Calculating force to displace water

In summary: But even then, you'd need to know the Reynold's number, the density of water, and the velocity of the water. Sorry, that's more detail than I wanted to go into!In summary, the weight of the plunger, 6kg, is pushing down on water that is sitting at a height of 50 cm above the plunger. The distance the plunger moves is 50 cm, and it takes 2 seconds for the plunger to move that distance. The water in the tank is displaced by 375 kg of water when the plunger is at full extension.
  • #1
Whatamiat
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I am trying to determine the force required to displace water as shown in the attached picture.

My problems here are that I am displacing water using a vertical plunger moving downward at 25cm/sec also as seen in the picture the plunger is at 45degrees.

I am confused as to how to calculate the force required to do this

Gravity in this case is working to our advantage when the plunger is going downwards and working against us on when the plunger is returning to its original position.

What I know:
Weight of plunger = 6kgs
125kgs of water of water displaced by plunger at full extension.
Distance = 50cm = plunger moves from start position 50cm downwards.
Time= 2 sec for plunger to move downward 50cm.
10000kg of water in the tank.
Horizontal force of water in tank= 375kg force per unit area = 3678.75 N

Can someone give me some insight into how this might be calculated? I don't think its as simple as P=F/a!
 

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  • #2
Whatamiat said:
I am trying to determine the force required to displace water as shown in the attached picture.

My problems here are that I am displacing water using a vertical plunger moving downward at 25cm/sec also as seen in the picture the plunger is at 45degrees.

I am confused as to how to calculate the force required to do this

Gravity in this case is working to our advantage when the plunger is going downwards and working against us on when the plunger is returning to its original position.

What I know:
Weight of plunger = 6kgs
125kgs of water of water displaced by plunger at full extension.
Distance = 50cm = plunger moves from start position 50cm downwards.
Time= 2 sec for plunger to move downward 50cm.
10000kg of water in the tank.
Horizontal force of water in tank= 375kg force per unit area = 3678.75 N

Can someone give me some insight into how this might be calculated? I don't think its as simple as P=F/a!


Start with Newton's first law for the plunger since it moves with constant velocity. You have a normal force, a downward weight force, and an upward buoyant force:

F_net = 0

N + W + F_b = 0

In the above equation, the unknown of interest is the normal force. The weight force can be calculated with -m*g and the buoyand force is rho_water*V_displaced*g.

N - m*g + rho*V*g = 0

The reason this problem is a bit tricky is because the volume of the plunger underwater is variable. Calculate V as a function of time using geometry. Then you can solve for the normal force as a function of time. The volume of water in the container is not relevant to this problem.
 
  • #3
Sorry, I don't think that's an easy problem. It is P=F/a, the hard part is figuring out what P is! The static case is pretty simple, but when the water is flowing past an object at ~25cm/s I don't know. It should be fairly straightforward to estimate the order of magnitude but if you want more accuracy than that the problem gets a lot harder. I'll let the hydrodynamics people comment, it's not really my area. I guess the first thing to look at would be the Reynold's number to decide if the drag is pressure dominated or viscosity dominated and to decide what level of accuracy you need; then go from there either with an analytical approximation or a computer simulation - whatever suits. Hydrodynamics is notorious for computation difficulty.
 
  • #4
Gazebo dude is correct. My solution would be the correct solution at low speed, but at 25 cm/s drag forces would likely be significant. With the changing orthographic projection of the plunger, this force would be variable despite the constant speed. You might be able to model the drag force with the "drag equation" (look it up on Wikipedia).
 
  • #5


To calculate the force required to displace water, we can use the formula F = ρVg, where F is the force, ρ is the density of water (1000 kg/m^3), V is the volume of water displaced, and g is the acceleration due to gravity (9.8 m/s^2).

In this case, the volume of water displaced by the plunger can be calculated by multiplying the cross-sectional area of the plunger (which can be determined from the picture) by the distance it moves (50 cm). This will give us the volume of water displaced in cubic meters.

Next, we need to take into account the angle of the plunger and the direction of movement. Since the plunger is moving downward at an angle of 45 degrees, we can use the cosine of 45 degrees (which is 0.707) to calculate the component of the force that is working against gravity. This will be multiplied by the weight of the plunger (6 kg) to get the force required to overcome the weight of the plunger.

To calculate the force required to overcome the weight of the water, we can use the formula F = mg, where m is the mass of the water displaced (125 kg) and g is the acceleration due to gravity (9.8 m/s^2). This will give us the force required to displace the water in the downward direction.

To calculate the total force required, we can add the forces calculated above for the weight of the plunger and the weight of the water. This will give us the total force required to displace the water at a rate of 25 cm/s.

It is also important to note that the horizontal force of the water in the tank can contribute to the overall force required. However, this force will depend on the size and shape of the tank and cannot be accurately determined without more information.

In summary, the force required to displace water can be calculated by taking into account the volume of water displaced, the angle and direction of movement of the plunger, and the weight of the plunger and water. Other factors, such as the horizontal force of the water in the tank, may also need to be considered.
 

1. How do you calculate the force needed to displace water?

To calculate the force needed to displace water, you can use the formula F = ρ * g * V, where ρ is the density of water, g is the acceleration due to gravity, and V is the volume of water displaced. This will give you the force in Newtons (N).

2. What is the density of water and why is it important in calculating force?

The density of water is approximately 1000 kilograms per cubic meter (kg/m³). It is important in calculating force because it determines how much mass is contained in a certain volume of water. This, combined with the acceleration due to gravity, allows us to calculate the force needed to displace the water.

3. Does the shape of the object affect the force needed to displace water?

Yes, the shape of the object does affect the force needed to displace water. Objects with a larger surface area will experience more resistance from the water and therefore require more force to displace it. This is why boats with wider hulls are able to displace more water and stay afloat.

4. Can you use this formula to calculate the force for any body of water?

Yes, you can use this formula to calculate the force for any body of water as long as you know the density of that particular body of water. However, keep in mind that the density of water can vary slightly depending on factors such as temperature and salinity.

5. How can this calculation be used in real life applications?

This calculation can be used in various real life applications such as designing boats, dams, and other structures that interact with water. It can also be used in understanding the forces at play in natural phenomena like ocean currents and tsunamis.

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