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Moist air exists under conditions of 24°C db temperature and relative humidity 50 percent. The pressure is 101.3 kPa. Using the psychrometric chart, determine (i) the wet-bulb temperature, (ii) the dew-point, (iii) the humidity ratio, (iv) the enthalpy, and (v) the specific volume. Please show all the steps on the psychrometric chart.

Water reaches the wellhead of a single flash geothermal plant at 2.0 MPa, 210°C, and 22.5 kg/s. The water is flashed to 800 kPa. The vapor portion goes through a turbine with an isentropic efficiency of 90% and the condenser pressure is 10 kPa. Both pumps have efficiencies of 68% and the injection well pressure is 4.0 MPa. Determine: a. The power produced by the turbine, in kW b. The total pump power input, in kW. c. The rate of heat input in the earth or "boiler," in kW d. The overall efficiency

Module Code: MECH267001 SECTION A (50%) ? : Section A and Section B. 1. The final treatment of a novel polymer material requires holding the material above a temperature of 100°C for 5 minutes. This is achieved by suspending the polymer rod in a moving airstream that has a free air temperature of 150°C. The rod is held vertically, with the air stream moving horizontally. There are two sections The air velocity is 10m/s. The polymer rod has a diameter of 5cm and a length of 2m. Physical properties are shown in the table below. Material Air Air Property Density Specific heat capacity Polymer Thermal conductivity Polymer Specific heat capacity Polymer Density a) Sketch a suitable arrangement including a heating element. Value 1.16 kg/m³ 1006 J/kgK 11.0 W/mK 1200 J/kgK 1500 kg/m³ [3 marks] b) Using a value of the heat transfer coefficient of 80 W/m°K, and taking care to justify the approach you adopt, calculate the total time required to heat- treat the sample. i. ii. [6 marks] c) Further study of the novel polymer suggests that the polymer should remain below a temperature of 135°C to minimise reduction in the structural strength of the polymer. Demonstrate whether this criterion is met or not. [6 marks] d) One of the engineering team working with you on this project proposes a reduction in the heated free air temperature to 110°C to save energy. Assess this proposal in terms of: Page 2 of 15 The total cycle time for treatment of one rod The relative energy cost when compared to the original condition of using heated air at 150°C. Note that the air is heated from an ambient temperature of 20°C and assume all properties of the gas (except the free air temperature) remain constant. Consequently, provide an informed response to the engineer's suggestion. [10 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 2. Biogas is produced through anaerobic digestion of waste food. It has a composition of 80% methane and 20% carbon dioxide (by volume). The biogas is burned stoichiometrically in air (of composition 21% oxygen and 79% nitrogen by volume) with the flame used to heat a tube containing flowing water. The biogas has an initial temperature of 25°C and the combustion gases exit from the burner at 102°C. a) Write a stoichiometric equation for the combustion of methane in air, and then adapt it for burning the biogas in air, assuming products are carbon dioxide, water, nitrogen only. [5 marks] b) Calculate the mass flowrate of air for the complete combustion of 1 kg/s of biogas. Molecular weights of appropriate elements and compounds can be found on page 9. [5 marks] c) From considering the combustion of the biogas, show that an energy transfer takes place of 35.5 kJ per kg of biogas that is burned. [5 marks] d) After heating, in the burner, the hot water passes through a shell and tube heat exchanger and is used to heat an oil flow. The water from the shell and tube heat exchanger passes directly back to the burner at 20°C. The flowrate of biogas into the combustor is 50 kg/s. Water enters the burner with a flow rate of 7kg/s at a temperature of 20?C. Oil enters the