OBJECTIVE
experiment is done to investigate the validation of the Bernoulli’s equation and also to measure pressure distribution along venture tube.

INTRODUCTION
This experiment is carried out to investigate the validity of Bernoulli’s theorem when applied to the steady flow of water in tapered duct and to measure the flow rates and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The Bernoulli’s theorem (Bernoulli’s theorem, 2011) relates the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity of which are negligible and the flow of which is steady, or laminar. In order to demonstrate the Bernoulli’s theorem Bernoulli’s Apparatus Test Equipment issued in this experiment.

THEORY
• Velocity of fluid is less fluid
• The fluid is incompressible and non- viscous
• There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.
• There are no pumps in the section of pipe

For an ideal fluid flow the energy density is the same at all locations along the pipe. This is the same as saying that the energy of a unit mass of the fluid does not change as it flow through the pipe system.

APPARATUS

EXPERIMENTAL PROCEDURE
1, A inspection was done to ensure that the unit was in proper operating condition, so that the experiment will not consist of errors.
2, A hose had to be connected to the nearest power supply.
3, The discharged pipe was then opened.
4, The cap nut of the probe compression gland was set to such condition, that the slight resistance could be felt on moving the probe, and the water flow created a sound which also helps to determine the flow pressure (by hearing it ).

5, The inlet and outlet valve was then opened.
6, Then the pump was switched on and the main cock was released slowly opened. 7, The vent...

...EXPERIMENT : - 2
EXPERIMENT Verification of Bernoulli’s Energy Equation
THEORY
For steady incompressible flow Bernoulli’s energy equation along a streamline is written as
[pic] constant
where
[pic] = pressure, [pic] = velocity and [pic] = height from datum
Purpose of this experiment is to verify this expression. In the special apparatus the pipe is tapered with the cross section decreasing in the direction of flow first and then increasing in the second half of its length.
Hydraulic Grade Line
The line which shows the sum of pressure head (p/() and the potential head z (i.e., p/(+z) is called the Hydraulic Grade Line.
Energy Grade Line
The line obtained by plotting the sum of pressure, elevation and velocity heads (i.e., p/(+z+V2/2g) along the pipe is called the Energy Grade Line.
[pic]
Figure BC4.1 Bernoulli’s Apparatus
OBJECTIVE
Verification of Bernoulli’sEquation.
APPARATUS
Bernoulli’s apparatus (refer to Figure BC4.1), stop watch, scale, measuring tank.
PROCEDURE
1. Measure cross section of pipe at inlet point, throat (mid section and outlet point). From this determine the cross section areas a to a at each piezometer tapping.
2. Start the water supply .The head under which the flow...

...Experiment No. 1: Bernoulli’s Theorem
Object:
To verify Bernoulli's theorem for a viscous and incompressible fluid.
Theory:
In our daily lives we consume a lot of fluid for various reasons. This fluid is
delivered through a network of pipes and fittings of different sizes from an overhead
tank. The estimation of losses in these networks can be done with the help of this
equation which is essentially principle of conservation of mechanical energy.
Formal Statement:
Bernoulli's Principle is essentially a work energy conservation principle which states that
for an ideal fluid or for situations where effects of viscosity are neglected, with no work
being performed on the fluid, total energy remains constant. Bernoulli's Principle is
named in honour of Daniel Bernoulli. This principle is a simplification of Bernoulli'sequation, which states that the sum of all forms of energy in a fluid flowing along an
enclosed path (a streamline) is the same at any two points in that path.
Mathematical Description:
A+dA
ρ+dρ,V+dV
P+dP
τ =0
A
ds
dz
θ
ρ,V
CV
P
dW
Figure 1 Forces and Fluxes for Bernoulli’sEquation for frictionless flow along a streamline.
Applying the conservation of mass and momentum equation yields the following
equation
BournoulliEquation
1
∂V
dP
ds +
+...

...bernoulli's theorem
ABSTRACT / SUMMARY
The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus, F1-15. In this experiment, the pressure difference taken is from h1- h5. The time to collect 3 L water in the tank was determined. Lastly the flow rate, velocity, dynamic head, and total head were calculated using the readings we got from the experiment and from the data given for both convergent and divergent flow. Based on the results taken, it has been analysed that the velocity of convergent flow is increasing, whereas the velocity of divergent flow is the opposite, whereby the velocity decreased, since the water flow from a narrow areato a wider area. Therefore, Bernoulli’s principle is valid for a steady flow in rigid convergent and divergent tube of known geometry for a range of steady flow rates, and the flow rates, static heads and total heads pressure are as well calculated. The experiment was completed and successfully conducted.
INTRODUCTION
In fluid dynamics, Bernoulli’s principle is best...

