ThermoFluids Tutorial/Midterm/Practice Exam Problems

Tutorial 10

1) Compare the behaviour of fully developed laminar flow and fully developed turbulent flow in a horizontal pipe under different conditions. (a) For the same flow rate, which will have the larger centreline velocity? Why? (b) If the pipe discharges to atmosphere, what would you expect the trajectory of the discharge stream to look like (for the same flow rate)? Sketch your expectations for each case. (c) For the same flow rate, which flow would give the larger wall shear stress? Why? Sketch the shear stress distribution τ/τo as a function of radius for each flow. (d) For the same Reynolds number, which flow would have the larger pressure drop per unit length? Why? (e) For a given imposed pressure differential, which flow would have the large flow rate? Why? - Comparing Laminar and Turbulent in different scenarios. 2) Water discharges to atmosphere from a large reservoir through a moderately rounded horizontal nozzle of 25 mm diameter (Cnozzle = 0.28). The free surface is 1.5 m above the nozzle exit plane. Calculate the change in flow rate when a short section of 50 mm diameter pipe is attached to the end of the nozzle to form a sudden expansion. Determine the location and estimate the magnitude of the minimum pressure with the sudden expansion in place. If the flow were frictionless (with the sudden expansion in place), would the minimum pressure be higher, lower or the same? Would the flow rate be higher, lower, or the same? 3) Water from a pump flows through a 0.25 m diameter commercial steel pipe for a distance of 6 km from the pump discharge to a reservoir open to the atmosphere. The level of the water in the reservoir is 10 m above the pump discharge, and the average speed of the water in the pipe is 2.5 m/s. Calculate the pressure at the pump discharge. The roughness for commercial steel pipe is 0.046 mm. Take νwater = 10-6 m2/s. 4) Two reservoirs are connected by three clean cast-iron pipes in series, L1 = 600 m, D1 = 0.3m, L2 = 900 m, D2 = 0.4 m, L3 = 1500 m, and D3 = 0.45 m. When the discharge is 0.11 m3/s of water at 15 C, determine the difference in elevation between the reservoirs. Take νwater = 10-6 m2/s, and k = 0.26 mm for cast-iron pipes (this can also be obtained from handbooks). 5) The resistance to motion of a good bicycle on smooth pavement is nearly all due to aerodynamic drag. Assume that the mass of the rider and bike is 100 kg. The frontal area measured from a photograph is 0.46 m2. Experiments on a hill, where the road grade is 8%, show that the terminal speed is 15 m/s. From these data, the drag coefficient is estimated to be 1.2. Verify this calculation of drag coefficient. Estimate the distance needed for the bike and rider to decelerate from 15 m/s to 10 m/s while coasting after reach level road. Take ρair = 1.2 kg/m3. 6) An aircraft is in level flight at 250 km/hr through air at standard conditions. The lift coefficient at this speed is 0.4 and the drag coefficient is 0.065. The mass of the aircraft is 850 kg. Calculate the effective lift area for the craft, and the required engine thrust and power. Take ρair = 1.23 kg/m3. 7) A golf ball (diameter D = 43 mm) with circular dimples is hit from a sand trap at 20 m/s with backspin of 2000 rpm. The mass of the ball is 48 g. Evaluate the lift and drag forces acting on the ball. Express your results as fractions of the weight of the ball. Take νair = 0.15×10-4 m2/s and ρair = 1.23 kg/m3.

Tutorial 9

1) Consider a soap bubble. It is known that the pressure inside the bubble must be greater than that outside, and that surface tension [N/m] acts like a "skin" to support this pressure difference. The pressure difference is then a function of surface tension and bubble radius and no other parameters. Determine the resulting dimensionless group(s). How many experiments would have to be performed based upon the number of resulting group(s) to describe the physics? Note that only two repeating parameters are required for this problem. Why is this the case? - Dimensional Analysis - Dimensionless. 2) A 1:30 scale model of a submarine is to be tested in a towing tank under two conditions: motion at the free surface and motion far below the free surface. The tests are performed in fresh water. On the surface, the submarine cruises at 20 knots. At what speed should the model be towed to ensure dynamic similarity? Far below the surface, the sub cruises at 0.5 knots. At what speed should the model be towed to ensure dynamic similarity? What must the drag of the model be multiplied by to give the drag of the full‐scale submarine? Take the specific gravity of seawater as 1.025 and the absolute viscosity as 1.08 x 10-3 Pa‐s, and the fresh water kinematic viscosity as 1.00 x 10-6 m2/s and density to be 1000 kg/m3. 3) Experiments show that the pressure drop due to flow through an orifice plate in a circular duct may be expressed as ΔP = f (ρ, μ, V, d, D). You are asked to organize some experimental data. An orifice plate is a plate inserted into the tube that has through hole with diameter d (d<D) that can be used to back out the flow rate. Obtain the resulting dimensionless parameters. - Dimensional Analysis. 4) The aerodynamic behaviour, e.g., lift force, of a flying insect is to be investigated in a wind tunnel assuming a ten‐times scale model. If the insect flaps its wings 50 times a second when flying at 1.25 m/s, determine the wind tunnel air speed and wing oscillation frequency required for dynamic similarity. Do you expect that this would be a successful or practical model for generating an easily measurable wind lift? If not, can you suggest a different fluid, e.g., water or air at a different temperature that would produce a better model? - Dimensional Analysis is used for this. 5) Consider fully developed laminar flow in the annulus between two concentric pipes. The outer pipe is stationary, and the inner pipe moves in the x direction with speed V. Assume the axial pressure gradient is zero. Obtain a general expression for the shear stress as a function of radius in terms of a constant C1. Obtain a general expression for the velocity profile in terms of two constants, C1 and C2. Obtain expressions for C1 and C2. 6) Water flows in a constant‐area pipeline; the pipe diameter is 50 mm and the average flow speed is 1.5 m/s. At the pipe inlet, the gage pressure is 588 kPa and the outlet is atmospheric pressure. Determine the head loss in the pipe. If the pipe is now aligned so that the outlet of the pipe is 25 m above the inlet, what will the inlet pressure need to be to maintain the same flow rate? If the pipe is now aligned so that the outlet is 25 m below the inlet, what will the inlet pressure need to be to maintain the same flow rate? Finally, how much lower than the inlet must the outlet be so that the same flow rate is maintained if both ends of the pipe are at atmospheric pressure, i.e., gravity feed? Take the density of the water to be 1000 kg/m3. 7) A hypodermic needle, with inside diameter d = 0.1 mm and length L=25 mm, is used to inject saline solution with viscosity five times that of water. The plunger diameter is D = 10 mm; the maximum force that can be exerted by a thumb on the plunger is F = 45 N. Estimate the volume flow rate of saline that can be produced. Take the viscosity of water to be 10-3 Pa‐s.

