How to Calculate Force Exerted on Rain Gauge Lid per ml of Rain Water?

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Discussion Overview

The discussion revolves around calculating the force exerted on the lid of a rain gauge by the water collected in it, specifically per milliliter of rainwater. The problem involves understanding the buoyant forces acting on a float within the gauge and how these forces change as the water level rises.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • The initial poster describes a rain gauge setup and seeks help in calculating the force on the lid as rainwater fills the gauge, noting the dimensions of the float and vessel.
  • One participant questions the assumptions about the float, including whether its weight can be neglected and its material properties, suggesting it is a buoyant force problem.
  • Another participant agrees that the weight of the float can be neglected.
  • A later reply clarifies that the float's buoyancy is countered by the lid, and emphasizes the need to calculate the buoyant force and the changing water depth as rainwater is added, suggesting that the force per milliliter will remain constant as the vessel fills.

Areas of Agreement / Disagreement

Participants generally agree on the neglect of the float's weight, but there is no consensus on the specifics of how to calculate the force exerted on the lid, particularly regarding the relationship between the buoyant force and the volume of water added.

Contextual Notes

The discussion includes assumptions about the float's properties and the relationship between the buoyant force and the water level, which may not be fully resolved. The calculations depend on the depth of water in the space between the float and the collection vessel, which is not explicitly defined for each milliliter of rainwater.

rohit405
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Homework Statement



The .png file attached shows a simple rain gauge where rain water is collected through a funnel of 25cm diameter. As water flows through the sides of the vessel and it fills the vessel it exerts an upward force on the bottom surface of the float. This force is transmitted to the top lid of the vessel(not shown in fig.). Given diameter of the collecting vessel is 13cm and that of the float is 12cm, calculate the force that will be exerted on the lid of the vessel per ml of rain water collected. Neglect weight of the float. Given: volume of float= 1 litre.



Homework Equations





The Attempt at a Solution



I have calculated the height of the float and found it to be 8.84cm.
(Since volume of float is 1litre= 0.001m^3 and dia of float is 12cm, we can find volume)
After this I am confused as to what to do since the water which will pour into the vessel will fill up and push the float upward till it comes in contact with the lid. This means a force will be exerted on the lid and which is to be calculated. How will this vary with increase per ml of rain water filled? Please help!
 

Attachments

  • rain gauge.png
    rain gauge.png
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Is the float filled with air? Can we neglect the weight of the float? Is the float made of a light weight material like Styrofoam? This is a buoyant force problem.
 
Yes, the weight of the float can be neglected.
 
It turns out that none of the questions I asked above is relevant to the problem. Essentially you have a float that wants to ride on top of the water but can't because there is a lid keeping it against the bottom of the collection vessel. The force pushing down on the lid will equal to the Buoyant force trying to push the force up. The rain water can only fill the volume between the float and collection vessel. You will need to find out how to calculate the buoyant force of a floating object. The challenge is determining the depth of water in the space between the float and collection vessel for every 1 ml of rain water. The force will indeed change as the vessel fills up but F/ml will be a constant (actually the slope of a line).
 

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