Page 98 - 4167

layer are of the greatest importance in determining the resistance to
flow and the transfer of heat to or from the moving fluid. Beyond the
boundary layer, the motion is highly irregular. Random local circular
currents called vortices develop within the fluid, with a large increase

in the resistance to flow. Flow of this sort is called turbulent
(fig.7.11b) .Experiment indicates that a combination of four factors
determines whether the flow of a fluid through a tube or pipe is

laminar or turbulent. This combination is known as the Reynolds
number, Re and is defined as
vD
Re  . (6.32)


where  is the density of the fluid, v the average forward velocity,  the
viscosity, and D the diameter of the tube. (The average velocity is de-
fined as the uniform velocity over the entire cross section of the tube,

which would result in the same volume rate of flow.) The Reynolds
number is a dimensionless quantity and has the same numerical value in
any consistent system of units.

A variety of experiments have shown that when the Reynold′s number
is less than 2000 the flow is laminar, whereas above 3000 the flow is
turbulent. In the transition region between 2000 and 3000 the flow is

unstable and may change from one type to the other. Thus, for water at
20° C flowing in a tube 1 cm in diameter, the flow is laminar when
Re  200.

The Reynolds number of a system forms the basis for the study of the
behavior of real systems through the use of small scale models. A
common example is the wind tunnel, in which one measures the aerody-
namic forces on a scale model of an aircraft wing. The forces on a full-

size wing are then deduced from these measurements.
Two systems are said to be dynamically similar if the Reynolds
number, is the same for both.

7.9 Questions

1.What's ideal fluid?

2. What's streamline of fluid?
3. What does equation of continuity state?
4.What does Bernoulli's equation state ?

5.What does Torricelli's theorem state?
6. What's pitot tube?

97