Find an expression for the net force of water on a dam

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Homework Help Overview

The discussion revolves around finding an expression for the net force exerted by water on a dam, considering the varying pressure with depth. The problem involves concepts from fluid mechanics, specifically related to pressure and integration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to integrate the expression for pressure, ρgwd, with respect to depth, d, due to the changing pressure at different depths. There is a focus on the correct application of integration and the variables involved, particularly the width of the dam.

Discussion Status

The conversation has included attempts at integration and clarifications regarding variable notation. Some participants have provided feedback on the original poster's attempts, and there is an acknowledgment of the need to correct variable usage. The discussion appears to be progressing with constructive input.

Contextual Notes

There is an emphasis on ensuring the correct interpretation of variables and the integration process, with some confusion regarding the notation used in the attempts. The participants are working within the constraints of a homework assignment, which may limit the depth of exploration.

Dusty912
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Homework Statement


Find the net force of water on the dam The dam has a width of w and the water is at a depth of d. So my question is, would you have to integrate ρgwd with respect to d? because the pressure is constantly changing every value of d.

Homework Equations


ρgwd
ρ is the density of water
g is 9.81 meters per second
w is width
and d is the depth of the water

The Attempt at a Solution


I would think that integrating with respect to d would yield ρghd2*(1/2)[/B]
 
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Dusty912 said:
The dam has a width of w and the water is at a depth of d. So my question is, would you have to integrate ρgwd with respect to d? because the pressure is constantly changing every value of d.
Sounds reasonable. Try it and show your attempt.
 
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I see that you've edited in your attempt. Good.

Dusty912 said:
I would think that integrating with respect to d would yield ρghd2*(1/2)

Where did the h come from? And what happened to the width?
 
sorry that h is supposed to be a w, and its a simple integration so I think I got it
 
Dusty912 said:
sorry that h is supposed to be a w, and its a simple integration so I think I got it
Okay! And yes, you got it :smile:
 
thanks for the help! nailed the test
 

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