Ok now lets talk little of science!!
HYDRODYNAMICS (FLUID IN
MOTION)
Definition: hydrodynamics is regular flow of a
fluid in such that the velocity of the fluid has a fixed magnitude and
direction at every point. The velocity does not change at a given point as the
time lapses but maybe different at places.
The volume of fluid passing a given point per unit time is
called discharge rate. It is numerically equal to the product of the cross –
sectional area of the pipe and linear velocity of the fluid. Its unit is cubic
meters per second (m3s-1).
Law of continuity: It state states that for a steady
flow of ideal incompressible fluid the discharge rate is constant.
Let’s consider two points along a pipe of cross – sectional
area A1 A 2 where the corresponding linear velocities of
a fluid are V1 V2 respectively.
The discharge rate: A1 A2 =
constant
Therefore for a continuous steady flow. The velocity
increases at narrow bores. Where the cross – sections are reduced in the steady
flow of fluid the pressure is least when the speed is greatest.
Types of flow
1.
Streamline
flow (laminar flow)
2.
Turbulent
flow (eddy flow)
Streamline flow: is that in which all the particles
of the liquid move in an orderly procession. And the path of every particle is
the same as that of the liquid as a whole. In the flow also, the velocity at
every point within the fluid remains constant both in magnitude and direction.
Turbulent flow: it occurs when the velocity of a
streamline flow increases causing the streamline flow highly irregular and
random motion.
Critical velocity
It is the velocity at which the streamline flow changes to
turbulent flow. It is also when the velocity above 2500
Bernoulli’s theorem
It stated that the sum of the pressure head and the velocity
head remain constant.
Where; p= pressure head
H= elevation
head
V= velocity head
= density of fluid
g= acceleration due
to gravity
Conservation laws
1.
Mass continuity (conservation of mass): it is the rate of change of fluid mass
inside a control volume must be equal to the net rate of fluid flow into the
volume. This means that mass is neither created nor destroyed in the control
volume and can translated integral form of the continuity equation.
Where: p= the fluid density
U = is the flow
velocity vector and
t = is time
The left hand side of the above equation contains a triple
integral over the volume, whereas the right – hand side contains a surface
integral volume. The differential form of the continuity equation is
2.
Conservation of momentum: (newton second law of motion) to the
control volume, requiring that any change in momentum of the air within a
control volume due to the net flow of air into the volume and action of
external forces on the air within the volume. In the integral formulation of
this equation body forces is represented by Fbody: the body force
per unit mass (NKg‑1). While surface mass is represented as Fsurf.
The net force due to stresses on the control volume surface.
The different form of the momentum conservation equation is as
follows, both surface and body surface are accounted for in one total force, F,
for example, f maybe expanded into the expression for the frictional and
gravitational forces acting on an internal flow
Conservation of energy: energy can be converted from one form
to another it cannot be destroyed. The total energy in a given closed system
remains constant.
Where: h= enthalpy
K= thermal
conductivity of the fluid
T= temperature
Ø= viscous
temperature
The viscous dissipation function governs the rate at which
mechanical energy of the flow is converted to heat.
Reynolds number
This the ratio between inertial and viscous forces, can be used
to evaluate whether viscous or equations are appropriate to the problem.
Strokes flow
This is a flow at very low Reynolds numbers such that internal
forces can be neglected compared to viscous forces.
Let the retreading viscous force “f” acting on the sphere be
proportional to ath of the radius bth power of its
velocity and cth power of the coefficient of viscosity of the fulod
in which u moves them
From equation (iii) find b
-2= -b-1
b=-1+2
b=1
Substitute for b in equation (ii)
1=a+1-1
1-1+1=a
a=1
a, b, c=1
Where K= 6
YOU ARE FREE TO ADD ALL YOU KNOW OF THIS SUBJECT!!
