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## MAE 241 – Homework 1 Page 1 of 3 MAE 241 – Spring 2019 – Homework 1 Administered 1/11/2019 – Due 11PM, Sunday 1/19/2019 to Gradescope Problem 1 – Review of units The Phoenix with a mass of 400 kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N, for the following situations: a. On the surface of Mars where the acceleration of gravity is 3.73 m/s2. b. On Earth where the acceleration of gravity is 9.81 m/s2. Problem 2 – review of chemistry A closed system consists of 0.4 kmol of octane (C8H18) occupying a volume of 2 m3. Determine: a. The weight of the system, in N. b. The molar-based specific volume, in m3/kmol. c. The mass-based specific volume, and m3/kg. Let g = 9.81 m/s2. Problem 3 – review of chemistry A closed vessel having a volume of 2.0 liter holds 2.0 x 1022 molecules of carbon dioxide gas. Determine: a. The number of moles, in kmol b. The mass of CO2 present, in kg and. c. The molar specific volume, in m3/kmol d. The specific volume of the CO2, in m3/kg. Hint: use Table A-1 of your textbook for molecular mass. Problem 4 – Quasistatic Equilibrium The figure below shows a gas contained in a vertical piston–cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 300 kPa. The masses of the piston and attached shaft are 30 kg and 0.5 kg, respectively. The piston diameter is D = 10 cm. The local atmospheric pressure is 100 kPa. The piston moves smoothly and slowly at constant velocity in the cylinder and g = 9.81 m/s2. MAE 241 – Homework 1 Page 2 of 3 Problem 5– Measurement of Pressure a. For the tank shown in the figure below derive an expression to compute the Length, L, of the column of fluid as a function of density of the fluid in the manometer, 𝜌, and the atmospheric pressure, Patm. b. Determine the value of L when the manometer liquid is water and the tank contains a gas at a pressure of 1.5 bar. A barometer indicates the local atmospheric pressure is 750 mmHg. You also know that the density of water is 997 kg/m3 and the density of mercury is 13.59 g/cm3. Let g = 9.81 m/s2. Problem 6 – Gage pressure measurement A pressure gage mounted at the inlet to an air compressor indicates that the gage pressure is 60.0 kPa. The absolute pressure of the at the exit of the compressor is 5.5 times the absolute pressure at the inlet. The atmospheric pressure is 1.01 bar. What is the absolute pressure of the gas at the inlet and what is the gage pressure of the gas at the exit? Problem 7 – Unit conversions Perform the following unit conversions. Please do not use an on-line unit converter since this problem is given to you as practice in preparation for what you need to be proficient in: a. 170.8 in3 to L b. 1089.438 ft-lbf to kJ c. 140.0 hp to kW d. 1400.0 lb/h to kg/s e. 41.1488 lbf/in2 to kPa f. 3500.0 ft3/min to m3/s g. 105.0 mile/h to km/h h. 1.4 ton (=2000 lbf) to N Problem 8 – Newton’s second law Estimate the magnitude of the force, in lbf, exerted on a 20-lb goose in a collision of duration 1.5 x 10−3 s with an airplane taking off at 150 miles/h. Assume the bird’s velocity is zero before the collision. MAE 241 – Homework 1 Page 3 of 3 Problem 9 – Temperature conversions On January 3, 2019, in Flagstaff, AZ, the lowest temperature was 14oF at 5 AM and the highest 44oF at 4 PM. a. Express these temperatures in oR, K and oC. b. Determine the temperature change in oF, oR, oC and K from morning low to afternoon high. c. What is the relationship between the temperature changes in oF and oR? d. What is the relationship between the temperature changes in oC and K? Problem 10 – Ideal gas law application A closed deformable system consisting of 2 lb of air undergoes a process during which the relation between pressure and volume is defined by the mathematical expression PVn = Constant. The process begins with P1 = 20 lbf/in2, V1 = 15 ft3 and ends with P2 = 100 lbf/in2. The value of n = 1.3. Determine: a. The final volume, V2, in ft3 b. The specific volume at states 1 and 2, in ft3/lb. c. Use the ideal gas law as you learned in your chemistry course to determine the initial temperature, in °F. Hint: if you need the molecular mass of air please use Table A-1 or A-1E.