Tutorial 1

1) Determine the mass and weight of the air contained in a room whose dimensions are 6 m x 6 m x 8 m. Assume the density of the air is 1.16 kg/m3. Ans: 334.1 kg, 3277 N. 2) A pool of volume V [m3] is to be filled with water using a hose of diameter D [m]. If the average discharge velocity is U [m/s] and the filling time t [s], obtain a relation for the volume of the pool based on considerations of the quantities involved. 3) Define isothermal, isobaric, and isochoric processes. 4) The temperature of a system rises by 45 C during a heating process. Express this rise in Kelvin. 5) A gas is contained in a vertical, frictionless piston-cylinder device. The piston has a mass of 4 kg and a cross-sectional area of 35 cm2. A compressed spring above the piston exerts a force of 60 N on the piston. If the atmospheric pressure is 95 kPa, determine the pressure inside the cylinder. Ans: 123.4 kPa 6) Complete this table for H2O T [C] P [kPa] v [m3/kg] Phase Description 50 4.16 200 Sat. Vapor 250 400 110 600 7) Complete this table for R-134a T [C] P [kPa] v [m3/kg] Phase Description -8 320 30 0.015 180 Sat. Vapor 80 600 8) A piston-cylinder device contains 0.85 kg of refrigerant-134a at -10 C. The piston that is free to move has a mass of 12 kg and a diameter of 25 cm. The local atmospheric pressure is 88 kPa. Now, heat is transferred to the refrigerant until the temperature is 15 C. Determine (a) the final pressure, (b) the change in the volume of cylinder, and (c) the change in the enthalpy of the refrigerant. Ans: (a) 90.4 kPa; (b) 0.02 m3; (c) ≈ 20 kJ/kg. 9) 10 kg of R-134a at 300 kPa fills a rigid container whose volume is 14 L. Determine the temperature and total enthalpy in the container. The container is now heated until the pressure is 600 kPa. Determine the temperature and total enthalpy when the heating is completed. Ans: (b) 846.4 kJ 10) A piston-cylinder device contains 0.8 kg of steam at 300 C and 1 MPa. Steam is cooled at constant pressure until one-half of the mass condenses. (a) Show the process on a T-v property diagram, (b) find the final temperature, and (c) determine the volume change. Ans: (b) 179.88 C, (c) -0.1282 m3 11) A rigid tank whose volume is unknown is divided into two parts by a partition. One side of the tank contains an ideal gas at 927 C. The other side is evacuated and has a volume twice the size of the part containing the gas. The partition is now removed and the gas expands to fill the entire tank. Heat is now applied to the gas until the pressure equals the initial pressure. Determine the final temperature of the gas. Ans: 3327 C 12) A piston-cylinder device with a set of stops initially contains 0.3 kg of steam at 1.0 MPa and 400 C. The initial location of the piston is above the stops, and the location of the stops corresponds to 60% of the initial volume. Now the steam is cooled. Determine the compression work if the final state is (a) 1.0 MPa and 250 C, (b) 500 kPa, and (c) the temperature at the final state in part (b). Note that the pressure exerted by the piston due to the load on it is always 1 MPa. Ans: (a) 22.16 kJ, (b) 36.79 kJ, (c) 151.83 C 13) A well insulated rigid tank contains 2 kg of a saturated liquid-vapor mixture of water at 150 kPa. Initially, three-quarters of the mass is in the liquid phase. An electric resistor placed in the tank is connected to a 110 V source, and a current of 8 A flows through the resistor when the switch is turned on. Determine how long it will take to vaporize all the liquid in the tank. Also, show the process on a T-v diagram with respect to saturation lines. Ans: 60.2 minutes 14) Saturated mixture at 75 kPa and 8% quality is contained in a spring-loaded piston cylinder device with an initial volume of 2 m3. Saturated mixture is now heated until its volume is 5 m3 and its pressure is 225 kPa. Determine the heat transferred to and the work produced by the steam during this process. Ans: (a) 450 kJ and (b) 12,750 kJ

