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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A laboratory room keeps a vacuum of 0.1 kPa. What net force does that put on the door of size 2 m by 1 m?
The pressure at the bottom of a swimming pool is evenly distributed. Suppose we look at a cast iron plate of 7272 kg lying on the ground with an area of 100 m2. What is the average pressure below that? Is it just as evenly distributed?
What is a temperature of –5oC in degrees Kelvin?
What is the smallest temperature in degrees Celsius you can have? Kelvin?
Density of liquid water is ρ = 1008 – T/2 [kg/m3] with T in oC. If the temperature increases 10oC how much deeper does a 1 m layer of water become?
Convert the formula for water density in problem 21 to be for T in degrees Kelvin.
A steel cylinder of mass 2 kg contains 4 L of liquid water at 25oC at 200 kPa. Find the total mass and volume of the system. List two extensive and three intensive properties of the water
An apple “weighs” 80 g and has a volume of 100 cm3 in a refrigerator at 8oC. What is the apple density? List three intensive and two extensive properties of the apple?
One kilopond (1 kp) is the weight of 1 kg in the standard gravitational field. How many Newtons (N) is that?
A pressurized steel bottle is charged with 5 kg of oxygen gas and 7 kg of nitrogen gas. How many kmoles are in the bottle?
The “standard” acceleration (at sea level and 45° latitude) due to gravity is 9.80665 m/s2. What is the force needed to hold a mass of 2 kg at rest in this gravitational field? How much mass can a force of 1 N support?
A force of 125 N is applied to a mass of 12 kg in addition to the standard gravitation. If the direction of the force is vertical up find the acceleration of the mass.
When you move up from the surface of the earth the gravitation is reduced as g = 9.807 − 3.32 × 10-6 z, with z as the elevation in meters. How many percent is the weight of an airplane reduced when it cruises at 11 000 m?
A model car rolls down an incline with a slope so the gravitational “pull” in the direction of motion is one third of the standard gravitational force (see Problem 2.1). If the car has a mass of 0.45 kg find the acceleration.
A car drives at 60 km/h and is brought to a full stop with constant deceleration in 5 seconds. If the total car and driver mass is 1075 kg find the necessary force.
A car drives at 60 km/h and is brought to a full stop with constant deceleration in 5 seconds. If the total car and driver mass is 1075 kg find the necessary force. Discuss.
A 1200-kg car moving at 20 km/h is accelerated at a constant rate of 4 m/s2 up to a speed of 75 km/h. Determine the force and total time required?
A steel plate of 950 kg accelerates from rest with 3 m/s2 for a period of 10s. What force is needed and what is the final velocity
A 15 kg steel container has 1.75 kilo moles of liquid propane inside. A force of 2 kN now accelerates this system. What is the acceleration?
A bucket of concrete of total mass 200 kg is raised by a crane with an acceleration of 2 m/s2 relative to the ground at a location where the local gravitational acceleration is 9.5 m/s2. Determine the required force.
On the moon the gravitational acceleration is approximately one-sixth that on the surface of the earth. A 5-kg mass is “weighed” with a beam balance on the surface on the moon. What is the expected reading? If this mass is weighed with a spring scale that reads correctly for standard gravity on
A 5 m3 container is filled with 900 kg of granite (density 2400 kg/m3) and the rest of the volume is air with density 1.15 kg/m3. Find the mass of air and the overall (average) specific volume.
A tank has two rooms separated by a membrane. Room A has 1 kg air and volume 0.5 m3, room B has 0.75 m3 air with density 0.8 kg/m3. The membrane is broken and the air comes to a uniform state. Find the final density of the air.
A 1 m3 container is filled with 400 kg of granite stone, 200 kg dry sand and 0.2 m3 of liquid 25°C water. Use properties from tables A.3 and A.4. Find the average specific volume and density of the masses when you exclude air mass and volume.
A 1 m3 container is filled with 400 kg of granite stone, 200 kg dry sand and 0.2 m3 of liquid 25°C water. Use properties from tables A.3 and A.4 and use air density of 1.1 kg/m3. Find the average specific volume and density of the 1 m3 volume.
One kilogram of diatomic oxygen (O2 molecular weight 32) is contained in a 500-L tank. Find the specific volume on both a mass and mole basis (v and v).
A 15-kg steel gas tank holds 300 L of liquid gasoline, having a density of 800 kg/m3. If the system is decelerated with 6 m/s2. Calculate the needed force?
