Sloshing in a Rectangular Container: Finding Time Period

In summary, the conversation is discussing the problem of finding the time period of the sloshing mode of a rectangular container partly filled with water. The person trying to solve the problem is attempting to use the equation of energy and differentiating it, but is unsure of what to include in the equation. They mention the angle made by the surface and the slant made by the surface after slosh, and also consider the center of mass not moving. However, they are unsure if this is the correct approach and ask for help.
  • #1
crotical
10
0

Homework Statement


A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode. take width to be

The Attempt at a Solution



I tried to put up the equation of energy , and differentiating it .

θ be the angle made by surface and the slant made by surface after slosh ,
1/2 Iω2 + mgh = U

but this doesn't lead me anywhere, can some one please tell what should i add in the energy equation .
 
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  • #2
welcome to pf!

hi crotical! welcome to pf! :wink:

what does mgh have to do with it?

surely the centre of mass isn't moving?​
 
  • #3
Then what should i add to the Energy equation
 
  • #4
love o:)
 
  • #5
So that means , no help ?
 
  • #6
crotical said:
A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode.
…
θ be the angle made by surface and the slant made by surface after slosh ,
1/2 Iω2 + mgh = U

but this doesn't lead me anywhere, can some one please tell what should i add in the energy equation .

i think I've misunderstood the question :redface: …

what exactly is the water doing?​

show us your full equation anyway :smile:
 
  • #7
Water is in a cup , find SHM of the surface , if slightly displaced
 
  • #8
Tiny ?
 
  • #9
crotical?

your equation?​
 

1. What is sloshing in a rectangular container?

Sloshing in a rectangular container refers to the movement of liquid inside a container that has a rectangular shape. This movement is caused by the container's vibrations or external forces acting on the liquid.

2. Why is finding the time period of sloshing important?

The time period of sloshing is important because it helps us understand the behavior of the liquid inside the container. It also allows us to predict and prevent potential hazards, such as spills or damage to the container.

3. How is the time period of sloshing calculated?

The time period of sloshing can be calculated using the formula T = 2π√(l/g), where T is the time period, l is the length of the container, and g is the acceleration due to gravity. This formula assumes that the container is completely filled and the liquid behaves like a simple pendulum.

4. What factors can affect the time period of sloshing?

The time period of sloshing can be affected by factors such as the shape and size of the container, the amount of liquid inside, the type of liquid, and external forces acting on the container.

5. How can we reduce sloshing in a rectangular container?

To reduce sloshing in a rectangular container, we can use baffles or partitions inside the container to break up the liquid's movement, fill the container partially instead of completely, or use a different type of liquid with lower viscosity. We can also reduce external forces on the container, such as vibrations, to minimize sloshing.

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