2013 Sem 1 Final

Thermo Questions Q1: i) Consider a piston in a sealed, leakproof cylinder. The fluid in the cylinder is initially steam at a pressure of 2 MPa and 250C. The cylinder is then placed in a refrigerator and cooled to 10C. The piston has a resistance such that the pressure of the fluid in the cylinder is kept constant. Sketch a T-v property diagram of the process. ii) Determine the specific enthalpy change of the water during the above process. iii)Using the definition of enthalpy, determine the specific internal energy change for this process. iv) During the process there is a phase change. Determine the specific work done on the piston by the fluid during the phase change from saturated gas to saturated liquid. v) If there is this mass of fluid in the cylinder and the phase change takes t time to complete (from saturated gas to saturated liquid), determine the power transferred to the fluid in Watts (determine the work per unit time). Q2: i) What is the temperature difference in C between air at P1 and density1 ad air at P2 and density2. R given ii) Consider the flow of air through an ideal turbine. The turbine inlet pressure is p1, with T1. The inlet velocity is v1. The exit pressure is p2 and T2 with a velocity V2. If the inlet and outlet areas of the turbine are equal at A, determine the kinetic energy change per unit mass and the flow work per unit mass. iii) Using the steady flow energy equation, determine the specific work out of the turbine. Cv of air given iv) An adiabatic process with gamma given, takes a gas from a pressure given to another pressure given. If the initial temp is T1, determine the final temperature. An extra part b is if this were helium instead of adiabatic. Q3: i) Sketch a T-s diagram for the Rankine Cycle ii) Prove that the thermal efficiency of a heat engine following the Rankine cycle is given by... n=(h3-h4)/(h3-h2) iii) Consider a steam turbine generator operating with boiler inlet water temperature of T2 and constant pressure P2. The water is heated until it becomes superheated steam with a temperature of T3. This superheated steam drives an ideal turbine. Determine the heat per unit mass into the boiler. iv) If the turbine exit temperature is equal to the boiler inlet temperature (T4=T2), determine the efficiency of the steam turbine in part iii. (consider the type of process occurring as the steam passes over the turbine). Fluids Questions: Q1: The parabolic gate shown is 2m wide with c=0.25, D=2m and H=3m. Determine the magnitude and position of the net vertical force (due to the water) acting on the gate. Q2: a) Why does turbulent pipe flow have a fuller (more uniform-like) profile than laminar pipe flow? b) Perform the dimensional analysis that underlines the organization of the data in the Moody diagram. c) Oil with this density and velocity has this flow rate through this length and diameter of a pipe. The pipe slopes downward at this angle to the horizontal. Find the head loss and the pressure drop in the pipe. e = elasticity and is given for the cast iron pipe. Q3: a) Beginning with the integral momentum equation, determine an algebraic relationship between the axial pressure drop and the wall shear stress in fully developed pipe flow. b) Consider the propelling jet flow behind the rocket shown. Note that this vehicle has weight W, is flying vertically, is self-propelled, and has a no-slip surface meaning that there will be boundary layers along the rocket surface. the rocket's upward motion is at constant velocity. i) carefully sketch the profile of the streamwise (x component) of velocity, u, across the center of the jet, meaning plot u as a function of y across the symmetry plane of the jet. Do this at a point lose to the rocket so that the jet has not yet spread laterally. When doing so, please make sure that it appropriately reflects a momentum flux consistent with a positive constant velocity. ii) Is the net streamwise momentum flux through a horizontal cross-section of the jet positive, negative or zero? Please justify your answer using equations. Remember, Newton has three laws.

Closed system (Piston, insolated tank)

W = mflow(u2-u1) Esystem=0 thus, 0=mcat or 0=mcat(spec. 1)+mcat(spec. 2)

