Basic Sciences Caraig

Solved Problems Solved by: Caraig, Kenneth John P. Co, Karl Anthony D. Garcia, Willord J. Nanao, Jeferson N. Rivera, Jericho Paolo O. Turalba, Richard Saul M.

Problem no. 1 A rigid vessel having a volume of 1.5m3 initially holds 5kg of air under high pressure. If 12% of the mass of air leaks out what is the final specific volume of air in the vessel? 430 Li/kg b. 340 Li/kg a.

c. 530 Li/kg d. 400 Li/kg

Solution

Problem no. 2 Define a new scale, say °N, in which the boiling and freezing points of water are 1000°N and 100°N, respectively. Correlate this scale with the Celsius scales. 90°C+100 b. 9°C+100 a.

c. 0.9°C+100 d. 9°C+1000

Solution By interpolation

Problem no. 3 A nuclear submarine is 200m below the surface of the sea. What is the pressure (bars) exerted on the hull (outer casing) by the water at this depth? 19.62 bar b. 1.962 bar a.

c. 196.2 bar d. 1962 bar

Solution

Problem no. 4 An open tank 1 meter in diameter and 1.5m in height is filled with diesel oil (ρ=850 kg/m3). Assuming 75% of its capacity is occupied by the diesel; calculate the absolute pressure of the fluid at the bottom of the tank. 110.71 KPa b. 1100.962 KPa a.

c. 1.196 Kpa d. 9.38 KPa

Solution

Problem no. 5 A motor driven pump transfers 5,000 liters of oil (SG=0.8) per hour through an elevation of 16 meters. If the delivery velocity is 10 m/s, calculate the water power required. 0.32 KW b. 0.23 KW a.

c. 21.096 KW d. 2.10 KW

Solution

Problem no. 6 A tank contains 75 liters of lubricating oil having a relative density of 0.9 and temperature of 10°C. The oil is heated for 15 minutes by a 2.16KW electric heater. Determine the final temperature of the oil assuming heat loss through the tank is 160W. (Specific heat of oil is 2 KJ/kg-K) 5°K b. 40°C a.

c. 40°K d. 50°C

Solution

Problem no. 7 A power station uses oil-fired boilers, which are supplied with fuel from four cylindrical oil storage tanks, each 15m in diameter and 10m high. The calorific value of oil is 38000 kJ/kg and its relative density is 0.80. The output from the power station is 60MW. Assuming that only 10% of the heat input is converted into electrical energy output, how long will the boilers run on the oil in the tanks? 1107hrs b. 147.5 hrs a.

c. 99.5 hrs d. 9.38 hrs

Solution

Problem no. 8 An elevator and its contents have a mass of 2,500 kg. What is the electrical power input to the lifting motor if the elevator is raised through a height of 36meters in 30 seconds? Assume that only 85% of the electrical power input to the motor is available to lift the elevator. 3.462 KW b. 342.6 KW a.

c. 34.62 KW d. 3462 KW

Solution

Problem no. 9 A 50KW electric furnace measures 1.2mx1.0mx0.8m. When the temperature inside the furnace is 1250°C, a block of aluminum with a mass of 300kg and a temperature of 16.5 °C is placed inside. Assuming the heat loss from the furnace walls is 500 W/m2, how long will it take to heat the block to the furnace temperature? (Specific heat of Aluminum=0.9 Kj/kgK) 1.96 hrs b. 1.28 hrs a.

c. 1.58 hrs d. 1.75 hrs

Solution

Problem no. 10 The volume clearance space of a 152.40mm x 254.0mm Otto gas engine is 1.70 liters. Find the ideal thermal efficiency of the engine on the standard air basis, if the exponent of the expansion and compression lines is 1.35. Express in percent. 38.55% b. 36.89% a.

c. 26.98% d. 35.95%

Solution

Problem no. 11 Calculate the approximate mass density of methane gas if the pressure and temperature are on atmosphere and 15.55°C. 675.8 kg/m3 b. 6.785 kg/m3 a.

c. 67.58 kg/m3 d. 0.6758 kg/m3

Solution

Problem no. 12 Ten kg of water initially at 15°C is to be freezed at -3°C. Calculate the total amount of heat to be removed in 5hrs during the cooling process? 39.83 KJ b. 403 KJ a.

c. 0.224KW d. 3983.1 KW

Solution

Problem no. 13 Determine the friction head loss for fully developed laminar flow of ethylene glycol at 40°C (ρ=1,101 kg/m3) through a 5 cm diameter, 50m long pipe, if a friction factor of 0.242 and flow rate of 0.1 kg/s. 6.42 cm b. 2.64 cm a.