shell and tube heat exchanger at a flow rate of 37.5 kg/s at a temperature of -5°C. i. ii. Sketch the arrangement Calculate the surface area of the heat exchanger, given an overall heat transfer coefficient of 750 W/m² K Take heat capacities as water 4.2 kJ/kgK oil 1.6 kJ/kgK Page 3 of 15 [10 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 SECTION B (50%) Water with a density of 1000 kg/m³ and dynamic viscosity of 1.0 x 10-³ Pa.s flows under gravity from a reservoir through a galvanized iron pipe with an equivalent roughness of 0.15mm at a flow rate of 600 litres per minute into the local atmosphere. The flow path comprises a sharp edged entrance from the reservoir into the pipe (loss factor (K?) of 0.5, based on average outlet velocity), a 4m horizontal length of the galvanized pipe of 80mm internal diameter, a fully open gate valve (KL = 0.15, based on average inlet velocity) and a 6m horizontal length of the galvanised pipe of 40mm internal diameter. There is no fitting or restriction at the outlet of the pipe into the local atmosphere and so no additional minor head loss. The liquid surface of the reservoir is exposed to the local atmosphere. a) 3. Sketch the system and calculate the mean velocity and the Reynolds number of the flow in the two different pipe sections and state whether the flow is laminar or turbulent in each. [6 marks] Determine the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. Note, the major and minor head losses can be summed in this flow path, like resistors in series, and the general equation for energy conservation in pipes compares the pressures at the inlet and outlet of the system only. [10 marks] c) The gate valve is replaced by a fully open globe valve (K? = 10, based on average inlet velocity). Determine the change in the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. b) d) Provide an explanation for the result obtained in part c). Page 4 of 15 [4 marks] [5 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 4. A new design of telecommunications tower is modelled as a 5m diameter perfectly smooth sphere on top of a vertical perfectly smooth cylinder, 30m high and 2m diameter. It has to withstand an aerodynamic force imposed by a 100 km/h wind. For air take the density to be 1.20 kg/m³ and the kinematic viscosity to be 1.5 x 10-5 m²/s. a) b) c) d) Estimate at 100km/h the aerodynamic drag force acting on the sphere. [7 marks] Estimate at 100km/h the aerodynamic drag force acting on the cylinder. [7 marks] Estimate the bending moment at the base of the tower. [5 marks] Discuss why these results should only be regarded as an estimate of the influence of drag on the real tower. Page 5 of 15 [6 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 Biot number, Bi = Nusselt number, Nux Prandtl number, Pr = Composite cylinders ? where v is kinematic viscosity Stefan-Boltzmann constant, o= 56.7 x 10 kWm -12 n-² K-4 Newton's Law of Cooling Composite plain walls One dimensional heat transfer Fourier's Law Tt - To To - Too hv KA = = exp V Rex hx k Rex ReL Page 6 of 15 FORMULA SHEET Heat Transfer A - [ht] = exp Forced Convection over a flat plate ?500 000 Nux > 500 000 Nux = 500 000 NUL Thermal diffusivity, a = Transient heat transfer: Lumped heat capacity system (Bi < 0.1) Stanton number, = = Grashof number, G? where t = is the time constant of the system. cpV hA Q = ?A = ?kA Heat diffusion equation in cartesian coordinates k ? 1/2 (²017) = ( ² ( ² ) + 2, (^²7) (?)={ (x + ²? (^ ²) + ²/? (^²} + a? (KZT) k k ?g ?? ??, ?z ?z. St = where v is kinematic viscosity No. of transfer units, NTU dT dx • (-/-) Q = -hA(T? - Tw) (Tb - Ta) {? (A) + ? (4)} = 0.332 Pr0.333 Re0.5 0.0296 Pr0.333 Re0.8 0.037 Pr0.333 Re8 k pcp h pcpu g??Td3 v² (Tb - Ta) (In(ro/ri)` {? (²n (7/²)) + ? (1/²/A)} 2?lk = = UA Cmin Nu Re Pr Turn the page over

The Earth spins on its axis once every 24 hours. The radius of the Earth is 6,370,000m. Calculate the speed of an object that is at rest on the Earth's surface at a latitude of 20°.