2013 Sem 2 Final

1) Please answer the following: a) Define a streamline b) Define incompressible flow considering density to be a function of space and time c) Define and provide a physical description of the Reynolds number d) Given the following scenario depicted in the figure, is the flow steady or unsteady? Provide a mathematically statement indicating why the flow is steady or unsteady. e) List the four assumptions that underline Bernoulli's equation. Out of the four, which is the key assumption? f) Provide a physical description of dynamic pressure? 2) a) A static pressure tap often consists of a machined tube that is mounted flush to the interior of a wind tunnel surface. Describe the effect of an imperfectly machined surface, as depicted below, on the pressure that would be measured by the tap. Draw streamlines and use equation(s) to validate your answer. b) A circular contraction is fitted with pitot tubes along its centerline as shown. Determine the height of the manometer column, h, assuming inviscid flow of air, for the scenario depicted in the figure. The following parameters are known. V1, P1, D1, D2, Density Air, Density Water. 3) Consider the flat plate shown below. Determine the drag force per unit width acting on the plate assuming a zero-pressure gradient boundary layer. Note that the dashed line is the edge of the boundary layer. the velocity profile at surface cd is given. 4) Consider the rigid gate, hinged at the point shown, openn if Y=0.8 m and row = 1000. H is the height of the water from the top of the gate to the free surface. Do not solve for H. a) Show that the resultant force of the water on the gate is equal to: Fr = 2(H+1)row*g*w, where w is width of the plate. 5) Water is transported for 500m in a 4cm horizontal pipe (k=0.046 mm). The flow rate is given. Calculate the pressure drop over the 500m length of pipe. The density of water is 1000 and the absolute viscosity is given. 6) Perform the dimensional analysis that underlies the organization of the Moody Diagram. 7) A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of P1 and P2. The mass flow rate of the steam is given. The quality of the steam at the turbine exit is 90 percent. a) Show and label the cycle on a T-s diagram with respect to the saturation lines, i.e., not any given information on the diagram and all processes. To receive full credit, sketch must be accurate with respect to the saturation lines. b) Determine the turbine inlet temperature so that the quality of the steam at the turbine exit is 90 percent. c) Determine the rate of heat input to the boiler if: v1 and h1 are given off of table. d) Determine the thermal efficiency of the cycle. 8) An ordinary egg can be approximated as 6 cm diameter sphere. the egg is initially at a uniform temperature of 10 degrees C and is dropped into boiling water at 100 C. The final temperature of the egg is 75 C. Treat the egg as an incompressible substance with constant specific heat. Note that the volume of a sphere is 4/3piR^3. a) The total amount of heat transferred to the egg. b) The entropy change of the egg. 9) The compression ratio of an air standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at P1, T1 (state 1), and 600 cm^3. The temperature at the end of the isentropic expansion is 800k (State 4). Assume constant specific heats at room temperature where Cv and Cp and R are given. As well as k = 1.4. a) Show and label the cycle on a P-v diagram, i.e, note any given information stated in the problem statement on the diagram by labelling all four state points and all processes that make up the otto cycle. b) Determine the mass contained in the system. c) Find the temperature and pressure at the beginning of the constant volume heat addition process. d) Find the temperature and pressure at the beginning of the isentropic expansion process. e) Determine the efficiency of the cycle.

Tutorial 8

1) A 30 degree reducing elbow is shown. The fluid is water. Evaluate the components of force that must be provided by the adjacent pipes to keep the elbow from moving. 2) A small round object is tested in a 1 m diameter wind tunnel. The pressure is uniform across sections 1 and 2. The upstream pressure is 20 mm H20 (gage), the downstream pressure is 10 mm H2O (gage), and the mean air speed is 10 m/s. The velocity profile at section 2 is linear; it varies from zero at tunnel centreline to a maximum at the tunnel wall. Calculate (a) the mass flow rate in the wind tunnel, (b) the maximum velocity at section 2, and (c) the drag of the object and its supporting vane. Neglect viscous resistance at the tunnel wall. 3) A conical spray head is shown. The fluid is water and the exit stream is uniform. Evaluate (a) the thickness of the spray sheet at 400 mm radius and (b) the axial force exerted by the spray head on the supply pipe. Assume a uniform velocity profile at the exit of the conical spray head. 4) Experimental measurements are made in a low-speed air jet to determine the drag force on a circular cylinder. Velocity measurements at two sections, where the pressure is uniform and equal, give the results shown. Evaluate the drag force on the cylinder, per unit width. 5) A plane nozzle discharges vertically downward to the atmosphere. The nozzle is supplied with a steady flow of water. A stationary, inclined, at plate, located beneath the nozzle, is struck by the water stream. The water stream divides and flows along the inclined plate; the two streams leaving the plate are of unequal thickness. Frictional effects are negligible in the nozzle and in the flow along the plate surface. Evaluate the minimum gauge pressure required at the nozzle inlet. Calculate the magnitude and direction of the force exerted by the water stream on the inclined plate. Sketch the pressure distribution along the surface of the plate. Explain why the pressure distribution is shaped the way you sketched it. 6) The boundary layer thickness, δ on a smooth at plate in an incompressible flow without pressure gradients depends on the free-stream speed, U, the fluid density ρ, the fluid viscosity μ, and the distance from the leading edge of the plate, x. Express these variables in dimensionless form. - dimensional analysis. 7) The mean velocity, u , for a turbulent flow in a pipe or boundary layer may be correlated using the wall shear stress, wτ , distance from the wall, y, and the fluid properties, ρ and μ . Use dimensional analysis to find one dimensionless parameter containing u and one containing y that are suitable for organizing experimental data. Show that the result may be written: = ντyufuu , where, 21= ρττ wu and ν= μ/ ρ. - dimensionless. 8) The speed V, of a free-surface gravity wave in deep water is a function of wavelength λ, depth D, density ρ, and acceleration of gravity g. Use dimensional analysis to find the functional dependence of V on the other variables. Express V in the simplest form possible. - dimensionless. 9) A continuous belt moving vertically through a bath of viscous liquid drags a layer of liquid, of thickness h, along with it. The volume flow rate of the liquid, Q, is assumed to depend on μ, ρ, g, h and V; where V is the belt speed. Apply dimensional analysis to predict the form of the dependence of Q on the other variables. - dimensionless. 10) Spin plays an important role in the right trajectory of golf, ping-pong, and tennis balls. Therefore, it is important to know the rate at which spin decreases for a ball in flight. The aerodynamic torque, T; acting on a ball in flight, is thought to depend on flight speed, V; air density, ρ; air viscosity, μ; ball diameter, D; spin rate (angular speed), ω; and diameter of the dimples on the ball, d. Determine the dimensionless parameters that result. - dimensional analysis

