Fluid mechanics calculating force needed to lift submerged disc

[Gman2013]

Homework Statement

The problem:

There is an illustration and the question is to find the force F to lift a concrete block gate if the the concrete weighs 160 lb/ft3. The block is 3' in diameter and 1' thick. It is in a tank of fresh water 15 ft down. the specific weight of the fresh water is 62.4 lb/ft3 and specific weight of the sea water on the other side is 64 lb/ft3

Knowns:
Specific weight fresh water:62.4 lbs/ft3
Specific weight salt water 64 lb/ft3
concrete: 160 lb/ft3, 3' diameterx1' thick

Homework Equations

equations I see:
wt=fb
F=F(water)-F(disc)

The Attempt at a Solution

Steps I see so far
1. Find area of the disc
2. calculate the Volume of the disc
3. Calculate weight of disc
4. Sum of forces acting on disc
-weight acting down
-Calculate force needed to act upward

-Does this use Bernoulli's equation?

 

[LawrenceC]

If the fluid is not moving you do not need to be concerned with Bernoulli's equation.

What about buoyancy? You did not mention it.

 

[Gman2013]

Looking at the problem again I did forget bouyant force so...
Weight=Bouyant force when an object floats... Analysis of the system bernoullis eqations at three points
1. top of sea water
2. At concrete disc
3. surface of freshwater

Would I calculate the pressures at the points to figure the impact on the Concrete disc and then factor that force needed to lift the disc is F(seawater)+Bouyant force.

 

[LawrenceC]

When the water is not flowing, there is no velocity so all you have is depth and pressures. You can think of Bernoulli's equation because two terms remain if you wish.

The buoyant force is the amount of force the liquid exerts on an object in the upward direction. It is created by pressure differences applied to the surface area of an object.

Do a force balance on the concrete. You have several forces to consider.

1. Its weight
2. Fresh water force
3. Salt water force
4. Force to dislodge it.

The sides don't matter because they are vertical so the pressure only causes forces perpendicular to the direction you are considering.

 

[asteriatic]

I would approach this problem by first identifying the knowns and unknowns. In this case, the knowns are the specific weights of fresh water and sea water, as well as the dimensions and weight of the concrete block. The unknown is the force needed to lift the block.

Next, I would consider the relevant equations and principles that can be applied to this problem. The equation wt=fb (weight=force x specific weight) is a good starting point, as it relates the weight of an object to the force acting on it and the specific weight of the fluid it is submerged in. However, I would also consider other principles such as Archimedes' principle, which states that the upward buoyant force on an object is equal to the weight of the fluid it displaces.

To solve for the force needed to lift the submerged disc, I would first calculate the volume of the disc using its dimensions. Then, I would use the specific weight of the fluid (fresh water or sea water) to calculate the weight of the displaced fluid. This weight would be equal to the upward buoyant force acting on the disc.

Next, I would consider the weight of the disc itself and the downward force it exerts. This would be subtracted from the upward buoyant force to determine the net force acting on the disc.

Finally, I would use Newton's second law (F=ma) to calculate the force needed to lift the disc, where the mass would be the weight of the disc and the acceleration would be the upward acceleration due to the net force acting on it.

In summary, I would approach this problem by considering relevant equations and principles, and then using them to calculate the net force needed to lift the submerged disc. This may or may not involve Bernoulli's equation, depending on the specific approach used.