c. 3.46 cm d. 5.32 cm

Solution

Problem no. 14 A supercharged six-cylinder four stroke cycle diesel engine of 10.48cm bore and 12.7 cm stroke has a compression ratio of 15. When it is tested on a dynamometer with a 53.34 cm arm at 2500rpm, the scale reads 81.65 kg, 2.86 kg of fuel of 45,822.20 KJ/kg heating value are burned during a 6 min test, and air metered to the cylinders at the rate of 0.182 kg/s. Find the brake thermal efficiency. 0.307 b. 0.367 a.

c. 0.307 d. 0.357

Solution

Problem no. 15 Calculate the enthalpy in KJ of 1.50 kg of fluid that occupies a volume of 0.565 m3 if the internal energy is 555.60 Kcal per kg and pressure is 2 atm abs. 2,603.7 KJ b. 3,603.7 KJ a.

c. 4,603.7 KJ d. 5,603.7 KJ

Solution

Problem no. 16 A closed vessel A contains 85 liters of air at 3.45MPa and temperature of 50OC. This vessel connects with vessel B, which contains an unknown volume of air at 105kPa and 10OC. After the valve separating the two vessels is opened, the pressure and temperature of the mixes are 1.38MPa and 21OC. Calculate the volume of vessel B. 6.14 ft3 b. 4.15 ft3 a.

c. 2.42 ft3 d. 5.5ft3

Solution

Problem no. 17 An air-standard Diesel Cycle operates with a compression ratio of 15. The maximum cycle temperature is 1,700OF. At the beginning of compression, the air is at 100kPa and 40OC. What is the cut-off ratio? 2.13 b. 1.32 a.

c. 3.21 d. 2.87

Solution

Problem no. 18 Steam with an enthalpy of 335kJ/kg enters a nozzle at a velocity of 80m/s. Find the velocity of the steam at the exit of the nozzle if its enthalpy is reduced to 314kJ/kg, assuming the nozzle is horizontal and disregarding the heat losses. Take g = 9.81 m/s2. 220 m/s b. 652 m/s a.

c. 265 m/s d. 625 m/s

Solution

Problem no. 19 A supercharged six-cylinder four stroke cycle diesel engine of 10.48cm bore and 12.7 cm stroke has a compression ratio of 15. When it is tested on a dynamometer with a 53.34 cm arm at 2500rpm, the scale reads 81.65 kg, 2.86 kg of fuel of 45,822.20 KJ/kg heating value are burned during a 6 min test, and air metered to the cylinders at the rate of 0.182 kg/s. Find the brake thermal efficiency. 0.307 b. 0.367 a.

c. 0.307 d. 0.357

Solution

Problem no. 20 A hydraulic turbine receives water from a reservoir at an elevation of 110m above it. What is the minimum water flow in kg/s to produce a steady turbine output of 30MW? 27,800 kg/s b. 28,700 kg/s a.

c. 72,800 kg/s d. 87,200 kg/s

Solution

Problem no. 21 A diesel engine is operating on a 4stroke cycle, has a heat rate of 11,315.6 kJ/kWh brake. The compression ratio is 13. The cut-off ratio is 2. Using k = 1.32, what is the brake engine efficiency? 63.5 b. 51.2 a.

c. 73.5 d. 45.3

Solution

Problem no. 22 A gas turbine unit operates at a moss flow of 30kg/s. Air enters the compressor at a pressure of 1 bar and a temperature of 15 degrees Celsius and is discharged from the compressor at pressure of 10.5 bars. Combustion occurs at constant pressure and results in a temperature rise of 420K. If the flow leaves the turbine at a pressure of 1.2bar, determine: the net power output from the unit, kW. 4,388.74 KW b. 5,388.74 KW a.

c. 6,388.74 KW d. 7,388.74 KW

Solution

Problem no. 23 Steam enters a nozzle steadily with a velocity of 100m/s and enthalpy of 1300 kJ/kg and leaves with an enthalpy of 1100kJ/kg. Neglecting heat transfer, what is the velocity of steam at the nozzle outlet? 720 m/s b. 640 m/s a.

c. 580 m/s d. 490 m/s

Solution

Problem no. 24 Calculate from the following data the kg of air per kg of fuel used by an automobile engine: air temperatures 21.50C, barometer 767.0 mm Hg, air entering 1.75 cu. m/min, measured gasoline 14.25 liters per hour, specific gravity of 0.8. What is the power output of the engine? 12.125 b. 15.45 a.

c. 14.45 d. 21.45

Solution

Problem no. 25 An engine has an efficiency of 26%. It uses 2 gallons of gasoline per hour. Gasoline has a heating value of 20500 BTU/lb and a specific gravity of 0.8. What is the power output of the engine? 20.8 KW b. 29 KW a.

c. 19.8 KW d. 18.9 KW

Solution

Problem no. 26 A diesel power station is to supply power demand of 30kW. If the overall efficiency of the power generating unit 40%, calculate the amount of diesel oil required, kg/hr. Note: The calorific value of fuel oil used is 12,000kcal/kg. And 1kWh = 860 kcal. 4.37 kg/hr b. 6.37 kg/hr a.

