Hydrostatics- need volume of submerged block- confused

[jonquest]

hydrostatics- bouyancy-need volume of submerged block- confused

Homework Statement

Need help with #11 attached

tank has 2m of water
gate is 1 m wide
pulley is 1/2 m above water
specific weight of concrete is 23.6 kN/m3
need to find volume of water to keep gate closed

Homework Equations

Bouyant force= volume x specific weight
Force= specific weight x area x centroid height

The Attempt at a Solution

Force on gate is: Force= specific weight x area x centroid height 9810 N/M x 1m2 x 1/2 m
force on gate + Bouyant force + weight of concrete= 0

I've got:
(9810 N/M x 1m2 x 1/2 m) - (23.6 kN/m3 x volume)+ weight of concrete=0

not sure where to get weight of concrete? do I count the weigh of the water above? does the height of the pully have to be considered?

 

[KataKoniK]

it is important to first understand the concepts of hydrostatics and buoyancy in order to solve this problem. In this case, we are dealing with a submerged block that is being held in place by a gate and pulley system.

To find the volume of water needed to keep the gate closed, we need to consider the forces acting on the gate. The force acting on the gate is the sum of the forces from the weight of the gate, the buoyant force from the water, and the weight of the concrete block.

First, let's consider the force from the weight of the gate. This can be calculated using the formula: Force = mass x gravity. In this case, the mass of the gate is the density of the gate times its volume, and the gravity is the acceleration due to gravity (9.81 m/s^2). So, the force from the weight of the gate is:

Force = (density of gate x volume) x 9.81 m/s^2

Next, we need to consider the buoyant force. This is the force that the water exerts on the submerged block, and it is equal to the weight of the water displaced by the block. The volume of water displaced is equal to the volume of the block, so the buoyant force can be calculated as:

Buoyant force = density of water x volume of block x 9.81 m/s^2

Finally, we need to consider the weight of the concrete block. This can be calculated by multiplying the density of concrete by its volume, and then multiplying by the acceleration due to gravity:

Weight of concrete = density of concrete x volume of block x 9.81 m/s^2

Now, we can set up an equation to solve for the volume of water needed to keep the gate closed:

Force from weight of gate + Buoyant force + Weight of concrete = 0

Substituting in the values we calculated above, we get:

(density of gate x volume) x 9.81 m/s^2 + (density of water x volume of block x 9.81 m/s^2) + (density of concrete x volume of block x 9.81 m/s^2) = 0

Simplifying and solving for the volume of water, we get:

Volume of water = (density of gate + density of concrete) x volume of block / (density of water - density

 

[Mene]

Hi there, it looks like you are trying to solve a problem related to hydrostatics and buoyancy. In order to find the volume of water needed to keep the gate closed, you need to consider the forces acting on the gate. The force of the water pushing against the gate is equal to the buoyant force, which is equal to the weight of the water displaced by the gate. This can be calculated using the equation Fb = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water above the gate.

In order to find the volume of water needed, you can set up an equation that balances the forces acting on the gate. This would include the force of the water pushing against the gate, the weight of the concrete, and the weight of the water above the gate. You can use the equation F = ma to find the weight of the water, where m is the mass of the water and a is the acceleration due to gravity. The weight of the concrete can be found by multiplying its specific weight by its volume. Once you have set up the equation, you can solve for the volume of water needed to keep the gate closed.

I hope this helps clarify the problem for you. If you are still confused, it would be helpful to provide more specific information about the problem, such as a diagram or the full question, so that I can give a more detailed response.