A hydraulic lift has a maximum fluid pressure of 500 kPa. What should the piston-cylinder diameter be so it can lift a mass of 850 kg?
A piston/cylinder with cross sectional area of 0.01 m2 has a piston mass of 100 kg resting on the stops, as shown in Fig. P2.45. with an outside atmospheric pressure of 100 kPa, what should the water pressure be to lift the piston?
A vertical hydraulic cylinder has a 125-mm diameter piston with hydraulic fluid inside the cylinder and an ambient pressure of 1 bar. Assuming standard gravity, find the piston mass that will create a pressure inside of 1500 kPa.
A valve in a cylinder has a cross sectional area of 11 cm2 with a pressure of 735 kPa inside the cylinder and 99 kPa outside. How large a force is needed to open the valve?
A cannon-ball of 5 kg acts as a piston in a cylinder of 0.15 m diameter. As the gun-powder is burned a pressure of 7 MPa is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally?
Repeat the previous problem for a cylinder (cannon) pointing 40 degrees up relative to the horizontal direction.
A large exhaust fan in a laboratory room keeps the pressure inside at 10 cm water relative vacuum to the hallway. What is the net force on the door measuring 1.9 m by 1.1 m?
What is the pressure at the bottom of a 5 m tall column of fluid with atmospheric pressure 101 kPa on the top surface if the fluid is a) Water at 20°C b) glycerine 25°C or c) light oil
A tornado rips off a 100 m2 roof with a mass of 1000 kg. What is the minimum vacuum pressure needed to do that if we neglect the anchoring forces?
The hydraulic lift in an auto-repair shop has a cylinder diameter of 0.2 m. To what pressure should the hydraulic fluid be pumped to lift 40 kg of piston/arms and 700 kg of a car?
A 2.5 m tall steel cylinder has a cross sectional area of 1.5 m2. At the bottom with a height of 0.5 m is liquid water on top of which is a 1 m high layer of gasoline. The gasoline surface is exposed to atmospheric air at 101 kPa. What is the highest pressure in the water?
At the beach, atmospheric pressure is 1025 mbar. You dive 15 m down in the ocean and you later climb a hill up to 250 m elevation. Assume the density of water is about 1000 kg/m3 and the density of air is 1.18 kg/m3. What pressure do you feel at each place?
A piston, mp= 5 kg, is fitted in a cylinder, A = 15 cm2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 25 m/s2 in the direction of piston motion towards the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
A steel tank of cross sectional area 3 m2 and 16 m tall weighs 10 000 kg and it is open at the top. We want to float it in the ocean so it sticks 10 m straight down by pouring concrete into the bottom of it. How much concrete should I put in?
Liquid water with density ρ is filled on top of a thin piston in a cylinder with cross-sectional area A and total height H. Air is let in under the piston so it pushes up, spilling the water over the edge. Deduce the formula for the air pressure as a function of the piston elevation from the
The density of atmospheric air is about 1.15 kg/m3, which we assume is constant. How large an absolute pressure will a pilot see when flying 1500 m above ground level where the pressure is 101 kPa.
A differential pressure gauge mounted on a vessel shows 1.25 MPa and a local barometer gives atmospheric pressure as 0.96 bar. Find the absolute pressure inside the vessel.
Two vertical cylindrical storage tanks are full of liquid water, density 1000 kg/m3, the top open to the atmosphere. One is 10 m tall, 2 m diameter; the other is 2.5 m tall with diameter 4 m. What is the total force from the bottom of each tank to the water and what is the pressure at the bottom of
Blue manometer fluid of density 925 kg/m3 shows a column height difference of 6 cm vacuum with one end attached to a pipe and the other open to P0 = 101 kPa. What is the absolute pressure in the pipe?
The absolute pressure in a tank is 85 kPa and the local ambient absolute pressure is 97 kPa. If a U-tube with mercury, density 13550 kg/m3, is attached to the tank to measure the vacuum, what column height difference would it show?
The pressure gauge on an air tank shows 75 kPa when the diver is 10 m down in the ocean, at what depth will the gauge pressure be zero? What does that mean?
A submarine maintains 101 kPa inside it and it dives 240 m down in the ocean having an average density of 1030 kg/m3. What is the pressure difference between the inside and the outside of the submarine hull?
