Hydrostatics Problem (Why is this Wrong?)

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In summary, the conversation discusses the calculation of the vertical force component and the correct method for finding the volume of the missing water. There is a discrepancy between the solution provided and the individual's method, which is ultimately resolved by identifying a typo in the solution.
  • #1
Saladsamurai
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Picture1-32.png


In calculating the vertical force component, you want to find the weight of the missing water.

This should be simple: Find the Volume of the missing water and multiply by specific weight.

Why is my volume calculation incorrect? I am using the volume of the rectangular prism whose top coincides with the surface and whose base coincides with B. Then I subtract the volume of the quarter cylinder:

[tex]V_{Tot}=V_{rect}-.25V_{cyl}[/tex]

[tex]V_{rect}=(1.5+0.75)(0.75)(1.2)[/tex]

[tex].25*V_{cyl}=.25*(\pi (0.75)^2(1.2)[/tex]

But this does not give the correct volume. The solution says to use:

Picture2-19.png


I am failing miserably to see how my method is different from theirs? Am I messing up a dimension here?
 
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  • #2
Aaahhhhhhhh! My brain!

Edit: How does what they wrote even make any sense?

The first term has dimensions of m^3 and the second has dimensions of m^2 !

Not to mention, if you put those numbers into your calculator they do not equal what they are saying they equal. WTF
 
Last edited:
  • #3
It looks like the second term in their solution has a typo: They left off the factor of 1.2m.
 
  • #4
Doc Al said:
It looks like the second term in their solution has a typo: They left off the factor of 1.2m.

Yeah. I think that makes it equivalent to mine if you tack that on.

Sometimes it does not help to be able to check your answers. :grumpy:
 

What is hydrostatics and why is it important?

Hydrostatics is the study of fluids at rest, specifically how they exert forces on objects immersed in them. It is important because it helps us understand the behavior of fluids and their impact on structures and objects in various applications, such as in engineering and environmental sciences.

What are some common mistakes in solving hydrostatics problems?

Some common mistakes in solving hydrostatics problems include using the wrong formula or equation, not considering all the forces acting on the object, and not accounting for changes in density or pressure.

Why is it important to account for the density of the fluid in hydrostatics problems?

Density is a crucial factor in hydrostatics problems because it affects the magnitude of the forces exerted by the fluid on the object. A higher density of the fluid will result in a greater force being exerted, while a lower density will result in a smaller force.

What are some real-life applications of hydrostatics?

Hydrostatics has many practical applications, such as in designing and building dams, ships, and submarines. It is also used in the study of ocean currents and weather patterns, as well as in the design of hydraulic systems and pumps for various industries.

How can I improve my understanding of hydrostatics and avoid making mistakes?

To improve your understanding of hydrostatics, it is important to practice solving problems and familiarize yourself with the different formulas and equations used. It is also helpful to seek guidance from experts or join study groups to discuss and learn from others' approaches and solutions.

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