c. 5.37 kg/hr d. 7.37 kg/hr

Solution

Problem no. 27 A hydroelectric generating station is supplied from a reservoir of capacity 6,000,000 cu. m at a head of 170m. Assume hydraulic efficiency of 80% and electrical efficiency of 90%. The fall in the reservoir level after a load of 15MW has been supplied for 3 hours, if the area of the reservoir is 2.5 sq. km is closest to: 5.39 cm b. 5.98 cm a.

c. 4.32 cm d. 4.83 cm

Solution

Problem no. 28 A hydroelectric plant having 50 sq. km reservoir area and 100m head is used to generate power. The energy utilized by the consumers whose load is connected to the power plant during a five-hour period is 13.5 x 106kWh. The overall generation efficiency is 75%. Find the fall in the height of water in the reservoir after a five-hour period. 2.13 m b. 1.32 m a.

c. 3.21 m d. 0.53 m

Solution

Problem no. 29 If 2 kg metal with 90 degrees Celsius temperatures is immersed into a 4kg of water at 11 degrees Celsius, what will be the final temperature of the water after immersion? (Cp of metal is 0.913 kJ/kg-K) 18.77 C b. 19.88 C a.

c. 20.55 C d. 21.22 C

Solution

Problem no. 30 A Carnot engine receives 130 BTU of heat from a hot reservoir at 700°F and rejects 49 BTU of heat. Calculate the temperature of the cold reservoir. (April ’97) -21.9°F b. -24.2°F a.

c. -20.8°F d. -22.7°F

Solution

Problem no. 31 The maximum thermal efficiency possible for a power cycle operating between 1200°F and 225°F is: (April ’97) 58% b. 58.73% a.

c. 57.54% d. 57.40%

Solution

Problem no. 32 A Carnot engine requires 35 KJ/sec from a hot source. The engine produces 15kW of power and the temperature of the sink 26°C. What is the temperature of the hot source? (April ’97) 245.57°C b. 210.10°C a.

c. 250.18°C d. 260.68°C

Solution

Problem no. 33 An air bubble form the bottom of a well where the temperature is 25°C, to the surface where the temperature is 27°C. Find the percent increase in the volume of the bubble if the depth of the well is 5m. Atmospheric pressure is 101,528 Pascals. (April ’96) 49.3% b. 41.3 % a.

c. 56.7% d. 38.6%

Solution

Problem no. 34 Steam Flows into a turbine at the rate of 10kg/s and 10Kw of heat are lost from the turbine. Ignoring elevation and kinetic energy effects, calculate the power output from the turbine. (October ’94) h1=2939.0 KJ/kg h2=2300.5 KJ/kg 4605 KW b. 4937 KW a.

c. 4375 KW d. 4000KW

Solution Input = Output + Losses Output = Input – Losses Output = m(h1 – h2) – losses Output = 10 kg/s (2939.0 – 2300.5) kJ/kg – 10kW Output = 6385kW – 10kW Output = 6375 kW

Problem no. 35 The enthalpy of air is increased by 139.586 KJ/kg in a compressor. The rate of air flow is 16.42 kg/min. The power input is 48.2 KW. Which of the following values most nearly equals the heat loss from the compressor in KW? (April ’97) -10.0 KW b. -9.95 KW a.

c. +10.0 KW d. +9.95 KW

Solution

Problem no. 36 At an average temperature of 100°C, hot air flows through a 2.5m long tube with an inside diameter of 50mm. The temperature of the tube is 20°C along the length. Convection film coefficient is 20.1 W/m2-K. Determine the convective heat transfer from air to the tube. (April ’97) 900 W b. 909 W a.

c. 624 W d. 632 W

Solution

Problem no. 37 Calculate the energy transfer rate across 6 in wall of firebricks with temperature difference across the wall of 50°C. The thermal conductivity of the firebrick is 0.65 BTU/hr-ft-°F at the temperature interest. (October ’94) 285 b. 369 a.

c. 112 d. 429

Solution

Problem no. 38 A piece of silver weighing 600 grams in air weighs 500 grams when immersed in glycerin whose specific gravity is 1,25. Find the volume of the cavity inside the silver. (October ’95) 24.32 cc b. 22.86 cc a.

c. 21.12 cc d. 26.86 cc

Solution

Problem no. 39 A heat engine is operated between the temperature limits f 1370 °C and 260 °C. Engine supplied wih 14,142 KWH. Find the Carnot cycle efficiency in percent. (October ’97) 70.10 b. 65.50 a.

c. 67.56 d. 69.32

Solution

Problem no. 40 An Otto engine has a clearance volume of 7%. It produces 300KW power. What is the amount of heat rejected in KW? (October ’97) 88.60 KW b. 95.32 KW a.

c. 152 KW d. 90.72 KW

Solution