Recent Updates

DERIVATION OF TOTAL PRESSURE


Today we will understand here the basic concept of total pressure, in the subject of fluid mechanics, with the help of this post.

Total pressure

Total pressure is also termed as hydrostatic force. Total pressure is basically defined as the hydrostatic force applied by a static fluid on a plane or curved surface when fluid will come in contact with the surfaces. This hydrostatic force will act normal to the surface.
Let us consider that we have one tank filled with liquid e.g. water. Let us consider that there is one object of arbitrary shape immersed inside the water as displayed here in following figure.

Now there will be one hydrostatic force exerted over the object due to the weight of fluid kept inside the tank and this hydrostatic force will be considered as total pressure.

Total pressure or hydrostatic force will be determined by the following formula as mentioned here.

Total Pressure =ρ g A ħ

Derivation of total pressure

In order to determine the total pressure, we will consider the object in terms of small strips as displayed here in following figure. We will determine the force acting on small strip and then we will integrate the forces on small strips for calculating the total pressure or hydrostatic force on object.


Let us consider the small strip of thickness dh, width b and at a depth of h from free surface of liquid as displayed here in above figure.
Intensity of pressure on small strip, dp = ρgh
Area of strip, dA = b x dh
Total pressure force on small strip, dF = dP x dA
Total pressure force on small strip, dF = ρgh x b x dh
Total pressure force on whole surface, F = Integration of dF

Where,
ρ = Density of liquid (Kg/m3)
g = Acceleration due to gravity (m/s2)
A = Area of surface (m2)
ħ = Height of C.G from free surface of liquid (m)   

Unit of total pressure

As total pressure is basically a hydrostatic force and therefore total pressure will be measured in terms of N or KN.

We will discuss Centre of pressure, in the subject of fluid mechanics, in our next post.
Do you have any suggestions? Please write in comment box.

Reference:

Fluid mechanics, By R. K. Bansal
Image Courtesy: Google 

Bright Idea Space 

We have started another website i.e. https://brightideaspace.com/ that basically provides the new ideas, Creative prompts and challenges, Self-improvement articles, Interviews with successful creatives, Resources and tools, innovative ideas and discuss about the various thought process that will continuously improve our thought process day by day. 


Let us see here few posts of https://brightideaspace.com/  


  1. The Psychology Of Facing New Challenges And How To Overcome Them

  2. Green Building Materials: A Guide To Sustainable Construction

  3. The Top 10 Sustainable Cities In The World And Their Clean Energy Innovations

  4. The Role Of Tree Relocation In Sustainable Development 

  5. How Does Laser Cleaning Work? A Comprehensive Guide

  6. Living With Purpose: Finding Your Passion And Living A Meaningful Life

  7. The Importance Of Living Life To The Fullest: Why Giving Your 100% Matters

  8. 9 Easy Ways To Reduce Plastic Waste In Your Daily Life

  9. Prioritizing What’s Important: Understanding What Truly Matters In Life And Focusing On Those Things

  10. How To Implement Your Strategic Plan: A Step-By-Step Guide

  11. From ‘Good’ To ‘Great’: How To Build On The Momentum Of A Good Day

  12. The Power Of Positive Self-Talk: Why A Bad Day Doesn’t Mean You’re Failing

  13. The Top 10 Must-Read Personal Development Books For Success

  14. Kanban: A Japanese Method To Overcome Laziness And Organize Your Tasks Efficiently

  15. The Importance Of A Growth Mindset In Decision-Making: How To Adopt A Positive And Open Attitude Towards Making Decisions

No comments:

Post a Comment

Popular Posts