Hydrostatic force on a submerged object

ForumIn summary, the conversation discusses a problem involving two tanks filled with different fluids and a wall with a hole and an aluminum rod placed in the hole. The goal is to find the force and moment exerted by the wall on the rod to keep it stationary. The problem involves drawing a free body diagram and calculating the sum of forces and moments. The conclusion is that the wall does not apply any force on the rod, but the moments do not balance due to the width of the wall. The suggestion is made to post the problem in the Introductory Physics Forum.
  • #1
ACE_99
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Homework Statement


Two large tanks are separated by a wall 20 cm thick, as shown in the figure below. One tank is filled with oil with ρoil = 876 kg/m3 and μoil = 0.45 Ns/m2. The other is filled with water with ρwater = 998 kg/m3 and μwater = 0.00100 Ns/m2. The depths of fluid in the two tanks are respectively 5 metres and 4 metres. A 90 cm diameter hole is drilled in the wall that separates the two tanks at a height of 3 metres above the bottom. An aluminum (ρaluminum = 2750 kg/m3) rod 90 cm in diameter and 80 cm long is placed in the hole, with equal amounts of the rod overhanging into the two tanks. There is no fluid between the aluminum rod and the wall (i.e. a perfect seal).

Find the force and moment (about the centre of the rod) that the wall exerts on the aluminum rod to ensure that the rod remains stationary

Homework Equations



F = PA = [tex]\rho[/tex]ghA

The Attempt at a Solution



I started the problem by drawing a free body diagram of the pipe, I attached a picture.

F Roil and F Rwater are the resultant hydrostatic forces applied at the center of pressure by the liquid in the x direction. F Ry oil and F Rywater are the resultant hydrostatic forces applied at the center of pressure in the y direction. W is the weight of the rod in each liquid and Fb is the buoyant force.

After drawing a FBD I did a sum of forces about the x and y axis. Then I did a moment balance about point O, the red dot on the FBD picture. I haven't actually crunched out the numbers yet but based on my reasoning the wall wouldn't apply any force on the rod since it would be the forces and moments applied by the liquids on each side that would balance in order to keep the rod stationary. I have a feeling this isn't right though. Any help would be great.

http://i429.photobucket.com/albums/qq12/ACE_99_photo/FBD.jpg"

http://i429.photobucket.com/albums/qq12/ACE_99_photo/samplefinal.jpg"
 
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  • #2
ACE_99 said:
I haven't actually crunched out the numbers yet but based on my reasoning the wall wouldn't apply any force on the rod since it would be the forces and moments applied by the liquids on each side that would balance in order to keep the rod stationary. I have a feeling this isn't right though.

Who said this?

And if you do have calculated the sum than you would have seen that the moments do not balance. The separating is not of zero width. Had it been zero, the moment due to the wall would have been zero.

PS You should post this in Introductary Phy
 

1. What is hydrostatic force on a submerged object?

Hydrostatic force on a submerged object is the force exerted by a fluid on an object that is fully or partially immersed in it. It is a result of the pressure distribution within the fluid, and it acts in the direction perpendicular to the surface of the object.

2. What factors affect the magnitude of hydrostatic force?

The magnitude of hydrostatic force is affected by the density of the fluid, the volume of the submerged object, and the depth at which the object is submerged. It also depends on the shape and orientation of the object, as well as the acceleration due to gravity.

3. How is hydrostatic force calculated?

The hydrostatic force on a submerged object can be calculated using the formula F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the object, and A is the surface area of the object perpendicular to the direction of the force.

4. How does the shape of an object affect hydrostatic force?

The shape of an object plays a crucial role in determining the magnitude and direction of hydrostatic force. A flat or curved surface will experience a different force than a pointed or rounded surface. The orientation of the object also affects the distribution of pressure and thus the hydrostatic force.

5. Why is hydrostatic force important in engineering?

Hydrostatic force is important in engineering because it helps in the design and analysis of structures that are submerged in fluids, such as ships, dams, and pipelines. Understanding hydrostatic force is crucial in ensuring the stability and safety of these structures under different conditions, such as changes in water levels or fluid pressures.

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