Force required to produce wave in tank

[Whatamiat]

Homework Statement

I am building a tank to produce waves.
I have two options to power the flap that will be produced to create the waves:

1. Pneumatic system
2. Motor and Cam system

Before I can order motors or pneumatic air cylinders I need to know what force will be required to move the flap the required distance to produce the waves.

Sketches of both systems are attached
Sketch of problem is attached

Homework Equations

Fxd = mgh

P= FxA ?

The Attempt at a Solution

From attached images:

Mass of Water = 7500kg

Finding Distance:
d = tan 18 x 1 = 32.5cm

Finding mass of displaced water:
d x h x w = .325 x 1 x .75 = 243.75kg
but we are dealing with triangle so
mass of displaced water =243.75/2 = 121.875kg of water displaced

Calculating Height of water when flap is extended:
Mass of water = length of tank x width of tank x height of tank
7.5 = (10-.1625) x .75 x h
h = 1.0165 cm

Calculating Force:
d = 32.5/2 = 16.25 (as we are dealing with triangle not rectangle)

F x 16.25 = 7500x9.81x1.0165

F = 4602.4kN

My Thoughts
Very sure I am missing something fundamental with this solution but not sure what!

I feel I have ignored the fact that the force is being applied at 1.25m not 1m but don't know how to incorporate this.

Im also unsure if I have used the wrong figures for my Fxd=mgh solution.

I feel P=F/A can be incorporated but not sure how?

Thanks for any feedback!

 

[tiny-tim]

Hi Whatamiat!

Are you using the work-energy theorem? (it would have been clearer if you'd said so)

If so, in the formula work done = force "dot" displacement, the displacement is the displacement of the point of application of the force.

 

[Mene]

Your solution seems to be on the right track, but there are a few things to consider. First, your calculation for the mass of displaced water is incorrect. It should be d x h x w = .325 x 1 x .75 = .24375 m^3. Then, using the density of water (1000 kg/m^3), the mass of displaced water would be 243.75 kg, not 121.875 kg.

Next, your calculation for the height of water when the flap is extended is also incorrect. It should be h = 1.0165 m, not cm.

Additionally, you are correct in thinking that the force is being applied at 1.25 m instead of 1 m. This means you will need to take into account the lever arm in your calculation. The correct equation to use would be F x 16.25 = 7500 x 9.81 x (1.0165 - 1.25), where 1.0165 is the height of the water when the flap is extended, and 1.25 is the distance from the pivot point to the point where the force is being applied.

You can also use the equation P = F/A, where A is the area of the flap, to calculate the required force. However, this will only give you the force required to move the flap, not the force required to produce waves in the tank. To calculate the force required for the waves, you will need to consider the mass of the water being moved by the flap and the force required to accelerate it to the desired speed.

Overall, your solution is on the right track, but there are a few errors and considerations that need to be taken into account. It's always a good idea to double check your calculations and make sure you are using the correct units and equations for the problem.