air follows.

Oh, and at the outlet the water pressure is astmospheric.

BvU said:
Several relations !
First you have the already mentioned ##\Delta p = \rho g\; \Delta h## for the water.
For the air, use ##pV = nRT##, the ideal gas law.
And you can't fix all variables you mention: for a given flow of water, the flow of air follows.

Oh, and at the outlet the water pressure is astmospheric.
Thanks for your comment, I kind of need a correlation...

Yes, the pressure at outlet is atmospheric pressure.

praveenncyr said:
...the water should be rised just above the tank.
You gave numbers for almost everything except the most important thing: we need to know how high the outlet is above the water level in the tank.

russ_watters said:
You gave numbers for almost everything except the most important thing: we need to know how high the outlet is above the water level in the tank.

The outlet is 0.75 m higher from the bottom of the tank.

praveenncyr said:
I am very interested in knowing the relation to determine the pressure required to push the water upstream.
So, with the tank full, you need a little more than atmospheric pressure to push some liquid out.
And with the tank as good as empty, that requires a little over 1.6 Bar
(to be precise: atmospheric + 0.6 ##\rho g ## ).

In between, the relationship is linear.

Pressure drop due to friction can be ignored at such a low flowrate.

Is this somewhat clear ?

(edit: at first the tank was 0.6 m... and the outlet just above. Just above is negligible, a quarter tank height is not !)

(edit2: is this a state secret project that you are so sparse, handing out required information bit by bit after being pressed ? )

russ_watters
praveenncyr said:
The outlet is 0.75 m higher from the bottom of the tank.
...we need to know how high the outlet is above the water level in the tank.

Edit: or more to the point, as the tank empties, the required pressure increases.

BvU said:
So, with the tank full, you need a little more than atmospheric pressure to push some liquid out.
And with the tank as good as empty, that requires a little over 1.6 Bar
(to be precise: atmospheric + 0.6 ##\rho g ## ).

In between, the relationship is linear.

Pressure drop due to friction can be ignored at such a low flowrate.

Is this somewhat clear ?

(edit: at first the tank was 0.6 m... and the outlet just above. Just above is negligible, a quarter tank height is not !)

(edit2: is this a state secret project that you are so sparse, handing out required information bit by bit after being pressed ? )
It is so obvious that the pressure inside the tank should be higher than the outlet pressure. Since the air is compressible, it is not necessary that the amount of air going inside would displace the same amount of water, also the space about the water level filled by air is time dependent. So, I would also like to know the flow rate of air necessary to displace the required amount of water at the outlet!

russ_watters said:
...we need to know how high the outlet is above the water level in the tank.

Edit: or more to the point, as the tank empties, the required pressure increases.
It is totally time dependent, initially its 0.2 m higher than the water level. Also I don't want the specific solution value to my problem. I would like to understand the calculation procedure and the relation between them!

BvU said:
So, with the tank full, you need a little more than atmospheric pressure to push some liquid out.
And with the tank as good as empty, that requires a little over 1.6 Bar
(to be precise: atmospheric + 0.6 ##\rho g ## ).

In between, the relationship is linear.

Pressure drop due to friction can be ignored at such a low flowrate.

Is this somewhat clear ?

(edit: at first the tank was 0.6 m... and the outlet just above. Just above is negligible, a quarter tank height is not !)

(edit2: is this a state secret project that you are so sparse, handing out required information bit by bit after being pressed ? )
Ha Ha... its not a state secret project...I don't have specific values...I just want to know how to solve it!

praveenncyr said:
It is so obvious that the pressure inside the tank should be higher than the outlet pressure.
Good. So you have a required pressure as a function of the liquid level.
praveenncyr said:
I would like to understand the calculation procedure and the relation between them!
See #9: the ideal gas law tells you how much air is needed in the gas volume.

russ_watters

## 1. What is the relationship between pressure and water discharge?

The pressure required for water discharge is directly proportional to the rate of water flow. This means that as pressure increases, the water discharge will also increase.

## 2. How is the pressure required for water discharge calculated?

The pressure required for water discharge can be calculated using the Bernoulli's equation, which takes into account factors such as the height of the water source, the diameter of the pipe, and the velocity of the water.

## 3. What is the minimum pressure required for water discharge?

The minimum pressure required for water discharge depends on the specific application and the desired rate of water flow. However, in general, a minimum pressure of 30 pounds per square inch (psi) is needed for a steady water flow.

## 4. How does the shape and size of a pipe affect the pressure required for water discharge?

The shape and size of a pipe can greatly impact the pressure required for water discharge. A larger diameter pipe will require less pressure to achieve the same rate of water flow compared to a smaller diameter pipe. Additionally, a smoother and more streamlined pipe shape will also require less pressure.

## 5. Can the pressure required for water discharge be too high?

Yes, the pressure required for water discharge can be too high. Excessively high pressure can cause damage to pipes and fixtures, as well as waste water. It is important to maintain a safe and efficient pressure level for water discharge.

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