Tutorial 2

1) A 4 m by 5 m by 6 m room is to be heated by a base-board resistance heater. It is desired that the resistance heater be able to raise the air temperature in the room from 5 to 25 C within 11 minutes. Assuming no heat losses from the room and an atmospheric pressure of 100 kPa, determine the required power of the resistance heater assuming constant specific heats at room temperature. Ans: 3.28 kW 2) A mass of 15 kg of air in a piston-cylinder device is heated from 25 to 77 C by passing current through a resistance heater inside the cylinder. The pressure inside the cylinder is held constant at 300 kPa during the process, and a heat loss of 60 kJ occurs. Determine the electric energy supplied, in kWh using variable specific heats. Ans: 0.235 kWh. 3) A piston-cylinder device contains 1.5 kg of nitrogen initially at 100 kPa and 17 C. The nitrogen is now compressed slowly in a polytropic process during which PV1.3=constant until the volume is reduced by one-half. Determine the (a) work done and (b) the heat transfer for this process assuming constant specific heats at the average process temperature. Ans: (b) 24.7 kJ 4) Consider a 1000 W iron whose base plate is made of 0.5 cm thick aluminum alloy 2024-T6 (ρ=2770 kg/m3 and c = 875 J/kg/K). The base plate has a surface area of 0.03 m2. Initially, the iron is in thermal equilibrium with the ambient air at 22 C. Assuming 90% of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 200 C. Ans: 71.9 sec 5) An ordinary egg can be approximated as a 5.5 cm diameter sphere. The egg is initially at a uniform temperature of 8 C and is dropped into boiling water at 97 C. Taking the properties of the egg to be ρ=1020 kg/m3 and c = 3.32 kJ/kg/K, determine how much heat is transferred to the egg by the time the average temperature o f the egg rises to 80 C. Ans: 21.2 kJ 6) Carbon steel balls (ρ=7833 kg/m3 and c =0.465 kJ/kg/C) 8 mm in diameter are annealed by heating them first to 900 C in a furnace, and then allowing them to cool slowly to 100 C in ambient air at 35 C. If 2500 balls are to be annealed per hour, determine the total rate of heat transfer from the balls to the ambient air. Ans: 542 W 7) A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is 1.20 kg/m3 at the inlet and 0.95 kg/m3 at the exit, determine the percent increase in the velocity of the air as it flows through the dryer. Ans: 26.3% 8) An air compressor compresses 6 L of air at 120 kPa and 20 C to 1 MPa and 400 C. Determine the specific flow work required by the compressor. Ans: 109 kJ/kg 9) Air flows steadily in a pipe at 300 kPa, 77 C, and 25 m/s at a rate of 18 kg/min. Determine (a) the diameter of the pipe, (b) the rate of flow energy, (c) the rate of energy transport by mass, and (d) the error involved in part (c) if the kinetic energy is neglected. Ans: (a) 0.0715 m, (b) 30.14 kW, (c) 105.94 kW, (d) 0.09% 10) Air enters an adiabatic nozzle steadily at 300 kPa, 200 C, and 45 m/s and leaves at 100 kPa and 180 m/s. The inlet area of the nozzle is 110 cm2. Determine (a) the mass flow rate through the nozzle, (b) the exit temperature of the air, and (c) the exit area of the nozzle. Ans: (a) 1.09 kg/s, (b) 185 C, and (c) 79.9 cm2 11) Steam flows steadily through an adiabatic turbine. The inlet conditions of the steam are 6 MPa, 400 C, and 80 m/s and the exit conditions are 40 kPa, 92% quality, and 50 m/s. The mass flow rate of the steam is 20 kg/s. Determine (a) the change in kinetic energy, (b) the power output, and (c) the turbine inlet area. Ans: (a) 1.95 kJ/kg, (b) 14.6 MW, and (c) 0.0119 m2 12) An adiabatic capillary tube is used in some refrigeration systems to drop the pressure of the refrigerant from the condenser level to the evaporator level. The R-134a enters the capillary tube as a saturated liquid at 50 C and leaves at -20 C. Determine the quality of the refrigerant at the inlet of the evaporator. Ans: 0.46 13) A thin-walled double-pipe counter-flow heat exchanger is used to cool oil (C=2.20 kJ/kg/C) from 150 to 40 C at a rate of 2 kg/s by water (c = 4.18 kJ/kg/C) that enters at 22 C at a rate of 1.5 kg/s. Determine the rate of heat transfer in the heat exchanger and the exit temperature of the water. Ans: 484 kW and 99.2 C

