Lecture no 1 to 10. Basic Fluid Mechanics. Summary of introductory concepts By Engr Sarfaraz Khan Turk. Introduction. What is Fluid Mechanics?
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Lecture no 1 to 10
Basic Fluid Mechanics
Summary of introductory concepts
By Engr Sarfaraz Khan Turk
What is Fluid Mechanics?
Fluid mechanics deals with the study of all fluids under static and dynamic situations. Fluid mechanics is a branch of continuous mechanics which deals with a relationship between forces, motions, and statically conditions in a continuous material. This study area deals with many and diversified problems such as surface tension, fluid statics, flow in enclose bodies, or flow round bodies (solid or otherwise), flow stability, etc.
Faces of Fluid Mechanics
(C. 287-212 BC)
In fact, almost any action a person is doing involves some kind of a fluid mechanics problem. Furthermore, the boundary between the solid mechanics and fluid mechanics is some kind of gray shed and not a sharp distinction for the complex relationships between the different branches which only part of it should be drawn in the same time.). The fluid mechanics study involve many fields that have no clear boundaries between them.
Field of Fluid Mechanics can be divided into 3 branches:
A streamline is a line that is tangential to the instantaneous velocity direction (velocity is a vector that has a direction and a magnitude)
Instantaneous streamlines in flow around a cylinder
Mechanics of fluids is extremely important in many areas of engineering and science. Examples are:
F = G m1m2/ r2
W = m2g ; g =(Gm1/r2) gravitational acceleration
g = 9.31 m/s2in SI units
g = 32.2 ft/sec2in English units
- Unit vector in x-direction
- Unit vector in y-direction
- Unit vector in z-direction
- Magnitude of in x-direction (tangent to surface)
- Magnitude of in y-direction (tangent to surface)
- Magnitude of in z-direction (normal to surface)
- For simplicity, let
Density and specific weight
Density (mass per unit volume):
Units of density:
Specific weight (weight per unit volume):
Units of specific weight:
Flow between no-slip parallel plates -each plate has area A
Force induces velocity on top plate. At top plate flow velocity is
At bottom plate velocity is
The velocity induced by moving top plate can be sketched as follows:
The velocity induced by top plate is expressed as follows:
For a large class of fluids, empirically,
Shear stress induced by is
From previous slide, note that
Thus, shear stress is
In general we may use previous expression to find shear stress at a point
inside a moving fluid. Note that if fluid is at rest this stress is zero because
Newton’s equation of viscosity
Shear stress due to viscosity at a point:
- viscosity (coeff. of viscosity)
Fixed no-slip plate
e.g.: wind-driven flow in ocean
As engineers, Newton’s Law of Viscosity is very useful to us as we can use it to
evaluate the shear stress (and ultimately the shear force) exerted by a moving
fluid onto the fluid’s boundaries.
Note is direction normal to the boundary
Coefficient of viscosity can be measured empirically using a viscometer
Example: Flow between two concentric cylinders (viscometer) of length
- radial coordinate
Inner cylinder is acted upon by a torque, , causing it to rotate about point at a constant angular velocity and
causing fluid to flow. Find an expression for
Because is constant, is balanced by a resistive torque exerted by the moving fluid onto inner cylinder
The resistive torque comes from the resistive stress exerted by the moving fluid onto the inner cylinder. This stress on the inner cylinder leads to an overall resistive force , which induces the resistive torque about point
increase in density
change in pressure where V is volume and p is pressure.
(It is inversely proportional to compressibility often denoted K sometimes B).
Vertical, drained compressibility's
certain fluids The degree of compressibility of a fluid has strong implications for its dynamics.
Vapor pressure of liquids
the liquid and gaseous states of the substance in the container
i.e. # of molecules escaping liquid surface = # of incoming molecules
the saturation pressure, rapid evaporation occurs (i.e. boiling)
Surface Tension-a force that tends to pull adjacent parts of a liquid’s surface together, thereby decreasing surface area to the smallest possible size.
~The higher the attraction forces (intermolecular forces), the higher the surface tension. Surface tension causes liquid droplets to take a spherical shape.
B. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water was running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.
C. Flotation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area.
D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its chemistry is the same.
E. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.
but what’s surface tension, really?