A barometer to measure absolute pressure shows a mercury column height of 725 mm. The temperature is such that the density of the mercury is 13 550 kg/m3. Find the ambient pressure.
An absolute pressure gauge attached to a steel cylinder shows 135 kPa. We want to attach a manometer using liquid water a day that Patm = 101 kPa. How high a fluid level difference must we plan for?
The difference in height between the columns of a manometer is 200 mm with a fluid of density 900 kg/m3. What is the pressure difference? What is the height difference if the same pressure difference is measured using mercury, density 13600 kg/ m3, as manometer fluid?
An exploration submarine should be able to go 4000 m down in the ocean. If the ocean density is 1020 kg/m3 what is the maximum pressure on the submarine hull?
Assume we use a pressure gauge to measure the air pressure at street level and at the roof of a tall building. If the pressure difference can be determined with an accuracy of 1 mbar (0.001 bar) what uncertainty in the height estimate does that corresponds to?
Assume we use a pressure gauge to measure the air pressure at street level and at the roof of a tall building. If the pressure difference can be determined with an accuracy of 1 mbar (0.001 bar) what uncertainty in the height estimate does that corresponds to? Discuss.
A barometer measures 760 mmHg at street level and 735 mmHg on top of a building. How tall is the building if we assume air density of 1.15 kg/m3?
A piece of experimental apparatus is located where g = 9.5 m/s2 and the temperature is 5°C. An air flow inside the apparatus is determined by measuring the pressure drop across an orifice with a mercury manometer (see Problem 2.77 for density) showing a height difference of 200 mm. What is the
Two piston/cylinder arrangements, A and B, have their gas chambers connected by a pipe. Cross-sectional areas are AA = 75 cm2 and AB = 25 cm2 with the piston mass in A being mA = 25 kg. Outside pressure is 100 kPa and standard gravitation. Find the mass mB so that none of the pistons have to rest
Two hydraulic piston/cylinders are of same size and setup as in Problem 2.73, but with negligible piston masses. A single point force of 250 N presses down on piston A. Find the needed extra force on piston B so that none of the pistons have to move.
A pipe flowing light oil has a manometer attached as shown in Fig. P2.75. what is the absolute pressure in the pipe flow?
Two cylinders are filled with liquid water, ρ = 1000 kg/m3, and connected by a line with a closed valve. A has 100 kg and B has 500 kg of water, their cross-sectional areas are AA = 0.1 m2 and AB = 0.25 m2 and the height h is 1 m. Find the pressure on each side of the valve. The valve is
The density of mercury changes approximately linearly with temperature as ρHg = 13595 − 2.5 T kg/ m3 T in Celsius, So the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 100 kPa is measured in the summer at
A mercury thermometer measures temperature by measuring the volume expansion of a fixed mass of liquid Hg due to a change in the density, see problem 2.35. Find the relative change (%) in volume for a change in temperature from 10°C to 20°C.
Using the freezing and boiling point temperatures for water in both Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between Kelvin and Rankine temperature scales.
The atmosphere becomes colder at higher elevation. As an average the standard atmospheric absolute temperature can be expressed as Tatm = 288 - 6.5 × 10−3 z, where z is the elevation in meters. How cold is it outside an airplane cruising at 12 000 m expressed in Kelvin and in Celsius?
Repeat problem 2.72 if the flow inside the apparatus is liquid water, ρ ≅ 1000 kg/m3, instead of air. Find the pressure difference between the two holes flush with the bottom of the channel. You cannot neglect the two unequal water columns.
The main waterline into a tall building has a pressure of 600 kPa at 5 m elevation below ground level. How much extra pressure does a pump need to add to ensure a water line pressure of 200 kPa at the top floor 150 m above ground?
A 5-kg piston in a cylinder with diameter of 100 mm is loaded with a linear spring and the outside atmospheric pressure of 100 kPa. The spring exerts no force on the piston when it is at the bottom of the cylinder and for the state shown, the pressure is 400 kPa with volume 0.4 L. The valve is
In the city water tower, water is pumped up to a level 25 m above ground in a pressurized tank with air at 125 kPa over the water surface. This is illustrated in Fig. P2.84. Assuming the water density is 1000 kg/m3 and standard gravity, find the pressure required to pump more water in at ground
Two cylinders are connected by a piston as shown in Fig. P2.85. Cylinder A is used as a hydraulic lift and pumped up to 500 kPa. The piston mass is 25 kg and there is standard gravity. What is the gas pressure in cylinder B?
