Fluid Dynamics - Calculate the resultant moment

In summary, we have a problem involving two liquid reservoirs separated by a rigid vertical wall. The first reservoir contains oil of density p=864 kgm-3 at a height of 6m above the ground, while the second reservoir contains water (1000kgm-3) at a height of 5m from the reservoir bottom. The task is to calculate the resultant moment at the bottom of the vertical wall. The equation used is FR = PCA = pgycA, where FR is the resultant force, P is the pressure, C is the centroid of the area, A is the area, p is the density, g is the acceleration due to gravity, y is the vertical distance to the centroid, and c is the
  • #1
Mtrn_engineer
1
0

Homework Statement



A rigid vertical wall separates two liquid reservoirs. The first reservoir contains oil of density p=864 kgm-3 at a height of 6m above the ground, while the second reservoir contains water (1000kgm-3) at a height of 5m from the reservoir bottom. Calculate the resultant moment, at the bottom of the vertical wall.

http://imgur.com/jjlf3eO

Homework Equations



FR = PCA = pgycA

The Attempt at a Solution



Area is not given so I will take that out of the equation

water = 1000*9.81*5/2 *5/3
minus
oil = 864*9.81 *6/2*6/3

Answer = 50855 - 40875 = 9.98 n.M

I think that the answer is right but I am not sure as to why it is right. Can someone please verify and explain. Thank you
 
Last edited:
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  • #2
Welcome to PF!

Hi Mtrn_engineer! Welcome to PF! :wink:

(I think the question is probably asking for the moment per mass, so you'll be factoring out an m = ρAL somewhere)

Call the area A, and slice each side into horizontal slices of area A thickness dh and depth h …

then find the moment for that slice, and then integrate wrt h.

Show us what you get. :smile:​
 

What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) behave when they are in motion. It involves understanding the forces and movements of fluids, and how they interact with their surroundings.

What is the resultant moment in fluid dynamics?

The resultant moment in fluid dynamics refers to the total rotational force acting on a body when it is immersed in a fluid. It is the product of the distance from the point of rotation to the force vector and the magnitude of the force.

How is the resultant moment calculated?

The resultant moment can be calculated by taking the cross product of the force vector and the distance vector from the point of rotation. This will give the magnitude and direction of the resultant moment.

What factors affect the resultant moment in fluid dynamics?

The resultant moment in fluid dynamics is affected by the magnitude and direction of the force acting on the body, as well as the distance from the point of rotation to the force vector. The density and viscosity of the fluid also play a role in determining the resultant moment.

Why is understanding the resultant moment important in fluid dynamics?

Understanding the resultant moment is important in fluid dynamics because it helps us predict and control the movements of fluids in various systems. This knowledge is crucial in designing and optimizing machines and structures that utilize fluids, such as airplanes, ships, and pipelines.

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