Fluid Dynamics - Calculate the resultant moment

Click For Summary
SUMMARY

The discussion focuses on calculating the resultant moment at the bottom of a vertical wall separating two liquid reservoirs: one containing oil with a density of 864 kg/m³ at a height of 6m, and the other containing water with a density of 1000 kg/m³ at a height of 5m. The resultant moment is calculated using the formula FR = PCA, leading to a final answer of 9.98 N·m after subtracting the moments due to both fluids. The calculation involves integrating the moments of horizontal slices of each fluid to arrive at the correct result.

PREREQUISITES
  • Understanding of fluid statics and hydrostatic pressure
  • Familiarity with the concept of moments in physics
  • Knowledge of integration techniques in calculus
  • Proficiency in applying the formula FR = PCA for fluid mechanics
NEXT STEPS
  • Study hydrostatic pressure calculations in fluid mechanics
  • Learn about the integration of fluid forces over surfaces
  • Explore the implications of density variations in fluid statics
  • Investigate the principles of moments and torque in mechanical systems
USEFUL FOR

Students studying fluid dynamics, engineers working on fluid mechanics problems, and anyone involved in calculating forces and moments in fluid systems.

Mtrn_engineer
Messages
1
Reaction score
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:
Physics news on Phys.org
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:​
 

Similar threads

Engineering Calculating the Moments on the Walls of a Tank filled with Water
  • · Replies 2 ·
Replies
2
Views
3K
Calculate the resultant thrust and overturning moment
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Calculating Water Pool Depth: Factors to Consider in Fluid Dynamics
  • · Replies 13 ·
Replies
13
Views
2K
Calculate velocity in fluid mechanics question
  • · Replies 1 ·
Replies
1
Views
3K
Heat transfer and Fluid Flow Struggling Problems
  • · Replies 25 ·
Replies
25
Views
5K
Hydrostatic Pressure: Resultant Thrust & Overturning Moment
  • · Replies 6 ·
Replies
6
Views
3K
MHB Pressure and Force - Fluid Dynamics
  • · Replies 2 ·
Replies
2
Views
2K
Fluid Flow rate and fluid dynamics
  • · Replies 15 ·
Replies
15
Views
3K
Graduate A Fluid Dynamics Problem with Confusing Results
  • · Replies 4 ·
Replies
4
Views
3K
How can the required force to open the gate be calculated?
  • · Replies 1 ·
Replies
1
Views
3K