A dam retains a lake 6 m deep. To construct a gate in the dam we need to know the net horizontal force on a 5 m wide and 6 m tall port section that then replaces a 5 m section of the dam. Find the net horizontal force from the water on one side and air on the other side of the port.
A mass of 2 lbm has acceleration of 5 ft/s2, what is the needed force in lbf?
How much mass is in 0.25 gallon of liquid mercury (Hg)? Atmospheric air?
Can you easily carry a one gallon bar of solid gold?
What is the temperature of –5F in degrees Rankine?
What is the smallest temperature in degrees Fahrenheit you can have? Rankine?
An apple weighs 0.2 lbm and has a volume of 6 in3 in a refrigerator at 38 F. What is the apple density? List three intensive and two extensive properties for the apple?
A 2500-lbm car moving at 15 mi/h is accelerated at a constant rate of 15 ft/s2 up to a speed of 50 mi/h. Calculate force and total time required?
Two pound moles of diatomic oxygen gas are enclosed in a 20-lbm steel container. A force of 2000 lbf now accelerates this system. What is the acceleration?
A valve in a cylinder has a cross sectional area of 2 in2 with a pressure of 100 psia inside the cylinder and 14.7 psia outside. How large a force is needed to open the valve?
One pound-mass of diatomic oxygen (O2 molecular weight 32) is contained in a 100-gal tank. Find the specific volume on both a mass and mole basis (v and v).
A 30-lbm steel gas tank holds 10 ft3 of liquid gasoline, having a density of 50 lbm/ft3. What force is needed to accelerate this combined system at a rate of 15 ft/s2?
A laboratory room keeps a vacuum of 4 in. of water due to the exhaust fan. What is the net force on a door of size 6 ft by 3 ft?
A 7 ft m tall steel cylinder has a cross sectional area of 15 ft2. At the bottom with a height of 2 ft m is liquid water on top of which is a 4 ft high layer of gasoline. The gasoline surface is exposed to atmospheric air at 14.7 psia. What is the highest pressure in the water?
A U-tube manometer filled with water, density 62.3 lbm/ft3, shows a height difference of 10 in. What is the gauge pressure? If the right branch is tilted to make an angle of 30° with the horizontal, as shown in Fig. P2.72, what should the length of the column in the tilted tube be relative to the
A piston/cylinder with cross-sectional area of 0.1 ft2 has a piston mass of 200 lbm resting on the stops, as shown in Fig. P2.45. with an outside atmospheric pressure of 1 atm, what should the water pressure be to lift the piston?
The main waterline into a tall building has a pressure of 90 psia at 16 ft elevation below ground level. How much extra pressure does a pump need to add to ensure a waterline pressure of 30 psia at the top floor 450 ft above ground?
A piston, mp = 10 lbm, is fitted in a cylinder, A = 2.5 in.2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 75 ft/s2. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
The atmosphere becomes colder at higher elevation. As an average the standard atmospheric absolute temperature can be expressed as Tatm = 518 - 3.84 × 10−3 z, where z is the elevation in feet. How cold is it outside an airplane cruising at 32 000 ft expressed in Rankine and in Fahrenheit?
The density of mercury changes approximately linearly with temperature as ρHg = 851.5 - 0.086 T lbm/ft3 T in degrees Fahrenheit so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 14.7 lbf/in.2 is measured in the
What is the lowest temperature (approximately) at which water can be liquid?
What is the percent change in volume as liquid water freezes? Mention some effects in nature and for our households the volume change can have.
When you skate on ice a thin liquid film forms under the skate; how can that be?
An external water tap has the valve activated by a long spindle so the closing mechanism is located well inside the wall. Why is that?
Some tools should be cleaned in water at a least 150oC. How high a P is needed?
Are the pressures in the tables absolute or gauge pressures?
If I have 1 L ammonia at room pressure and temperature (100 kPa, 20oC) how much mass is that?
How much is the change in liquid specific volume for water at 20oC as you move up from state I towards state j in figure 3.12 reaching 15 000 kPa?
For water at 100 kPa with a quality of 10% find the volume fraction of vapor.
Sketch two constant-pressure curves (500 kPa and 30 000 kPa) in a T-v diagram and indicate on the curves where in the water tables you see the properties.
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