CVE 240 – Fluid Mechanics

FLUID STATICS

FLUID STATICS

This section will study the forces generated by fluids at rest.

Introduce the concept of pressure;

Prove it has a unique value at any particular elevation;

Show how it varies with depth according to the hydrostatic equation;

Show how pressure can be expressed in terms of head of fluid.

This understanding of pressure will then be used to demonstrate methods of pressure measurement that will be useful later with fluid in motion and also to analyze the forces on submerges surface/structures.

Objectives

Introduction

It is important not only to civil engineers but also naval architects….

The design of water storage tanks and dams

What are the forces created by water and how strong must a tank or a dam be to resist them?

The design ships and submarines

How deep can a submarine go before the pressure becomes too great and damage it?

• The term pressure is used to describe the force exerted by water on each square metre of some object submerged in water (i.e., force per unit area).

Pressure

)(m area

(N) force)(N/m pressure

22

2N/m 11Pa

Figure 3.1: Pressure forces on a wedge-shape fluid element in equilibrium.

Engineering Fluid Mechanics 8/E by Crowe, Elger, and RobersonCopyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Pressure Intensity

The pressure (scalar quantity) at a point in a static fluid acts with the same magnitude in all directions.

pn= px= pz

Pressure Transmission

• Pascal Law: A pressure change produced at one point in a closed system will be transmitted throughout the entire system

Force = pressure x area [N = N/m2 x m2]

For 25 cm-diameter piston:

If air pressure is 600 kN/m2

what is the force liftingup the car?

Ans: 29.5 kN

Engineering Fluid Mechanics 8/E by Crowe, Elger, and RobersonCopyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

HYDRAULIC LIFT

Absolute pressure, Gage pressure and Vacuum

Absolute pressure = gauge pressure + atmospheric pressure

Example:

Which produces the larger pressure, a 0.3m diameter foot of an elephant of mass 5000kg or 0.01m diameter heel of a woman’s shoe when she has a mass of 60kg?

Which would you rather have standing on your foot!

Practical Hydraulics by Melvyn KayCopyright © 1998 by E & FN Spon All rights reserved.

Solution:

Practical Hydraulics by Melvyn KayCopyright © 1998 by E & FN Spon All rights reserved.