Force on a water container

In summary, the force on the wall of a dam depends on the width of the dam, the height of the water filled, the density of water, and gravity. It does not depend on the length of the river. When calculating the force due to water on a cuboid lying horizontally on the floor, the length of the cuboid does not directly affect the force on the front wall. However, if the volume is kept constant, increasing the length will decrease the height of the water and therefore decrease the force on the front wall.
  • #1
Dr.Brain
538
2
Ok there is a dam of width "b" and water is fille don one side of it to a height h . Now i need to calculate the force on the wall of the dam on the side where water is filled .
This is what I did:

I considered a small layer of water of dx (vertical) at a distance x from top of water surface .

Then:

[itex] \int dF= \int \delta xg (bdx)[/itex]

Limits 0--->h on RHS

[itex] F=\frac {b \delta gh^2}{2} [/itex]

Therefore the force on the wall depends on :

Width of the dam
The height "h" to which water is filled
Density of water
and g

But one thing i noticed is that the force on the wall doesn't depend on the length of the river..!

2) Now suppose i want to calculate force due to water ina cuboid lying horizontally on floor ..Its length is l breadth is b and height h ... now if it lies on floor with breadth as its height...then it means as per previous conclusion that length of the cuboid lying horizontally wouldn't make any difference...So this means i keep on increasing its length without any effect on force due to water on the front face?
 
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  • #2
Dr.Brain said:
Ok there is a dam of width "b" and water is fille don one side of it to a height h . Now i need to calculate the force on the wall of the dam on the side where water is filled .
This is what I did:

I considered a small layer of water of dx (vertical) at a distance x from top of water surface .

Then:

[itex] \int dF= \int \delta xg (bdx)[/itex]

Limits 0--->h on RHS

[itex] F=\frac {b \delta gh^2}{2} [/itex]

Therefore the force on the wall depends on :

Width of the dam
The height "h" to which water is filled
Density of water
and g

But one thing i noticed is that the force on the wall doesn't depend on the length of the river..!

2) Now suppose i want to calculate force due to water ina cuboid lying horizontally on floor ..Its length is l breadth is b and height h ... now if it lies on floor with breadth as its height...then it means as per previous conclusion that length of the cuboid lying horizontally wouldn't make any difference...So this means i keep on increasing its length without any effect on force due to water on the front face?

Yes, that's exactly what it means. The pressure water exerts on a surface depends only on the height of the water above that surface.
 
  • #3
Dr.Brain said:
[itex] \int dF= \int \delta xg (bdx)[/itex]

Limits 0--->h on RHS

[itex] F=\frac {b \delta gh^2}{2} [/itex]
But one thing i noticed is that the force on the wall doesn't depend on the length of the river..!

I don't know if I'm right here, but in your calculations you accounted for the force caused by the hydrostatic pressure of the water held by the dam. If it is a still body of water, then this is the only pressure on the dam and that's it, it doesn't depend on the size of the body of water, just on the depth next to the dam.

But if you're holding off a river that's slamming into the dam, then you have to deal not only with hydrostatic pressure, but also with kinetic energy of the river. Which probably will depend on speed of the river, it's length, angle of fall, etc.

Once more, this is not my field of science, just my reasoning about the problem :))

Hope it helped even just a bit
 
  • #4
Dr.Brain said:
But one thing i noticed is that the force on the wall doesn't depend on the length of the river..!
That's right. The water pressure depends only on the depth of the water, not on how much water there is.
2) Now suppose i want to calculate force due to water ina cuboid lying horizontally on floor ..Its length is l breadth is b and height h ... now if it lies on floor with breadth as its height...then it means as per previous conclusion that length of the cuboid lying horizontally wouldn't make any difference...So this means i keep on increasing its length without any effect on force due to water on the front face?
If I understand you correctly, yes.

Let me rephrase it. Let's say you have a cuboid with sides a (x-direction), b (y-direction), c (z-direction = vertical). The net force on vertical side b-c depends on b and c, but not on a. (I think that's what you are saying.) The net force due to water pressure on any vertical surface does not depend on the dimension of the cuboid perpendicular to that surface. (As long as changing that dimension has no effect on the water pressure.)
 
  • #5
Ok, one thing more... I think the length of the cuboid has an indirect on the force on the front wall..because if we keep the volume fixed, then if we increase the length , then the height of the water decreases and the force decreases ...therefore keeping the volume fixed , the force on wall is inversely proportional to the length of the cuboid.
 
  • #6
Dr.Brain said:
Ok, one thing more... I think the length of the cuboid has an indirect on the force on the front wall..because if we keep the volume fixed, then if we increase the length , then the height of the water decreases and the force decreases ...therefore keeping the volume fixed , the force on wall is inversely proportional to the length of the cuboid.
Not exactly. It depends on how much the water level increases. Which is why I added the statement: "As long as changing that dimension has no effect on the water pressure."

In a large body of water, no problem: the increased height of the water could be neglected; in a small volume of water, not so.
 
  • #7
Doc Al said:
Not exactly. It depends on how much the water level increases. Which is why I added the statement: "As long as changing that dimension has no effect on the water pressure."

In a large body of water, no problem: the increased height of the water could be neglected; in a small volume of water, not so.


Oh yes..I actually posted that before reading your previous post, Your facts are right. Thanx
 

What is the force on a water container?

The force on a water container is the amount of energy exerted on the container by the water inside. This force is dependent on the weight of the water as well as any external forces acting on the container.

How is the force on a water container calculated?

The force on a water container can be calculated using the formula F = m x a, where F is force, m is the mass of the water, and a is the acceleration due to gravity. Alternatively, it can also be calculated by taking the product of the density of the water, the volume of water, and the acceleration due to gravity.

What factors affect the force on a water container?

The force on a water container is affected by the weight and density of the water inside, as well as the acceleration due to gravity. External factors such as wind, pressure, and temperature can also impact the force on the container.

How does the shape of a water container affect the force?

The shape of a water container can affect the force exerted on it by the water inside. A wider and shorter container will experience a greater force due to the larger surface area of the water, while a taller and narrower container will experience a smaller force due to the smaller surface area.

Why is understanding the force on a water container important?

Understanding the force on a water container is important for designing and constructing containers that can withstand the weight and pressure of the water inside. It is also crucial for ensuring the safety and stability of structures that rely on water containers, such as dams and water towers.

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