...In fluid dynamics, Bernoulli's principle states that for an in viscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is named after the Swiss scientist Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.
Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli'sequation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers (usually less than 0.3). More advanced forms may in some cases be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).
Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a...

...CHAPTER 1
INTRODUCTION:
Bernoulli's Principle is a physical phenomenon that was named after the Swiss scientist Daniel Bernoulli who lived during the eighteenth century. Bernoulli studied the relationship of the speed of a fluid and pressure.
The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) discovered the principle that bears his name while conducting experiments concerning an even more fundamental concept: the conservation of energy. This is a law of physics that holds that a system isolated from all outside factors maintains the same total amount of energy, though energy transformations from one form to another take place.
The principle states that "the pressure of a fluid [liquid or gas] decreases as the speed of the fluid increases." Within the same fluid (air in the example of aircraft moving through air), high-speed flow is associated with low pressure, and low-speed flow is associated with high pressure.
OBJECTIVE:
*USE BERNOULLI’S PRINCIPLE TO EXPLAIN HOW THE ENERGY OF A FLUID AND ITS PRESSSURE ARE RELATED.
*EXPLAIN SOME SITUATIONS USING BERNOULLI’S PRINCIPLE.
SCOPE:
*the first fly of airplane
In 1899, after Wilbur Wright had written a letter of request to the Smithsonian Institution for information about flight experiments, the Wright Brothers designed their first aircraft: a small, biplane glider flown as a kite to test their solution for controlling the craft by...

...Bernoulli’s theorem
i
Bernoulli’s theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematicianDaniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow and is the basis for many engineering applications.
Bernoulli’s theorem implies, therefore, that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity. If the fluid is flowing through a horizontal pipe of varying cross-sectional area, for example, the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest. This phenomenon is sometimes called the Venturi effect, after the Italian scientist G.B. Venturi (1746–1822), who first noted the effects of constricted channels on fluid flow.
Application of Bernoulli's Theorem
When we blow air...

...determine the bulk velocity of the stream using Equation 1.
(Eqn. 1)
Where is the flowrate in m3/s and A is the cross-sectional area of the pipe. To find the flowrate, we multiply the flowmeter reading by the constant
and convert from gallons to cubic meters as follows:
The cross sectional area of the 7.75mm pipe is
Plugging these values into Equation 1, we obtain a bulk velocity .
With the bulk velocity value, we can find the Reynolds number of the flow using Equation 2.
(Eqn. 2)
Plugging in known values to Equation 2, we find:
The experimental friction factor of the pipe can be calculated as:
(Eqn. 3)
Using the pressure drop for the chosen sample from smallest smooth copper pipe across the known distance L, we obtain an experimental friction factor
The theoretical friction factor for smooth pipes can be calculated with the Petukhov formula:
(Petukhov Formula)
Using this formula with our calculated Reynolds number yields a theoretical friction factor of
Because Pipe 4 is a rough pipe, this Petukhov Formula does not apply and we must perform additional sample calculations. From the first data point for the fourth pipe we obtain the following flow properties:
Using Equations 2 and 3 we can find the following Reynolds number and experimental friction factor:
The theoretical friction factor for a rough pipe can be found by calculating the parallel...

...1. Which equation below represents the quadratic formula?
*a. -b±b2-4ac2a = x
b. a2+b2=c2
c. fx=a0+n=1∞ancosnπxL+bnsinnπxL
2. Which of the following represents a set of parallel lines?
a. Option one
b. Option two
*c. Option three
3. What is the definition of an obtuse angle?
*a. an angle greater than 90°
b. an angle equal to 90°
c. an angle less than 90°
4. Which formula below represents the area of a circle?
a. A=2πr
*b. A=πr2
c. A=π2r
d. A= √π
5.
What geometric term is represented by the image below?
a. a corner
*b. a cross-section
c. the circumference
d. the perimeter
11. Using the data in the table below, calculate the mean, or average, number of points scored by Player B.
| Game 1 | Game 2 | Game 3 | Game 4 | Game 5 |
Player A | 13 | 12 | 9 | 11 | 13 |
Player B | 12 | 11 | 15 | 20 | 12 |
*a. 14
b. 11.5
c. 13
d. 13.67
6. This instrument is commonly used by surveyors. It measures horizontal and vertical angles to determine the location of a point from other known points at either end of a fixed baseline, rather than measuring distances to the point directly. What is it called?
a. triangulator
b. binocular
c. tripod
*d. theodolite
7. What is the name of the missing shape in the flowchart below?
a. Acute
b. Obtuse
*c. Isosceles
d. Right
8. What category includes all of the items on the list below?
* Square
* Rectangle
*...

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