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## MAE 241 – Homework 2 Page 1 of 2 MAE 241 – Spring 2019 – Homework 2 Administered 1/18/2019 – Due 11PM, Sunday 1/27/2019 to Gradescope Problem 1 The average water head (vertical height of water column) maintained in Hoover dam reservoir is about 500 ft. Assume water density of 62.43 lb/ft3. a. Determine the maximum pressure at the bottom of reservoir. b. Find the power generation potential of the water at that pressure if the discharge rate is 500×103 ft3/s. Problem 2 The Vestas V164 is one of the largest wind turbines in the world, with diameter of 164 m. If the theoretical limit on the capacity of a wind turbine is 1/3rd of its power generation potential, determine the capacity of the turbine when it is placed in a location where the average wind speed is 10 m/s. Assume air density as 1.25 kg/m3. Problem 3 An automobile has a mass of 1200 kg. What is its kinetic energy, in kJ, relative to the road when traveling at a velocity of 50 km/h? If the vehicle accelerates to 100 km/h, what is the change in kinetic energy, in kJ? Problem 4 A 5 kg brick is dropped from a height of 12 m onto a spring with a spring constant 8 kN/m. If the spring has a unstretched length of 0.5m, find (a) the shortest length the spring will be compressed before recoil, and (b) the final length of spring once the whole system becomes static. Problem 5 A piping installation is used to transport 20 L/s of water from a reservoir (location 1) to a point of use (location 2) 20 meters above. The absolute pressure of water at the inlet of the installation is 110 kPa; the gauge pressure measured right before the point of use is 552 kPa. Determine the power input required, in kW. Assume that because the piping at locations (1) and (2) have the same diameter the average velocities of water are equal and the density of water is 1000 kg/m3. Problem 6 A system receives 10 MJ in the form of heat in a process and it produced 4 MJ of work. The system velocity changes from 10 m/s to 25 m/s. For a 50 kg mass of the system, determine the change in internal energy of the system. MAE 241 – Homework 2 Page 2 of 2 Problem 7 On a recent energy assessment performed to an industrial facility in Tempe by a team of ASU’s Industrial Assessment Center, the team evaluated a boiler whose rated input was 6 MBTUH (6 million BTU per hour). After measuring the composition of flue gases it was apparent that the boiler was not be operating at its best operating point; this suspicion was validated by determining that the combustion efficiency was equal to 0.65. As corrective measure the boiler received a tune up that increased the combustion efficiency to 0.8. The boiler operates 48 weeks per year continuously while the plant is in production. Taking the cost of energy to be \$13 per MBTU, determine: a. The annual energy cost. b. The annual cost savings as a result of tuning up the boiler. c. List the assumptions used in your computations. Problem 8 Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as 𝐹𝑏 = 𝜌𝑎𝑖𝑟𝑔𝑉𝑏𝑎𝑙, will push the balloon upward. (a) If the balloon has a diameter of 15 m and carries eight people, 75 kg each, determine the acceleration of the balloon when it is first released. (b) The change in air density with altitude can be approximated up to 10km using a linear function 𝜌𝑎𝑖𝑟 = 1.173 − 8 × 10−5ℎ where ℎ is the altitude in m. At what theoretical altitude the balloon will stop climbing upwards? Assume the density of air is 1.173 kg/m3 at ground level, and neglect the weight of the ropes and the cage. Problem 9 A differential manometer is used to measure pressure difference between two fluid systems. Two parallel pipes carrying freshwater and seawater are connected to each other by a double U-tube differential manometer, as shown in Figure. (a) Determine the pressure difference between the two pipelines if ℎ = 10 cm. (b) If the pressure difference between the pipes is doubled, what will be the difference in heights (ℎ) of mercury? Take the density of seawater at that location to be 1035 kg/m3, and the specific gravity of the oil is 0.72. Assume all fluids are incompressible.

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## b. Search the internet to find various steps in Engineering Decision Making Process. These steps may be different than listed in the book. Describe each of them briefly in your own words and submit url of all the material found on internet.

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## a. Search the internet to find at least 5 bridges around the world based on cantilever design. Describe each of them briefly in your own words and submit url of all the material found on internet.

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