#### Energy Systems

Identify the key difference between the 4-stroke and 2-stroke gasoline engines. Then, identify their applications, advantages, shortcomings, and key technical attributes, etc. Are these the only types of gasoline engines?

13-7 Calculate the average current velocity that is necessary for an 8-m-diameter water turbine with a coefficient of performance of 0.3 to generate 1 MW.

13-5 What is the power available from an underwater turbine with a coefficient of performance of 0.4 that is 10 m in diameter in a current of seawater traveling at a velocity of 2.0 m/s?

13-4 A water turbine 15 m in diameter is placed in a channel with a tidal current moving with a velocity of 3.5 m/s. Estimate the power produced by the turbine.

13-2 What is the total tidal energy available (at 100% efficiency) during the falling tide from a basin of area 100 km² with a tidal range of 8 m?

13-1 Calculate the total kinetic energy (in MJ and in kWh) of a 1-m³ parcel of sea- water moving with a velocity of 1 m/s.

12-6 In a storm, waves may have a height of 12 m and a period of 15 s. Compare the power per meter of wave front to the average values shown in Figure 12.1.

13-7 Calculate the average current velocity that is necessary for an 8-m-diameter water turbine with a coefficient of performance of 0.3 to generate 1 MW.

13-5 What is the power available from an underwater turbine with a coefficient of performance of 0.4 that is 10 m in diameter in a current of seawater traveling at a velocity of 2.0 m/s?

13-4 A water turbine 15 m in diameter is placed in a channel with a tidal current moving with a velocity of 3.5 m/s. Estimate the power produced by the turbine.

13-2 What is the total tidal energy available (at 100% efficiency) during the falling tide from a basin of area 100 km² with a tidal range of 8 m?

13-1 Calculate the total kinetic energy (in MJ and in kWh) of a 1-m³ parcel of sea- water moving with a velocity of 1 m/s.

12-6 In a storm, waves may have a height of 12 m and a period of 15 s. Compare the power per meter of wave front to the average values shown in Figure 12.1.

5. Consider the following two energy conversion questions: a) A rollercoaster car is at the top of a 20 ft hill moving at 3 ft/s. What is its velocity when it reaches the bottom of the hill in ft/s? Ignore friction and air resistance. b) A 10 ft tall water storage tank is pressurized to 10 psig when a valve at the base of the tank is opened. What is the velocity of the water exiting the tank in ft/s?

4. One method for producing hydrogen for use in fuel cells is the reforming of methane. In this reaction, methane is reacted with steam to produce carbon monoxide (CO) and hydrogen (H₂), also known as synthesis gas. Assume that the H₂ produced is then separated from the CO and used as a fuel. a) Using the provided heats of formation, calculate the energy released/required (in kJ/mol) during reforming. b) Which stream (methane + steam or synthesis gas) contains more chemical energy? Briefly explain. c) Additional hydrogen can be released by the water-gas shift reaction where CO and water vapor react to form CO2 and H₂. Using the provided heats of formation, calculate the energy released/required (in kJ/mol) during this reaction. d) In a fuel cell-powered car the hydrogen is oxidized with O₂ to produce water. How much energy is released per mass of H₂ consumed in this reaction in kJ/g? e) Assume that the efficiency of the conversion of hydrogen to mechanical energy in a fuel cell-powered engine is 75%. How much methane (in grams) would have to be converted to produce enough hydrogen to enable 150 kJ of work to be done? Assume both steam methane reforming and the water-gas shift reaction are used to produce the hydrogen.

3. Consider a 500 MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10 MPa and 550 °C and is cooled in the condenser to 45 °C. You may assume the compressor work on the liquid phase is negligible. Find the thermal efficiency of the cycle and the mass flow rate of the steam. What would the efficiency be if you modeled it as a Carnot cycle instead? Draw a diagram of each thermodynamic cycle and label heat/work inputs and outputs.

2. The point of the previous problem is to make some simple approximations that are based on practical knowledge to enable comparisons between energy expenditures that are on a human scale, at an automobile scale, and at a nationwide scale. Write your own multi-part homework problem that makes a comparison between different usages and scales of energy by asking the problem-solver to make approximations and simple engineering calculations. Be creative. Provide your own solution the problem, clearly explaining how you came up with the approximations you chose.

Energy Fundamentals 1. In this problem, we will explore how the amount of work that can be done by a human compares to the amount of work that can be extracted by burning fossil fuels in an internal combustion engine. Clearly state any assumptions you make. a) Estimate the total kWh an average human could realistically produce in a year pedaling a bicycle with an average output of 0.25 hp. Clearly explain your approximations such as time for resting. b) If all 8 billion people in the world cycled for 1 hour per day for a year, could they generate enough energy to power the US? The current consumption level of primary energy in the US is 100 quads per year. c) How much energy (in kWh) is produced by burning a gallon of gasoline? Assume that the gasoline is made up of a representative hydrocarbon molecule (a branched hexane or heptane) and compute the heat of combustion for that compound. d) Assuming a reasonable efficiency for an automotive internal combustion engine (ICE), how much gasoline would it take to do the same work as a human for one year? e) For how much time would an average human have to cycle to move a car 250 miles? Assume the car can drive 25 miles per gallon of gas and use the same ICE efficiency from part d.