top-rated free essay

Basic Equations of Fluid Statics

By 696ishan Jan 30, 2013 383 Words
Basic equations of fluid statics| | | | |
| | | | | | | | |
| | An equation representing pressure field P = P (x, y, z) within fluid at rest is derived in this section. Since the fluid is at rest, we can define the pressure field in terms of space dimensions (x, y and z) only. Consider a fluid element of rectangular parellopiped shape( Fig : L - 7.1) within a large fluid region which is at rest. The forces acting on the element are body and surface forces. | |

Body force : The body force due to gravity is
                                                                  L -7.1 where is the volume of the element.
Surface force : The pressure at the center of the element is assumed to be P (x, y, z). Using Taylor series expansion the pressure at point on the surface can be expressed as

                                    L -7.2 When , only the first two terms become significant. The above equation becomes                                                                L - 7.3

Similarly, pressures at the center of all the faces can be derived in terms of P (x, y, z) and its gradient. Note that surface areas of the faces are very small. The center pressure of the face represents the average pressure on that face. The surface force acting on the element in the y-direction is                                           L -7.4

Similarly the surface forces on the other two directions (x and z) will be                      
The surface force which is the vectorical sum of the force scalar components                                                                L - 7.5 The total force acting on the fluid is
                                                               L - 7.6

The total force per unit volume is
For a static fluid, dF=0 .
Then,                                                 L -7.7                 
If acceleration due to gravity is expressed as , the components of Eq(L- 7.8) in the x, y and z directions are                    
The above equations are the basic equation for a fluid at rest.  
Simplifications of the Basic Equations
If the gravity is aligned with one of the co-ordinate axis, for example z- axis, then                      
The component equations are reduced to
                                                               L -7.9                      
Under this assumption, the pressure P depends on z only. Therefore, total derivative can be used instead of the partial derivative.                                                                L - 7.10| | | | |  | | | | |

| | This simplification is valid under the following restrictions a. Static fluid b. Gravity is the only body force. c. The z-axis is vertical and upward.| | |

Cite This Document

Related Documents

  • Basic Fluid Mechanics

    ...Basics of Fluid Mechanics Genick Bar–Meir, Ph. D. 2729 West Jarvis Ave Chicago, IL 60645-1335 email:barmeir at Copyright © 2010, 2009, 2008, 2007, and 2006 by Genick Bar-Meir See the file copying.fdl or copyright.tex for copying conditions. Version (0.2.4 March 2, 2010) ‘We are like dwarfs sitting on the shoulders of gi...

    Read More
  • Fluid

    ...Experiment 3: Fluid Flow Friction and Fitting Loss Objective To determine the pressure or head loss in different diameters pipes, joints and valves Theory Pipe flows belong to a broader class of flows, called internal flows, where the fluid is completely bounded by solid surfaces. In contrast, in external flows, such as flow over a flat ...

    Read More
  • Statics

    ...FRICTION Problem 507 The 2225-N block shown in Fig. P-507 is in contact with 45° incline. The coefficient of static friction is 0.25. Compute the value of the horizontal force P necessary to (a) just start the block up the incline or (b) just prevent motion down the incline. (c) If P = 1780 N, what is the amount and direction of the friction ...

    Read More
  • Fluids

    ...1. Identify each of the following statements as either true or false. If false, explain why. (a) Viscosity is a measure of how easily a fluid flows. (b) Although important, fluids are not essential to many living things. (c) A meniscus forms when water particles adhere to the sides of their container. (d) Buoyancy, like water pressure, acts...

    Read More
  • Fluid Mechanics

    ...1. Using diagrams and/or graphs, explain the following terms: a. Pressure Head pressure head [′presh·ər ‚hed] (fluid mechanics) Also known as head. The height of a column of fluid necessary to develop a specific pressure. The pressure of water at a given point in a pipe arising from the pressure in it....

    Read More
  • Basic accounting equations

    ...Week One Exercise Assignment Basic Accounting Equations 1. Recognition of normal balances The following items appeared in the accounting records of Triguero's, a retail music store that also sponsors concerts. Classify each of the items as an asset, liability; revenue; or expense from the company's viewpoint. Also indicate the normal a...

    Read More
  • Statics Lab

    ...UNIVERSITI TUNKU ABDUL RAHMAN Faculty Course Year/ Semester Session : : : Engineering & Science ME, MM, MH, BI, CI, CL Y1S1, Y1S2, Y1S3 : Unit Code Unit Title Lecturer : : : UEME1132 Statics Ms. Lam Foong Sin 201405 Experiment 1: Young’s Modulus Introduction The Young’s Modulus Apparatus is a bench-to...

    Read More
  • fluid

    ...Fluid Balance Explain in detail the fluid compartments of the body, including distribution of fluid and electrolytes within each compartment and the movement between compartments. In the average person water constitutes 60% to the total body weight.: 42L in a 70kg individual. 40% is intracellelular fluid, while remaining 20% is extracellu...

    Read More

Discover the Best Free Essays on StudyMode

Conquer writer's block once and for all.

High Quality Essays

Our library contains thousands of carefully selected free research papers and essays.

Popular Topics

No matter the topic you're researching, chances are we have it covered.