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.