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I'm trying to design a kind of water valve with inexpensive materials as a first prototype. The water flow from the PVC pipe (1) reach the body of the valve and pass through an aluminum grid (3) to the water tank. When the water level goes up pushes the float closing the water intake at point (2). enter image description here

How can I calculate the buoyancy force needed to stop the water flow? And, what will be the mass of the float? Let’s back to the basics; here I present the problem and some math that I been doing, I would like your opinion:

  • Connected to the PVC pipe (2) I have a garden hose whit a water flow pressure of, let's say...49 kPa (I need to check this with a manometer), and I attached a 25 diameter and 0.5 meters long PVC pipe. Let’s pretend that the float seals the other side of the PVC pipe, so I need to calculate the force generate by the water flow pressure against the float.

Please take in consideration that I'm not a fluid mechanic expert.

When I open the garden hose, the PVC pipe starts to fill, so based on this situation:

enter image description here

P1+ρgh_1+(v^1 ρ)/2=P2+ρgh_2+(v^2 ρ)/2

If I took the height of P1 as the reference, h=0, and the diameter of the PVC pipe and the garden hose pipe are the same (25 mm), the water flow velocity at those points are equals:

P1=P2+ρgh_2

So, if the garden hose pressure is 49 Kpa:

49000 kg/(m s^2 )=P2+9.8 m/(s^2 ) x 1000 kg/m^3 x 0.5 m

P2=53900 kg/(m s^2 )

P2=53.9 Kpa

Ok, assuming this math is correct…now I have to calculate the force against the bottom of the PVC pipe at point 2:

P=F/A

In order to simplify this example, I took the diameter of the PVC pipe as the contact area.

A=πr^2=π(〖0.025〗^2 )=0.002 m^2

F=107.8 N

If the pressure of the water flow generates a force of 107.8 N, I need an opposite force with a higher value to counteract it. Is that correct? My goal is to find a material (mass; area) that generate enough buoyancy force to stop the water flow through the valve and seal the water intake, and when the water level goes down, the float valve will let pass the water flow to continue to fill the water tank.

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Joaquin Osses
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  • You need to make sure that the force due to buoyancy is larger than the force due to the water pressure. This does not depend on the speed of the water but simply on the pressure provided by your tap. – Edgar H Jan 22 '18 at 13:52
  • I'm voting to close this question as off-topic because it is about fluid dynamics / mechanics / physics / hardware instead of programming / coding / programming tools / software algorithms. – Pang Dec 12 '18 at 07:39

1 Answers1

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I agree with the previous comment : the pressure at the contact is the total pressure at the line feed (corrected for gravity at height 1). When water is flowing, some of that pressure is converted to dynamic pressure, meaning you will measure a lower pressure at point 1; the total sum at p+1/2 v^2 should remain more or less the same irrespective of v - if we neglecting head losses running up to point 1 which depend on the flow rate.

Anyway, when the valve is closed, the flow is stopping anyway, so you it is even more obvious to work with the static pressure measured in the absence of flow.

You need to choose the density and form of your floater such that the buoyancy force, given by $(density of water - density of floater material)*(submerged volume at chosen reservoir height)$ is equal to $p2 * A$.

Koen Hillewaert
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