 FLUID MECHANICS, HEAT TRANSFER, AND MASS TRANSFER

. DIMENSIONAL ANALYSIS

• Differentiate between units and dimensions by means of examples.
• Examples of dimensions include weight, time, length, and so on.
• Examples of units include seconds, days, years, inches, centimeters, kilometers, grams, pounds, and so on.

What are the methods used to carry out dimensionalanalysis?

• Rayleigh’s method.
• Buckingham p-theorem.

Under what circumstances dimensional analysis becomes a tool for obtaining solutions to problems?

• When two variables are to be correlated, a simple plot of one variable versus the other will describe the problem.
• When three variables are to be correlated, for each value of the third variable, a plot of the other two as in the above case will describe the problem; that is, a number of plots, each for one value of the third variable, will be required.
• When more than three variables are involved in a correlation, the correlation becomes complex and requires a set of curves for each of the fourth variable.
• In such situations involving four or more variables, dimensional analysis becomes a necessity as correlations progressively become very complex.

What is viscosity? What are its units?

& Viscosity is the measure of the internal friction of a fluid. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force
required to cause this movement, which is called shear. Shearing occurs whenever the fluid is physically moved or distributed, as in pouring, spreading, spraying, mixing, and so on. Highly viscous fluids,
therefore, require more force to move than less viscous materials.

Units of Viscosity: 1 poise is equal to 100 centipoise
(cP). SI units of viscosity are kg/(m s) or Pa s.

What is kinematic viscosity? Give its units.

Kinematic viscosity, n, is the ratio of viscosity to density, m/r. SI units of kinematic viscosity are m^2/s.
The cgs unit is Stoke, which is 1 cm^2/s.
Kinematic viscosity is a measure of how resistive the flow of a fluid is under the influence of gravity.
Kinematic viscometers usually use the force of gravity to cause the flow through a calibrated orifice, while timing the flow.

What are static and dynamic pressures?

Static pressure is the pressure exerted by a fluid at rest. Dynamic pressure is the pressure exerted by a fluid in motion.
Static pressure is uniform in all directions, so pressure measurements are independent of direction in an immobile (static) fluid. Flow, however, applies additional pressure on surfaces perpendicular to the flow direction, while having little impact on surfaces parallel to the flow direction. This directional component of pressure in a moving (dynamic) fluid is called dynamic pressure.

“Values of high vacuum are generally expressed in
terms of Torr.” What is Torr?

The unit of pressure in mmHg is often called Torr, particularly used in vacuum applications. 760 mmHg ¼ 760 Torr. 1 kPa ¼ 1 Torr 0.13332.