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).
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 with a water flow pressure of, let's say... 49 kPa (I need to check this with a manometer), and I attached a 25 mm diameter and 0.5 m 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 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:
$$P_1+\dfrac{\rho gh_1+v^2\rho}{2}=P_2+\rho gh_2+\dfrac{v^2\rho}{2}$$
If I took the height of $P_1$ 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:
$$P_1=P_2+\rho gh_2$$
So, if the garden hose pressure is 49 kPa:
$$\begin{gather} 49000\text{ kg}/\text{ms}^2=P_2+9.8\text{ m}/\text{s}^2\cdot 1000\text{ kg/m}^3\cdot 0.5\text{ m} \\ P_2=53900\text{ kg/ms}^2 \\ P_2=53.9\text{ kPa} \end{gather}$$
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.
$$\begin{gather}A=\pi r^2=\pi\cdot0.025^2=0.002\text{ m^2} \\ F=107.8\text{ N} \end{gather}$$
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.