OneStopGate.Com
OnestopGate   OnestopGate
   Thursday, February 29, 2024 Login  
OnestopGate
Home | Overview | Syllabus | Tutorials | FAQs | Downloads | Recommended Websites | Advertise | Payments | Contact Us | Forum
OneStopGate

GATE Resources
Gate Articles
Gate Books
Gate Colleges 
Gate Downloads 
Gate Faqs
Gate Jobs
Gate News 
Gate Sample Papers
Training Institutes

GATE Overview
Overview
GATE Eligibility
Structure Of GATE
GATE Coaching Centers
Colleges Providing M.Tech/M.E.
GATE Score
GATE Results
PG with Scholarships
Article On GATE
Admission Process For M.Tech/ MCP-PhD
GATE Topper 2012-13
GATE Forum




GATE 2025 Exclusive
Organizing Institute
Important Dates
How to Apply
Discipline Codes
GATE 2025 Exam Structure

GATE 2025 Syllabus
Aerospace Engg..
Agricultural Engg..
Architecture and Planning
Chemical Engg..
Chemistry
Civil Engg..
Computer Science / IT
Electronics & Communication Engg..
Electrical Engg..
Engineering Sciences
Geology and Geophysics
Instrumentation Engineering
Life Sciences
Mathematics
Mechanical Engg..
Metallurgical Engg..
Mining Engg..
Physics
Production & Industrial Engg..
Pharmaceutical Sciences
Textile Engineering and Fibre Science

GATE Study Material
Aerospace Engg..
Agricultural Engg..
Chemical Engg..
Chemistry
Civil Engg..
Computer Science / IT
Electronics & Communication Engg..
Electrical Engg..
Engineering Sciences
Instrumentation Engg..
Life Sciences
Mathematics
Mechanical Engg..
Physics
Pharmaceutical Sciences
Textile Engineering  and Fibre Science

GATE Preparation
GATE Pattern
GATE Tips N Tricks
Compare Evaluation
Sample Papers 
Gate Downloads 
Experts View

CEED 2013
CEED Exams
Eligibility
Application Forms
Important Dates
Contact Address
Examination Centres
CEED Sample Papers

Discuss GATE
GATE Forum
Exam Cities
Contact Details
Bank Details

Miscellaneous
Advertisment
Contact Us


Home » GATE Study Material » Civil Engineering » The Bernoulli Equation

The Bernoulli Equation

Looking for GATE Preparation Material? Join & Get here now!

** Gate 2013 Question Papers.. ** CEED 2013 Results.. ** Gate 2013 Question Papers With Solutions.. ** GATE 2013 CUT-OFFs.. ** GATE 2013 Results.. **

Next>>
The Bernoulli Equation

The Bernoulli equation

1. Work and energy

We know that if we drop a ball it accelerates downward with an acceleration (neglecting the frictional resistance due to air). We can calculate the speed of the ball after falling a distance h by the formula

(a = g and s = h). The equation could be applied to a falling droplet of water as the same laws of motion apply

A more general approach to obtaining the parameters of motion (of both solids and fluids) is to apply the principle of conservation of energy. When friction is negligible the


 

sum of kinetic energy and gravitational potential energy is constant.

Kinetic energy

Gravitational potential energy

(m is the mass, v is the velocity and h is the height above the datum).

To apply this to a falling droplet we have an initial velocity of zero, and it falls through a height of h.

Initial kinetic energy

Initial potential energy

Final kinetic energy

Final potential energy

We know that

kinetic energy + potential energy = constant

so

Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy

 

so

 


 

Although this is applied to a drop of liquid, a similar method can be applied to a continuous jet of liquid.

 

 

The Trajectory of a jet of water

We can consider the situation as in the figure above - a continuous jet of water coming from a pipe with velocity . One particle of the liquid with mass travels with the jet and falls from height to . The velocity also changes from to . The jet is travelling in air where the pressure is everywhere atmospheric so there is no force due to pressure acting on the fluid. The only force which is acting is that due to gravity. The sum of the kinetic and potential energies remains constant (as we neglect energy losses due to friction) so

 

As is constant this becomes

 

This will give a reasonably accurate result as long as the weight of the jet is large compared to the frictional forces. It is only applicable while the jet is whole - before it breaks up into droplets.

Flow from a reservoir

We can use a very similar application of the energy conservation concept to determine the velocity of flow along a pipe from a reservoir. Consider the 'idealised reservoir' in the figure below.

 

 

An idealised reservoir

The level of the water in the reservoir is . Considering the energy situation - there is no movement of water so kinetic energy is zero but the gravitational potential energy is .

If a pipe is attached at the bottom water flows along this pipe out of the tank to a level . A mass has flowed from the top of the reservoir to the nozzle and it has gained a velocity . The kinetic energy is now and the potential energy . Summarising

Initial kinetic energy

Initial potential energy

Final kinetic energy

Final potential energy

We know that

kinetic energy + potential energy = constant

so

 

so

 

We now have a expression for the velocity of the water as it flows from of a pipe nozzle at a height below the surface of the reservoir. (Neglecting friction losses in the pipe and the nozzle).

