1. Revision Sheet (1) Mob. 0100 4444 149 Page (1)
Revision Sheet (1)
Define incompressible flow and incompressible fluid
A fluid flow during which the density of the fluid remains nearly constant is called
incompressible flow.
A flow in which density varies significantly is called compressible flow. A fluid whose density
is practically independent of pressure (such as a liquid) is commonly referred to as an
“incompressible fluid,”
What is the no-slip condition? What causes it?
A fluid in direct contact with a solid surface sticks to the surface and there is no slip. This is
known as the no-slip condition, and it is due to the viscosity of the fluid.
What is forced flow? How does it differ from natural flow? Is flow caused by
winds forced or natural flow?
In forced flow, the fluid is forced to flow over a surface or in a tube by external means such as a
pump or a fan. In natural flow, any fluid motion is caused by natural means such as the buoyancy
effect that manifests itself as the rise of the warmer fluid and the fall of the cooler fluid. The flow
caused by winds is natural flow for the earth, but it is forced flow for bodies subjected to the
winds since for the body it makes no difference whether the air motion is caused by a fan or by
the winds.
What is a boundary layer? What causes a boundary layer to develop?
When a fluid stream encounters a solid surface that is at rest, the fluid velocity assumes a value
of zero at that surface. The velocity then varies from zero at the surface to the free stream value
sufficiently far from the surface. The region of flow in which the velocity gradients are
significant and frictional effects are important is called the boundary layer. The development of a
boundary layer is caused by the no-slip condition.
What is a steady-flow process?
A process is said to be steady if it involves no changes with time anywhere within the system or
at the system boundaries.
What are system, surroundings, and boundary?
A system is defined as a quantity of matter or a region in space chosen for study. The mass or
region outside the system is called the surroundings. The real or imaginary surface that separates
the system from its surroundings is called the boundary.
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When is a system a closed system, and when is it a control volume?
Systems may be considered to be closed or open, depending on whether a fixed mass or a
volume in space is chosen for study. A closed system (also known as a control mass or simply a
system) consists of a fixed amount of mass, and no mass can cross its boundary. An open system,
or a control volume, is a properly selected region in space.
What is the difference between the classical and the statistical approaches?
The classical approach is a macroscopic approach, based on experiments or analysis of the
gross behavior of a fluid, without knowledge of individual molecules, whereas the statistical
approach is a microscopic approach based on the average behavior of large groups of individual
molecules.
What is specific gravity? How is it related to density?
The specific gravity, or relative density, is defined as the ratio of the density of a substance to
the density of some standard substance at a specified temperature (the standard is water at
4°C, for which ρH2O = 1000 kg/m3
).
When specific gravity is known, density is determined from ρ = SG×ρH2O .
What does the coefficient of compressibility of a fluid represent? How does it
differ from isothermal compressibility?
The coefficient of compressibility represents the variation of pressure of a fluid with volume
or density at constant temperature. Isothermal compressibility is the inverse of the coefficient
of compressibility, and it represents the fractional change in volume or density corresponding
to a change in pressure.
What does the coefficient of volume expansion of a fluid represent? How
does it differ from the coefficient of compressibility?
The coefficient of volume expansion represents the variation of the density of a fluid with
temperature at constant pressure. It differs from the coefficient of compressibility in that the
latter represents the variation of pressure of a fluid with density at constant temperature.
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Can the coefficient of compressibility of a fluid be negative? How about the
coefficient of volume expansion? fluid represent?
The coefficient of compressibility of a fluid cannot be negative, but the coefficient of volume
expansion can be negative (e.g., liquid water below 4°C). This is the reason that ice floats on water
What is viscosity? What is the cause of it in liquids and in gases? Do liquids
or gases have higher dynamic viscosities?
Viscosity is a measure of the “stickiness” or “resistance to deformation” of a fluid. It is due
to the internal frictional force that develops between different layers of fluids as they are forced
to move relative to each other.
Viscosity is caused by the cohesive forces between the molecules in liquids, and by the
molecular collisions in gases. In general, liquids have higher dynamic viscosities than gases.
What is a Newtonian fluid? Is water a Newtonian fluid?
Fluids whose shear stress is linearly proportional to the velocity gradient (shear strain) are
called Newtonian fluids. Most common fluids such as water, air, gasoline, and oils are
Newtonian fluids.
Consider two identical small glass balls dropped into two identical
containers, one filled with water and the other with oil. Which ball will
reach the bottom of the container first? Why?
the ball dropped in water will reach the bottom of the container first because of the much
lower viscosity of water relative to oil.
How does the dynamic viscosity of (a) liquids and (b) gases vary with
temperature?
The dynamic viscosity of liquids decreases with temperature. (b) The dynamic viscosity of
gases increases with temperature.
How does the kinematic viscosity of (a) liquids and (b) gases vary with
temperature?
For liquids, the kinematic viscosity decreases with temperature. (b) For gases, the
kinematic viscosity increases with temperature.
What is surface tension? What is it caused by? Why is the surface tension also
called surface energy?
The magnitude of the pulling force at the surface of a liquid per unit length is called surface
tension σs. It is caused by the attractive forces between the molecules. The surface tension is also
surface energy (per unit area) since it represents the stretching work that needs to be done to
increase the surface area of the liquid by a unit amount.
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Consider a soap bubble. Is the pressure inside the bubble higher or lower
than the pressure outside?
The pressure inside a soap bubble is greater than the pressure outside, as evidenced by the
stretch of the soap film.
What is the capillary effect? What is it caused by? How is it affected by the
contact angle?
The capillary effect is the rise or fall of a liquid in a small-diameter tube inserted into the
liquid. It is caused by the net effect of the cohesive forces (the forces between like molecules,
like water) and adhesive forces (the forces between unlike molecules, like water and glass). The
capillary effect is proportional to the cosine of the contact angle, which is the angle that the
tangent to the liquid surface makes with the solid surface at the point of contact.
A small-diameter tube is inserted into a liquid whose contact angle is 110°.
Will the level of liquid in the tube rise or drop? Explain.
The liquid level in the tube will drop since the contact angle is greater than 90°, where
cos(110°) < 0.
Is the capillary rise greater in small- or large-diameter tubes?
The capillary rise is inversely proportional to the diameter of the tube, and thus capillary rise is
greater in the smaller-diameter tube.
What is the difference between gage pressure and absolute pressure?
The pressure relative to the atmospheric pressure is called the gage pressure, and the
pressure relative to an absolute vacuum is called absolute pressure.
Explain why some people experience nose bleeding and some others
experience shortness of breath at high elevations.
Atmospheric air pressure which is the external pressure exerted on the skin decreases with
increasing elevation. Therefore, the pressure is lower at higher elevations. As a result, the
difference between the blood pressure in the veins and the air pressure outside increases.
This pressure imbalance may cause some thin-walled veins such as the ones in the nose to
burst, causing bleeding. The shortness of breath is caused by the lower air density at higher
elevations, and thus lower amount of oxygen per unit volume.
Someone claims that the absolute pressure in a liquid of constant density
doubles when the depth is doubled. Do you agree? Explain.
No, the absolute pressure in a liquid of constant density does not double when the depth is
doubled. It is the gage pressure that doubles when the depth is doubled.
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You may have noticed that dams are much thicker at the bottom. Explain
why dams are built that way.
Dams are built much thicker at the bottom because the pressure force increases with depth,
and the bottom part of dams are subjected to largest forces.
Under what conditions can a moving body of fluid be treated as a rigid body?
A moving body of fluid can be treated as a rigid body when there are no shear stresses (i.e., no
motion between fluid layers relative to each other) in the fluid body.
