Find the Height for Equal Pressure in a Cylinder of Water

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Homework Help Overview

The problem involves a cylinder filled with water and seeks to determine the height at which the pressure on the side walls equals the pressure at the bottom. The subject area pertains to fluid mechanics and hydrostatic pressure.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of pressure in a fluid, questioning whether the original poster refers to total force or pressure values. There is mention of using mean values to estimate forces acting on the cylindrical wall.

Discussion Status

The discussion is exploring different interpretations of pressure and force in the context of the problem. Some participants provide insights into the hydrostatic pressure concept, while others seek clarification on the original question. There is no explicit consensus on the correct height yet.

Contextual Notes

Participants are navigating assumptions about pressure distribution in a fluid and the implications of those assumptions on the problem's setup.

prasanna
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Can somebody help me out in this problem?
There is a cylinder of diameter d,it is filled with water.
Upto what height should water be filled so that the pressure on the side
walls of the cylinder is equal to the pressure on the bottom?
 
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The pressure on the wall is not the same as the pressure on the bottom since it varies from top to bottom. Do you mean the total force acting on the wall due to the pressure?
 
prasanna:
Since the hydrostatic pressure is a linear function of the vertical variable, the mean value of the pressure is the arithmetic mean of the top and bottom values.
This can be used to estimate the total force on the cylindrical wall.
 
To Tide
Yes I mean the force due to pressure (sorry)
 
arildno said:
prasanna:
Since the hydrostatic pressure is a linear function of the vertical variable, the mean value of the pressure is the arithmetic mean of the top and bottom values.
This can be used to estimate the total force on the cylindrical wall.

So, When you solve I get the height is d/2.
Am I right??
 

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