Tutorial 3

1) A 600 MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40%. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why? Ans: 900 MW 2) An automobile engine consumes fuel at a rate of 28 L/h and delivers 60 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the efficiency of this engine. Ans: 21.9% 3) In 2001, the United States produced 51% of its electricity in the amount of 1.878 x 1012 kWh from coal fired power plants. Taking the average thermal efficiency to be 34%, determine the amount of thermal energy rejected by the coal-fired plants in the United States that year. Ans: 3.646 x 1012 kWh. 4) A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate of the heat transfer to the kitchen air. Ans: (a) 0.83 kW and (b) 110 kJ/min 5) A house that was heated by electric resistance heaters consumes 1200 kWh of electric energy in a winter month. If this house were heated instead by a heat pump that has an average COP of 2.4, determine how much money the home owner would have saved that month. Assume a price of 0.085$/kWh for electricity. Ans: $59.50 6) A cold canned drink is left in a warmer room where its temperature rises as a result of heat transfer. Is this a reversible process? Explain. 7) A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its temperature at -8 C. If the air surrounding the refrigerator is at 25 C, determine the minimum power input required for this refrigerator. Ans: 0.623 kW 8) A heat pump is used to maintain a house at 22 C by extracting heat from the outside air on a day when the outside air temperature is 2 C. The house is estimated to lose heat at a rate of 110,000 kJ/h, and the heat pump consumes 5 kW of electric power when running. Is this heat pump powerful enough to do the job?

Tutorial 7

1) A Pitot‐static tube is used to measure the speed of air at standard conditions at a point in a flow. To ensure that the flow may be assumed incompressible for calculations of engineering accuracy, the speed is to be maintained at 100 m/s or less. Determine the manometer deflection, in millimetres of water that corresponds to the maximum desirable speed. Assume density of air and water to be 1.23 and 1000 kg/m3. Ans: 627 mm 2) An open‐circuit wind tunnel draws in air from the atmosphere through a well‐contoured nozzle. In the test section, where the flow is straight and nearly uniform, a static‐pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that static pressure within the tunnel is 45 mm of water below atmospheric. Assume that the air is incompressible, and at 25 °C, 100 kPa (absolute). Calculate the air speed in the wind‐tunnel test section. Ans: 27.5 m/s 3) The water flow rate through the syphon is 0.02 m3/s, its temperature is 20 °C, and the pipe diameter is 50 mm. Compute the maximum allowable height, h, so that the pressure at point A is above the vapour pressure (pvap) of the water. Take pvap=2.33 kPa. Ans: 4.77 m 4) The inlet contraction and test section of a laboratory wind tunnel are shown. The air speed in the test section is U=22.5 m/s. A total‐head Pitot tube pointed upstream indicates that the stagnation pressure on the test section centreline is 6.0 mm of water below atmospheric. The corrected barometric pressure and temperature in the laboratory are 99.1 kPa (absolute) and 23 °C. Evaluate the dynamic pressure on the centreline of the wind tunnel test section. Compute the static pressure at the same point. Qualitatively compare the static pressure at the tunnel wall with that at the centreline. Explain why the two may not be identical. Ans: 291.1 Pa, -349.9 Pa. 5) The radial variation of velocity at the midsection of the 180o bend shown is given by rVθ = constant. The cross section of the bend is square. Assume that the velocity is not a function of the in-plane direction z. Derive an equation for the pressure difference between the outside and inside of the bend. Express your answer in terms of the mass flow rate, the fluid density, the geometric parameters R1 and R2, and the depth of the bend, h=(R2-R1). Ans: 6) Water flows from a large open reservoir and discharges through a circular, horizontal pipe fitted with a nozzle into air at atmospheric pressure, as shown in the figure. Subsequently, it strikes the ground a distance x upstream of the nozzle. Neglecting losses, find: (a) The velocity at the nozzle exit. Ans: (b) The velocity and pressure in the pipe near the nozzle, where the diameter of the pipe ceases to be 10 cm. Ans: (c) The distance x. Ans: (a) 7.67 m/s, (b) 25.6 kPa, and (c) 7.74 m 7) The velocity field in the region shown is given by kbjzaV ˆˆ += where a=10 s-1 and b=5 m/s. For the 1 m x 1 m triangular control volume (depth w=1 m perpendicular to the diagram), an element of area 1 may by represented by ( )kdyjdzw ˆˆ +− and an element of area 2 by jdzw ˆ . (a) Find an expression for 1AdV ⋅ . (b) Evaluate ∫ ⋅11AAdV . (c) Find an expression for 2AdV ⋅ (d) Find an expression for ( ) 2AdVV ⋅ . (e) Evaluate ( )∫ ⋅22AAdVV . 8) The area shown shaded is in a flow where the velocity field is given by kcjybixaV ˆˆˆ ++−= ; a=b=1 s-1 and c = 1 m/s. Write a vector expression for an element of the shaded area. Evaluate the integral ∫ ⋅ 1AdV and ( )∫ ⋅ 2AdVV over the shaded area. 9) Oil flows steadily in a thin layer down an inclined plane. The velocity profile is: −= 22yhygu μθρ sin . Express the mass flow rate per unit width in terms of ρ , μ, g, θ, and h.

