Laboratory Report on CAT Hydroelectric Power Experiment Paper Example

Introduction

The primary objective of this report is to explain all aspects surrounding the impact of a water jet experiment that was conducted in the laboratory. In the field of engineering, the reaction forces produced by fluid jets after impact on solid surfaces is a vital topic especially in engineering applications relating to turbines and electrical power generation. According to Munson and Young (1990), water turbines are commonly used globally for the production of hydroelectric power. Such turbines include impulse turbines such as the Pelton wheel shown in the figure below. During the production of power, water under high pressure is directed to the turbine whereby the pressure energy of the water is converted into kinetic energy as the water forms a jet which escapes through the nozzles. That water jet then hits the Pelton wheel tangentially on the underside of the vanes making it to rotate (The Constructor, 2016). The rotation of the Pelton wheel produces kinetic energy which is then converted to electrical energy by connecting the wheel to a generator.

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Aim

The experiment sought to investigate the generation of hydroelectric power, the operation of water generators, and their efficiency by measuring the power generated by such setups.

Objectives

Research and understand the three Newton's laws of motion as applied to this experiment.

Research and understand the two Faraday's laws of electromagnetic induction as applied to this experiment.

Investigate the generation of hydroelectric power experimentally through application of Newton's three laws of motion and Faraday's two laws of electromagnetic induction.

Background

Hydroelectric power is among the most common sources of green and renewable energy in the modern world. The art of harvesting the vast amounts of potential energy stored in water sources has in the recent past become increasingly important. That is due to the looming danger of climate change caused by global warming and the emission of harmful gasses by other energy sources such as fossil fuels. As such, the total share of hydroelectric power on the U.S total energy basket has grown from 9% in 2012 to more than 12% in 2017 (EIA, 2018). That figure is projected to increase in future as calls for use of green energy continue to gain ground. The main advantages of hydroelectric power that drive increase in its popularity include no pollution to the environment and it is abundantly available all over the world (EIA, 2018). While there are many types of hydroelectric power plants, the common ones include pumped storage, diversion, and impoundment power plants. despite having different names, it is important to note that all of them use turbines to generate electricity. Thus, this experiment focuses on the generation of hydroelectric power through a turbine.

Typically, a hydroelectric power plant involves the tapping of potential energy stored in water by directing the water to hit a turbine. Upon hitting the turbine, the potential energy of the water is converted into kinetic energy as the water forms a jet which escapes through the nozzles. That water jet then hits the Pelton wheel tangentially on the underside of the vanes making it to rotate (The Constructor, 2016). The rotation of the Pelton wheel produces kinetic energy which is then converted to electrical energy by connecting the wheel to a generator. Kinetic energy is converted to electric energy by magnets that cut across the coil loop in the generator. The process of production of electricity by a hydroelectric turbine is closely similar to that of the wind turbine as they both involve capturing the movement of natural resources (wind and water) and converting it into electricity.

The figure below shows a simple sketch of the arrangement of a hydropower plant. For many years, history shows that moving water has been used widely to achieve varying goals such as grinding grain, cutting wood, and recently to produce electricity. Given that water is the most abundant natural resource, this experiment investigates the key methods, computations, and theory behind harnessing the power of water.

Tasks

In order to achieve the primary goal of the experiment, the following tasks were done:

• Deep research on the theory of fluids in motion and gain a better understanding of the fundamentals of momentum equation as used in the experiment.
• Measure the voltage (V) produced by the setup
• Measure the current (A).
• Determine the water velocity (m/s) hitting the turbine.
• Measure the kinetic energy of the water in the buckets.

These variables were then used to compute the power in, power out, and the efficiency of the generator used in the experiment.

Apparatus

The setup comprised of two buckets (bucket A and bucket B) and a hydroelectric generator. Bucket A was used to continually fill bucket B so as to maintain a constant height of water hence a steady amount of potential energy of the water flowing out of bucket B onto the impulse turbine connected to the hydroelectric generator. The figures below depict a sketch of the setup and the design of the water wheel (connected to the generator) respectively.

The tubes used had same diameters while the two buckets were identical and had volumes of 10liters. The height of the water in the buckets was varied for each trial. A nozzle was used to control the flow of the water via the tube. A voltmeter was used to measure voltage, ammeter to measure current, Vernier software and associated, and flow rate meter were used to record all the necessary data.

