The force with which a stream of water pushes an object

[Iacob Sorin]

Hello! I'm having trouble finding out how to calculate the force with which a river can push an object, well an propeller to be more exact. I would like to know what do I need to find about the river, like speed and cubic metres, and how do I use this information to calculate the force with which that propeller will be turned. I want to know all of this because I am planning to build a hydrogenerator. Furthermore, can I calculate what kind of force will a couple of the propellers produce when they will all be hooked up to a shaft(torque, RPM)

 

[A.T.]

It seems you are asking about a turbine, and it's power output (torque * RPM) rather than force (drag). Neither is simple to estimate and depends on the flow speed, turbine geometry and the load (generator) you attach to it. To maximize the power output (given some constraints like size) you have to find the optimal combination of those parameters, which is not a trivial task.

 

[sophiecentaur]

There is a way to estimate the maximum possible force (totally unreal situation but it would give you a number to play with).
If the flow of fluid is being obstructed by an obstacle of area A and the speed of the flow is v then, if you assume that the fluid is actually brought to a halt (but you'd have to get rid of the stationary fluid and that is where the idea breaks down - never mind, proceed) The fluid hitting the obstacle in 1s would have a mass M of Avρ (where ρ is the density of the fluid). This mass would be brought to a halt by a force F, which acts for 1 second.
Impulse = Change in momentum
which can be stated as
Force X time = velocity X Mass
so Force = vM/t
the time is 1s so
F= v Avρ = Av²ρ
Put in the values of your situation (using metres and density in kg/m³) and that should give you the force in Newtons.
As I mentioned above, the fluid has to be constantly shifted out of the way and a turbine will also modify the force you get but this method would be a quick and dirty way of getting some idea. Be pessimistic and assume a reduction to a quarter of what you calculated. See what you get.

 

[anorlunda]

@A.T. gave you good advice. It is not so simple. It is not even clear if a propeller type turbine is appropriate for your situation. Kaplan and Pelton turbines are other major kinds of hydro turbine designs, not to mention old fashioned water wheels which can do a fantastic job in some cases (and which are very rustic in appearance)..
You have at least three ways to go forward.

1. If your calculus is solid, find textbooks on hydro turbine design. That is probably overkill for a DIY project.
2. Google for hydro turbine online calculators. Those sites might give you numerical estimates and advice.
3. Take the tinkerer's approach. Built one that suits your situation, your skills, and your budget and see what you get without calculations in advance. Youtube has dozens of videos on DIY backyard hyrdro projects.

By the way, maximum power is not the only consideration. Experimental propeller type hydro turbines were fastened to the bottom of the East River in New York City. The currents proved to be too strong for the foundations and threatened to wash them away. My point is that strength and durability in worst case conditions are important if you want it to last.

Good luck, I always wanted to do my own hydro project, but I never had the opportunity.

 

[A.T.]

if you assume that the fluid is actually brought to a halt (but you'd have to get rid of the stationary fluid and that is where the idea breaks down - never mind, proceed)

And if you do mind, then use Betz' limit:
https://en.wikipedia.org/wiki/Betz's_law

 

[russ_watters]

Combining several of the above, if you do a really good job the most you can hope for is about 50% extraction of available energy. More realistic might be 30%. So if you have a turbine size (cross sectional area) and flow rate, calculate the kinetic energy of the water that passes the turbine and divide by 3 for a realistic possible extraction rate.

 

[sophiecentaur]

And if you do mind, then use Betz' limit:
https://en.wikipedia.org/wiki/Betz's_law

My method was just the sort of calculation you could do in a noisy pub on a beer mat. It would give you an answer which could tell you if it's worth while pursuing the idea. Some great ideas have been hatched that way.

 

[Iacob Sorin]

Thank you all for the answers, sophiecentaur gave me the kind of answer I was looking for, really rough numbers to see if it is worth it without much effort, but if I start building it, I will look more into the more complicated stuff to maximise the efficiency.

 

[houlahound]

I don't think the calculation approach is how most of these projects I have seen start. Acquire a motor eg a washing machine from a dump. Hack it until its a generator. Build a mount based on whatever propeller and gear system you have assembled.

Suck it and see.

 

[anorlunda]

Thank you all for the answers, sophiecentaur gave me the kind of answer I was looking for, really rough numbers to see if it is worth it without much effort, but if I start building it, I will look more into the more complicated stuff to maximise the efficiency.

y

Why not give us some numbers and we can estimate your results. How much water flow? How much vertical height drop? How much electric power do you need to declare success? Is your project strictly intended to save money, Or do you have other motivations?

 

[russ_watters]

y

Why not give us some numbers and we can estimate your results. How much water flow? How much vertical height drop? How much electric power do you need to declare success? Is your project strictly intended to save money, Or do you have other motivations?

Agreed. it is a lot of work to find out (perhaps) that there isn't even a useful amount of power available. So even if you succeed you might fail!