Lab 1: Bernoulli
Principle
Objective
This experiment is aimed to check the validity of
Bernoulli Theorem and applied to non-viscous fluid that is flowing through
circular pipe of cross sectional area. It is also intended to measure the total
and static heads for both converging and diverging tubes.
Literature
Review
Bernoulli Theorem was formulated by Daniel Bernoulli
in 1738. According to this theorem, for non-viscous flow, there is an increase
in velocity of the fluid as the pressure is decrease due to decrease in the
potential energy of the fluid. This theorem is also a principle and directly
correlates with the conservation of energy. The velocity increase as the
pressure increase. This increase in the velocity causes dynamic head to
increase and this is reason why we obtain higher and lower total head for
convergent and divergent flows.
Mathematically,
Equation 1
Where
p is the pressure, is the density of the fluid, V is the
velocity, h is the elevation and g is the gravitational acceleration constant.
There are many experiments and researches done on
this theorem. Khadanga, Shakti
Prasanna, (193-197) presented their work
that gives an idea about the investigation of Bernoulli apparatus for
unidirectional flow. Their apparatus comprises of two dimensional rectangular
divergent section duct. It was designed in such a way that there is a constant
head inlet and outlet. They have utilized 11 static tubes of manometer attached
to convergent duct. The piezometer tubes are attached at an equal interval at
gauges. They have concluded that the total head of the streamline remained
constant through varying duct tube area.
Ruqiong g Qin, and Chunyi Duan, (1-6) in their article of “Principle and application of Bernoulli Equation”. They have
explained the working of designed agricultural sprayer machine as shown in
Figure.1.
The liquid
trapped inside the knapsack is dispersed into air by pushing the tube and air
was formed in the narrow tube opening. The narrow opening at A is the region
where the pressure is small and flow rate is high. A vertical tube that is
above CB, this region has the pressure less than the vessel bottom and tube
above this solution. As the cross section area of the nozzle converge, this
increases flow and air from the environment pass through negative pressure.
This gradient of pressure allows the liquid to get ejected through the nozzle.
Henry, S. (1958) demonstrated
the application of Bernoulli application through Venturi meter. This literature
simulated the pipe framework through which the liquid passes through a
constricted rate. This is called Venturi throat. This is the region where fluid
accelerates and pressure diminished. This pressure difference for the rate of
flow proves the validity of Bernoulli theorem. Figure.2. shows the illustration
of typical Venturimeter.
W?cel, Daniel, Tadeusz Chmielniak, and Janusz Kotowicz (301-306) shows another application of Bernoulli theorem
through Pitot tube. This tube was named after French scientist Pitot. It
comprises of a tube that is bent perpendicularly as shown in Figure.3. Pointing
the tube directly to the flow stream. This measures the pressure difference
through Pitot tube and measures the pressure of air flow. This gives an
accurate measurement of the velocity.
Ansaldo, E. J (1982)
shows another application of Bernoulli equation. A siphon that is typically a
bent tube, used to transfer fluid from one vessel at higher level into another
vessel at lower level. The liquid is filled with the liquid in the tube to
provide flow medium as shown in Figure.4. By applying the Bernoulli theorem, we
can estimate the maximum height h associated with the bending of the tube.
Mathematically,
Equation 2
Equation 3
Methodology
The experimental setup was already arranged by the lab
instructor. It was carried out on
Bernoulli Theorem Hydraulic Bench provided by. We have first level the
apparatus and make sure that everything is working properly. Manometer was
carefully placed inside the water so that all the bubbles and air pockets can
be easily discharged. The flow was adjusted through control valves. As we have
opened he valves the manometer gauge rises between highest and lowest
consecutive values. This was that point, we started to note down the readings.
The volumetric rate was measured individually by filling volumetric flask in an
average interval of time. The probe was then placed at a parallel position of
the duct and the scale reading was then recorded for mathematical calculation.
Hi!
I'm Barry!
Would you like to get a custom essay? How about receiving a customized one?
Check it out