Tutorial 4

1) A rigid tank contains an ideal gas at 40 C that is being stirred by a paddle wheel. The paddle wheel does 200 kJ of work on the ideal gas. It is observed that the temperature of the ideal gas remains constant during this process as a result of heat transfer between the system and the surroundings at 30 C. Determine the entropy change of the ideal gas. An: 0 2) An insulated piston-cylinder device contains 0.05 m3 of saturated R-134a vapor at 0.8 MPa. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.4 MPa. Determine (a) the final temperature in the cylinder, (b) the work done by the refrigerant. Ans: (a) 8.91 C and (b) 27.09 kJ 3) R-134a enters an adiabatic compressor as saturated vapor at 160 kPa at a rate of 2 m3/min and is compressed to a pressure of 900 kPa. Determine the minimum power that must be supplied to the compressor. Ans: 9.71 kW 4) A 25 kg iron block initially at 350 C is quenched in an insulated tank that contains 100 kg of water at 18 C. Assuming that the water vaporizes during the process condenses back in the tank, determine the total entropy change during this process. Ans: 4.08 kJ/K 5) An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 5 kmol of an ideal gas at 250 kPa and 40 C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Determine the total entropy change during this process. Ans: 28.81 kJ/K 6) Air at 800 kPa and 400 C enters a steady-flow nozzle with a low velocity and leaves at 100 kPa. If the air undergoes an adiabatic expansion process through the nozzle, what is the maximum velocity of the air at the nozzle exit? Ans: 778.5 m/s

Tutorial 5

1) Carnot Cycle. An air-standard cycle is executed in a closed system and is composed of the following four processes: 1-2 Isentropic compression from 100 kPa and 27 C to 1MPa 2-3 P=constant heat addition in the amount of 2800 kJ/kg 3-4 v=constant heat rejection to 100 kPa 4-1 P=constant heat rejection to the initial state a) Show the cycle on P-v and T-s diagrams b) Calculate the maximum temperature in the cycle (ans: 3365 K) c) Determine the thermal efficiency (ans: 21%) -- P-v and T-s graphs given for a closed system air standard cycle. 2) The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at 100 kPa, 35 C and 600 cm3. The temperature at the end of the isentropic expansion process is 800 K. Using specific heat values at room temperature, determine (a) the highest temperature and pressure in the cycle; (b) the amount of heat transferred in, kJ; (c) the thermal efficiency; and (d) the mean effective pressure (MEP). Ans: (a)1969 K and 6073 kPa, (b) 0.59 kJ, and (c) 59.3%, and (d) 652 kPa -- P-v and T-s graphs given. 3) A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of 3 MPa in the boiler and 30 kPa in the condenser and a turbine inlet temperature of 700 C. The boiler is sized to provide a steam flow of 50 kg/s. Determine the power produced by the turbine and consumed by the pump. Ans: 65 MW and 151.7 kW 4) A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of 15 MPa in the boiler and 100 kPa in the condenser. Saturated steam enters the turbine. Determine the work produced by the turbine, the heat transferred in the boiler, and thermal efficiency. Ans: 699.3 kJ/kg, 2177.8 kJ/kg, and 31.4%. 5) A commercial refrigerator with R-134a as the working fluid is used to keep the refrigerated space at -30 C by rejecting its waste heat to cooling water that enters the condenser at 18 C at a rate of 0.25 kg/s and leaves at 26 C. The refrigerant enters the condenser at 1.2 MPa and 65 C and leaves at 42 C. The inlet state of the compressor is 60 kPa and -34 C and the compressor is estimated to gain a net heat of 450 W from the surroundings. Determine (a) the quality of the refrigerant at the evaporator inlet, (b) the refrigeration load, (c) the COP of the refrigerator, and (d) the theoretical maximum refrigeration load for the same power input to the compressor. Ans: (a) 0.4795, (b) 5.4 kW, (c) 2.2, and (d) 12.72 kW. 6) A 10 kW cooling load is to be served by operating an ideal vapor-compression refrigeration cycle with its evaporator at 400 kPa and its condenser at 800 kPa. Calculate the refrigerant mass flow rate and the compressor power requirement when R-134a is used. Ans: 0.06247 kg/s and 0.896 kW.

Tutorial 6

1) The maximum blood pressure in the upper of arm of a healthy person is about 120 mmHg (gauge pressure). If a vertical tube open to the atmosphere is connected to the vein in the arm of the person, determine how high the blood will rise in the tube. Take the density of the blood and mercury (Hg) to be 1050 and 13600 kg/m3, respectively. Ans: 1.55 m 2) The water in a tank is pressurized by air, and the pressure is measured by a multi-fluid manometer as shown in the below figure. Determine the gage pressure of air in the tank if h1= 0.2 m, h2 = 0.3 m, and h3 = 0.46 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively. Ans: 56.9 kPa 3) A company's engineering department is evaluating a sophisticated $80,000 laser system to measure the difference in water level between two large tanks. It is important that small differences be measured accurately. You suggest that the job can be done with a $200 manometer arraignment. Oil less dense than water can be used to give a 10:1 amplification of meniscus movement; a small difference in level between the tanks will cause 10 times as much deflection in the oil levels in the manometer. Determine the specific gravity of the oil required for 10:1 amplification. Ans: 0.9 4) A triangular access port must be provided in the side of a form containing liquid concrete. Using the coordinates and dimensions shown, determine the resultant force that acts on the port and its point of application. The specific gravity of concrete is 2.5. Ans: 392.4 N, and 0.3 m from top. 5) A certain volume of water contained in the square vessel shown in the figure. Where the sealing edges of the inclined plate come into contact with the vessel walls, the reactive force normal and parallel to the wall is zero. (a) Find the magnitude and direction of the single force F required to hold the plate in position. The weight of the plate may be neglected. Ans: 2.6 N (b) Where does this force F act? Ans: 3.9 cm along the plate, starting at the top edge. (c) If the inclined plate is replaced by a horizontal one, find the relative position of the new plate if the force used to maintain its position has the same magnitude as before. The volume of the fluid remains constant. Ans: 10.6 cm 6) The two containers shown in the figure have both equal width w, and are filled with water to equal height h. Assume that the weight of the container is negligible. For the hydrostatic equation we know that the pressure at the bottom of the two tanks should be the same. If both have the same equal bottom area A, the force exerted on the bottom of the tanks by the water is the same, in spite of the difference in the weight of the water in the container. Resolve this apparent paradox, by showing that the net upward reactive force on each container is always equal to the weight of the liquid. 7) As water rises on the left side of the rectangular gate, the gate will open automatically. At what depth above the hinge will this occur? Neglect the mass of the gate. Ans: 2.598 m

