can water falling under gravity create suction force and if so, how much force..if i put a huge strong tank on top of a hill and on top there is a tap connected to a huge body, then i put a another pipe on the bottom of the tank to empty..assuming that the tank n piping is water/air tight such that the only opening are at the pipe in the large water body like sea/lake and the other at the emptying point…i want to fill the system completely and then i empty..can i create a perpetual suction??
[Physics] can water falling/running down in pipe cause suction capable of creating a continuous flow
fluid dynamics
Related Solutions
The pressure on each side of the pipe is given by $P = \rho g h$ where $\rho$ is the density, $g$ is the acceleration due to gravity and $h$ is the depth of the pipe.
From the Euler equations of motion in 1D and steady state, we have:
$$ \frac{1}{2}\frac{d u^2}{d x} = - \frac{1}{\rho} \frac{dP}{dx}$$
If we make some more assumptions, namely that the pipe is full of seawater (which makes sense in the steady state because the water will flow from the sea to the lake) and that the pressure at the fresh water end is constant (so we ignore dilution/mixing, the sea water just instantly drops under the fresh), and we integrate from $x = 0$ at the sea end to $x = L$ at the fresh end:
$$ u^2 |_0^L = - 2\frac{1}{\rho} P|_0^L$$
and taking the velocity to be zero at $x = 0$ gives:
$$ u(L)^2 = -2\frac{1}{\rho_s}(P(L)-P(0))$$ $$ u(L)^2 = -2\frac{1}{\rho_s}(\rho_f g h - \rho_s g h)$$
Taking $\rho_s = 1020 \text{kg}/\text{m}^3$ and $\rho_f = 1000 \text{kg}/\text{m}^3$ with $g = 9.8 \text{m}/\text{s}^2$ yields:
$$ u(L)^2 = 0.0961h $$
or
$$ u(L) \approx 0.31h^{1/2}$$
Obviously this makes some pretty big assumptions. No viscosity, which is probably not that bad of an assumption unless your pipe is really deep, and the pressure on the fresh water end is constant implying the salt water just "disappears" by dropping very quickly out of the pipe under the fresh water.
Why does the length of the pipe matter
It doesn't actually. You'll notice $L$ doesn't appear anywhere in the expression. The velocity at the end of a mile long pipe or a 1 inch long pipe is the same and given by that expression.
What is the significance of $h^{1/2}$
Again, there really isn't any significance. The units of pressure/density are $\text{m}^2/\text{s}^2$ which is what RHS of $ u(L)^2 = 0.0961h $ is. So the units on the 0.0961 are $\text{m}/\text{s}^2$ and $h$ is $\text{m}$. So when you take the square root of both sides to get into $\text{m}/\text{s}$, you end up with the $h^{1/2}$.
So the significance is really just that there is a non-linear relationship between velocity and the depth of the pipe. If you put your pipe four times deeper, you'll only get twice the velocity.
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).
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.
Best Answer
I think you are asking two questions.
First : Can falling water create suction? The answer is Yes, but the effect is quite weak. It makes use of the siphon effect and is limited by atmospheric pressure, so the maximum column of water you could lift is about 10m.
https://en.wikipedia.org/wiki/Siphon
Second : Is it is possible to use this effect to create a perpetual motion device, or perhaps create a source of unlimited free energy? The indisputable answer is No. There are many websites which explain why such devices are impossible.
https://en.wikipedia.org/wiki/Perpetual_motion#Apparent_perpetual_motion_machines