Method

After setting the apparatus, the nozzles in both buckets were opened. A total of ten trials were conducted. During the start of each trial, both buckets were filled at same heights and their nozzles opened simultaneously to facilitate collection of accurate data on the potential energy and to minimize delay hence likelihood of error in computations. The pipe transporting water from bucket B to the Pelton wheel was held by hand, which might have introduced errors into experiment that are discussed in the errors section.

Data was collected at intervals of one minute for each trial. Caution was taken not to make any changes to the buckets or any other apparatus throughout the experiment.

Results

Data for each trial was recorded in a notebook and later entered in an excel spreadsheet. The data collected for each trial included the speed of rotation of the Pelton wheel, voltage, and current. This data was used to calculate the power output, power input, and efficiency of the generator.

Power out= V X I (where V is voltage and I is current) .........Equation 1

Power in = h x Qx9.8 (where Q is the flow rate and h the pressure head)...Eqn 2

Efficiency= power out/power in ............equation 3

From equation 2 above, pressure head= 2.8bar, 28.56

Volume= 10L

Time= 5.87s

Therefore. Power in= 28 x 1/5.87 x 9.81= 476W

The table below shows the data collected

From the data in the table above, a graph of efficiency against rotations per minute was drawn.

Discussion

This experiment used an impulse turbine and in particular the Pelton wheel. As shown in the graph above, the efficiency of the turbine was low at the beginning when the revolutions per minute were low. However, the efficiency increased with increase in revolutions to reach the peak after which it started to drop. In order to understand the relationship between revolutions and efficiency, it is important to examine the Newton's laws of motion (Zimba, 2009) that state that:

• A body will remain in the same condition of rest or motion with uniform velocity in a straight line until acted upon by an external force.
• The rate of change of momentum of a body is proportional to the force acting upon it and takes place in the line of action of the force.
• To every action there is an equal and opposite reaction (Zimba, 2009).

Based on these principles, whenever a jet of water hits the surface of a vane and is deflected from its original path or its speed is changed in magnitude or direction, there is always an external force in action and the jet will exert an equal and opposite force. The magnitude of the force exerted is equal to the rate of change of momentum of the jet.

From the Newton's second law of motion, the rate of change of momentum of the turbine will be directly proportional to the force acting on it and will take place in the line of action of the force. Therefore, F=MV where m is the mass flow rate of the water and V is the velocity of the water. The resultant velocity of the jet after hitting the turbine will be changed and will be deflected through 180 degrees (Cengal & Cimbala, 2006; Seddighi, 2016). As such, the Pelton wheel will make several revolutions per minute.

According to Zhang (2016), the higher the rate of revolution of a turbine, the higher the power produced. The figure below shows the typical design of a generator.

As shown in the figure above, the shaft in the turbine is connected to the generator. As the turbine rotates, so does the shaft. The conversion of the mechanical energy into electrical energy in the generator is based on principles discovered by Michael Faraday in 1831 (EIA, 2017). Faraday discovered that when a magnet is passed on a conductor or inside the coils of wires, electric current flows in the wire. In a generator, direct current is circulated through loops of wire to make electromagnets. The electromagnets are then wound around magnetic laminations that are made of steel and are known as field poles. The field poles are then wounded around the rotor. As noted earlier, the rotor is connected to the turbine which revolves at varying velocities. As the rotor revolves due to rotation of turbines, the electromagnets cross the conductors which induces electric current to flow through the wire coil. As such, each wire coil becomes a small independent electrical conductor. The small electric currents then join to form large currents which are conducted to the power lines (Eom, 2013).

Faraday's first law of electromagnetic induction states that whenever a conductor is rotated in a magnetic field, an emf is produced. The second law states that the induced emf is equivalent to the rate of change of flux linkages, where flux linkages is given by the number of turns/coils and the flux (Tricker, 2013). That is demonstrated in the equations below,

Assuming that, Initial flux linkages = Nf1

Final flux linkages = Nf2

Change in flux linkages= Nf2 - Nf1

= N((f2-f1)

Hence, the more the more the flux linkages are cut, the more the electric current produced (Eom, 2013). Therefore, a turbine with a high rate of revolutions makes the shaft to cut the electromagnetic field severally hence producing large electric voltage. On the other hand, a turbine with low revolutions per minute causes the shaft to cut the magnetic field fewer times hence low electric voltage.

Errors

There were many sources of errors in this experiment. Some of them include procedural errors especially during taking the measurements. However, the experiment was able to overcome them by carrying out several trials. Another source of error was the difference in height between the buckets hence different val...