Midterm Questions - Answers on ipad

1. You are working in a company making computer chips, and want to estimate the amount of heat dissipated when the chips are running. To achieve this, you insert a working computer chip in a duct and blow air using a fan with a flow rate of 30 m^3/hr. If the inlet and outlet temperatures are 20C and 30C respectively, what is the heat dissipated by the computer chip (in W)? (You can assume air to be an ideal gas with Cv = 0.718 kJ/kg K, Cp = 1.005 kJ/kg K, and R = 0.287 kJ/kg K.) 2. At home you are trying to boil water in your 2kW boiler. You fill the boiler with water at 20C to 1 liter mark, and put the switch on. i) How long will it take the water to start boiling? ii) If you forget that the boiler is on and leave it running (and unfortunately the boiler does not turn off automatically), how long will it take before the water completely boils off and the boiler will be in danger of catching fire? 3. Gas is flowing through a pipe of constant cross-section with a valve in between. You measure the temperature of the gas before and after the valve, and notice a change in temperature. i) Is this gas behaving like an ideal gas? ii) Why?

Isentropic Process (Open system) 1st law

Tds=du+pd(specificV) ==> ds=0 thus... 0=Cv*ln(t2/t1)+R*ln(specV2/specV1)

2016 Final

Thermodynamics: Q1: a) The figure shows an air-standard cycle on a P-v diagram. This is an ideal Diesel cycle. Describe the process from (all processes). b) Prove the thermal efficiency for the above cycle can be expressed as... Given... c) An engine operating on this cycle has a compression ratio of 18 and cut-off ratio of 1.719. It Takes in atmospheric air at this T1 and after combustion the temperature is T2. Determine mass specific heat input and the net work. d)For a Carnot heat engine operating at this combustion temperature and an exhaust temperature of 15C, what is the maximum efficiency possible? Q2: a) A nozzle is used to accelerate the exhaust gas of a turbine. The working fluid is air, inlet temperature is T1, inlet pressure is P1, and the outlet is atmospheric P2. The isentropic efficiency of the nozzle is 70%. Assuming the inlet velocity is negligible, determine the exit velocity of the air. b) Determine the heat loss through the nozzle walls. Given Cp Q3: a) To determine state of the steam in a pipe, some of the steam was condensed in a container, with the initial and final conditions accurately measured. The container was made of copper, weighed 850kg, and was originally filled with 8kg of liquid water. This whole system was measured to be at T1. After the steam was condensed in the container the new weight was 9.04kg and the new temperature was T2. The steam was originally this P1. To safely pass the steam into the container, it was first passed through an isenthalpic throttle device to reduce the pressure to atmospheric P2. Determine the state of the steam in the pipe. Q4: a) Calculate the specific volume of air at a gauge pressure of P1 and a Temperature of T1. R and row given. b) Write the Clausius Statement and the Kelvin-Planck statement of the 2nd law of thermodynamics. c)Consider a reversible heat exchanger transferring Q of energy from hot air within the heat exchanger to a cold lake of water. Calculate the entropy change of the lake. d) From the first law of thermodynamics, complete the following hypothetical heat engine cycles. e)From the second law, identify if any of the cycles from (d) is thermodynamically impossible. State the Carnot thermal efficiency for each cycle. Q5: All the same as Q3, 2013 Sem 1, From the thermo section. Fluid Mechanics: Q1: The drag force on a golf ball depends upon the speed of the ball, U, the rotation rate, the diameter, the dimple depth and so on. Use the second theorem to determine the non-dimensional parameters that the drag coefficient, Cd, depends upon. Q2: Water with a mass density and kinematic viscosity has a volume flow rate of a horizontal steel pipe that has a diameter of this. Find the head loss due to friction, and the static pressure drop in the pipe. Q3: Laminar flow of water develops in a circular tube upstream of the circular nozzle shown. The radius of the tube is R. The velocity profile of the tube before the nozzle is given by. More is given. Using this information, estimate the x-component force acting on the nozzle. (Adding up all the x-direction forces.

Open system (compressor)

Win = mflow(h2-h1)