An airstream of speed 160 m/s and temperature 3000 K travels on the inside of a 30 cm I.D. steel tube whose wall thickness is 2.5 mm. On the outside of the tube, water coolant flows coaxially in an annular space 6.1 mm thick. The coolant velocity is 10 m/s, and it has a local temperature of 15°C. Both flows are approximately fully developed. The pressure of the airstream is around 140 kPa. Estimate the maximum wall temperature of the tube.

In Fig. 33-41, a beam of unpolarized light, with intensity43 W/m , is sent into a system of two polarizing sheets with polarizing directions at angles 01 = 70° and 02 = 90° to they axis. What is the intensity of the light transmitted by the system?

2 Consider a current I = 1 A flowing in the positive y direet ion through a rectan-gular conductor as shown in Figure Q2. The conductor has length L = 4 cm,width a = 1 cm, and height b = 0.1 cm. Suppose that a magnetic field B = Bàpermeates uniformly the conductor, with B = 10 T. Briefly explain why a potential difference AV = V - V, arises at the equilibrium between the left and right sides of the conductor, as shown in the figure. Starting from J = n, q?a and considering the Lorentz force, derive the force acting on the carriers responsible for the current I function of the relevant parameters a, b, I, B and the carrier density ng: Use such result to demonstrate that the carriers responsible for the current in the metal are negatively charged if the potential difference measured between the left and the right facets of the conductor is positive:deltaV = V - V, > 0. To this end, consider that V- V, is positive if the carriers accumulated on the right side have a negative charge. Suppose that the carriers are electrons ( -1.6x 10-19 C) and thatAV = V,- V, = 22 x 10-6 V. Caleulate the carrier density ngmetal, expressed in units of m .%3Din the Hence or otherwise, suppose that the current I is induced by a generator keeping the potential difference between the input and and output facets (sand S) at a constant value DElta Vt/0=0.002 V what is the resistivity p of the conductor

S.6 The plane boundary defined by z = 0 separates air from a block of iron. IfB = 4x – 6? + 82 in air (z > 0), find B, in iron (z < 0), given that u = 5000 H :No surface current is found on the boundary.

3.14 As noted in Section 3.1, the power in a light beam is proportional to the square of its electric field, and the electric field for a beam traveling in an attenuating medium can be given by Eq. (3.8). The attenuation coefficient in that equation determines the loss. On the other hand, we more frequently discuss the loss in terms of decibels per kilometer.Show that the power change in dB/km and the attenuation coefficient a are related b yy = -8.685a, where a is given in the units km.