Now apply this to this example: A reservoir of water has the surface at 310m above the outlet nozzle of a pipe with diameter 15mm. What is the a) velocity, b) the discharge out of the nozzle and c) mass flow rate. (Neglect all friction in the nozzle and the pipe).

 

Volume flow rate is equal to the area of the nozzle multiplied by the velocity

 

The density of water is so the mass flow rate is

 

In the above examples the resultant pressure force was always zero as the pressure surrounding the fluid was the everywhere the same - atmospheric. If the pressures had been different there would have been an extra force acting and we would have to take into account the work done by this force when calculating the final velocity.

We have already seen in the hydrostatics section an example of pressure difference where the velocities are zero.

 

The pipe is filled with stationary fluid of density has pressures and at levels and respectively. What is the pressure difference in terms of these levels?

Next>>



Discussion Center

Discuss/
Query

Papers/
Syllabus

Feedback/
Suggestion

Yahoo
Groups

Sirfdosti
Groups

Contact
Us

MEMBERS LOGIN
  
Email ID:
Password:

  Forgot Password?
 New User? Register!

INTERVIEW EBOOK
Get 9,000+ Interview Questions & Answers in an eBook. Interview Question & Answer Guide
  • 9,000+ Interview Questions
  • All Questions Answered
  • 5 FREE Bonuses
  • Free Upgrades
GATE RESOURCES
 
  • Gate Books
  • Training Institutes
  • Gate FAQs
  • GATE BOOKS
     
  • Mechanical Engineeering Books
  • Robotics Automations Engineering Books
  • Civil Engineering Books
  • Chemical Engineering Books
  • Environmental Engineering Books
  • Electrical Engineering Books
  • Electronics Engineering Books
  • Information Technology Books
  • Software Engineering Books
  • GATE Preparation Books
  • Exciting Offers



    GATE Exam, Gate 2009, Gate Papers, Gate Preparation & Related Pages


    GATE Overview | GATE Eligibility | Structure Of GATE | GATE Training Institutes | Colleges Providing M.Tech/M.E. | GATE Score | GATE Results | PG with Scholarships | Article On GATE | GATE Forum | GATE 2009 Exclusive | GATE 2009 Syllabus | GATE Organizing Institute | Important Dates for GATE Exam | How to Apply for GATE | Discipline / Branch Codes | GATE Syllabus for Aerospace Engineering | GATE Syllabus for Agricultural Engineering | GATE Syllabus for Architecture and Planning | GATE Syllabus for Chemical Engineering | GATE Syllabus for Chemistry | GATE Syllabus for Civil Engineering | GATE Syllabus for Computer Science / IT | GATE Syllabus for Electronics and Communication Engineering | GATE Syllabus for Engineering Sciences | GATE Syllabus for Geology and Geophysics | GATE Syllabus for Instrumentation Engineering | GATE Syllabus for Life Sciences | GATE Syllabus for Mathematics | GATE Syllabus for Mechanical Engineering | GATE Syllabus for Metallurgical Engineering | GATE Syllabus for Mining Engineering | GATE Syllabus for Physics | GATE Syllabus for Production and Industrial Engineering | GATE Syllabus for Pharmaceutical Sciences | GATE Syllabus for Textile Engineering and Fibre Science | GATE Preparation | GATE Pattern | GATE Tips & Tricks | GATE Compare Evaluation | GATE Sample Papers | GATE Downloads | Experts View on GATE | CEED 2009 | CEED 2009 Exam | Eligibility for CEED Exam | Application forms of CEED Exam | Important Dates of CEED Exam | Contact Address for CEED Exam | CEED Examination Centres | CEED Sample Papers | Discuss GATE | GATE Forum of OneStopGATE.com | GATE Exam Cities | Contact Details for GATE | Bank Details for GATE | GATE Miscellaneous Info | GATE FAQs | Advertisement on GATE | Contact Us on OneStopGATE |
    Copyright © 2024. One Stop Gate.com. All rights reserved Testimonials |Link To Us |Sitemap |Privacy Policy | Terms and Conditions|About Us
    Our Portals : Academic Tutorials | Best eBooksworld | Beyond Stats | City Details | Interview Questions | India Job Forum | Excellent Mobiles | Free Bangalore | Give Me The Code | Gog Logo | Free Classifieds | Jobs Assist | Interview Questions | One Stop FAQs | One Stop GATE | One Stop GRE | One Stop IAS | One Stop MBA | One Stop SAP | One Stop Testing | Web Hosting | Quick Site Kit | Sirf Dosti | Source Codes World | Tasty Food | Tech Archive | Software Testing Interview Questions | Free Online Exams | The Galz | Top Masala | Vyom | Vyom eBooks | Vyom International | Vyom Links | Vyoms | Vyom World
    C Interview Questions | C++ Interview Questions | Send Free SMS | Placement Papers | SMS Jokes | Cool Forwards | Romantic Shayari