Academic Honesty Pledge I understand that students are expected to refrain from all forms of academic dishonesty as defined in the college policies and as explained and defined by college policies and procedures and directions from teachers or other college personnel. By signing this cover page I am confirming that the work presented here, including all the figures, tables, calculations, data and text, is mine and mine only. I hereby state that all work submitted in this report is mine and solely mine. Signature: Note: Only reports that include a signed cover sheet will be graded. 1 2 3 Objective of Evaluation Report presentation (must be typed) Observation and Analysis (Part I) Observation and Analysis (Part II) Total HCT PHY1203 PHYSICS II LAB 1 202210 Max. marks 5 65 30 100 Marks obtained 1 Objective: To determine the specific heat of a solid body. Background The specific heat of a substance is the quantity of heat necessary to raise a unit mass of the substance by a unit temperature difference. When a heat interchange takes place between two bodies initially at different temperatures, the quantity of heat lost by the hot body is equal to that gained by the cold body, and some intermediate equilibrium temperature is finally reached. This is true provided no heat is gained from or lost to the surroundings. In this case, we can apply the principle of conservation of energy. Heat lost by hot body = Heat gained by cold body Experimental setup and theory In this experiment, a solid sample of known mass (ml) is heated to a certain temperature near the boiling point of water (Ts). It is then quickly transferred to a calorimeter of known mass (mcal), which contains cold water of known temperature (Tw) and mass (mw). It should be assumed that temperature of calorimeter is the same as (Tw). When the solid sample and the calorimeter (including water) come to thermal equilibrium, the final temperature (T;) is noted. It is assumed that the heat loss to the thermometer is negligible and if the heat exchange with the environment is kept small, then the heat lost by the solid sample (-Qsol) is equal to the total heat gained by the calorimeter (Qcal) and the water (Qw). Thus, applying the principle of conservation of energy to our isolated system (the net heat gained by the system is zero): Q=mcAT Qw-Q sol+Qcal=0 W mwcw T-Tw-m sol sol Tsol-Tf+m calcat (T-Tw=0 W f W C sol mwcw Tf-Tw+mcal Ccal Tf-Tw W msol (Tsol-Tr If we ignore the heat gained by the calorimeter, the equation becomes: mw Cw Tf - Tw W C sol m sol T % error= sol Calculate the percentage error in experimental value - accepted value accepted value HCT PHY1203 PHYSICS II LAB 1 202210 × 100 (3) (1) (2) (5) (4) (6) 2 Apparatus: 0 0 0 0 0 000 Calorimeter Stirrer Thermometer Hotplate Metal sample Water Weighing scale Measuring cylinder Figure 1: Simulation of the specific heat capacity Experiment Experiment Step 5 300mL 200mL Run Demonstration 100ml LIQUIDS SOLIDS SOLUTIONS Unknown metal I Procedure and implementation 1. Follow the simulation link given below. Mass (g) Temp (°C) Show specific heat (J/g°C) 0.388 Overview Learning Outcomes Experiment Please choose one: HCT PHY1203 PHYSICS II LAB 1 202210 12.5 100. 20.92°C Run Experiment -600mL 500mL 400mL 300mL 200mL 100mL LIQUIDS Water - H?O SOLIDS SOLUTIONS Mass (g) Temp (°C) XShow specific heat (J/g°C) 4.184 https://media.pearsoncmg.com/bc/bc_Omedia _chem/chem_sim/calorimetry/Calor.php 2. Click experiment and then run the experiment, as shown below. Chemistry Simulations: Calorimetry Click here 100. 20.0 RUN EXPERIMENT Then click here Show graph view Show microscopic view Replay 3. Then click on the solid and choose unknown metal 1. Also fix the mass of the solid (ms) and the temperature of the solid (Tl) to record in the table 1. This temperature is the initial temperature of the solid (Tsol). 4. Then click next to choose the liquid. Select water and fix the mass of the water (mw). Reset 3 5. Record the fixed initial temperature of the water (Tw) at around 20 °C. 6. Now click 'next' to run the experiment and wait until the system reaches to thermal equilibrium and record this temperature as the final temperature (T?) Observation and Analysis (Part I) (20 marks) Enter your measurements into the following table. Remember to enter the correct units. Mass (…............ ..) Specific Heat c (J/g °C) Initial temperature T (…….........…... ..) Final temperature (............ ..) Metal Water 4.186 Table 1: Data collected with the metal, water and calorimeter. HCT PHY1203 PHYSICS II LAB 1 202210 1) Insert the screen shot of the system when it reaches the thermal equilibrium. marks) (5 2) Using equation (5), (considering only the water and metal), calculate the specific heat of the metal (ignore the heat loss due to calorimetry). You must show sufficient working to score full credit. (10 marks) 4 3) Determine which of the metals listed in the table (in appendix) has been used in this experiment. Give a justification for your choice. (5 marks) 4) Using equation (6), calculate the percentage error between the calculated value (in table 1 above) and the theoretical value of the specific heat of the solid metal used (refer to appendix). (5 marks) 5) Now use the same simulation link above and choose unknown metal 2 to enter your measurements into the following table. Remember to enter the correct units. marks) (20 Mass (…............ ..) Specific Heat c (J/g °C) Initial temperature T (.............….....) Final temperature (…....….... HCT PHY1203 PHYSICS II LAB 1 202210 .) Metal Water 4.186 5