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Population-growth dynamics are important in a variety of planning studies for areas such as transportation and water-resource engineering. One of the simplest models of such growth incorporates the assumption that the rate of change of the population p is proportional to the existing population at any time t:
where
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- The following table lists temperatures and specific volumes of water vapor at two pressures: p = 1.0 MPa p = 1.5 MPa T (°C) v(m³/kg) T (°C) v(m³/kg) 200 0.2060 200 0.1325 0.1483 0.1627 0.2275 240 280 240 280 0.2480 Data encountered in solving problems often do not fall exactly on the grid of values provided by property tables, and linear interpolation between adjacent table entries becomes necessary. Using the data provided here, estimate i. the specific volume at T = 240 °C, p = 1.25 MPa, in m³/kg the temperature at p = 1.5 MPa, v = 0.1555 m³/kg, in °C the specific volume at T = 220 °C, p = 1.4 MPa, in m³/kg ii. iii. 11.arrow_forwardQ: The flow through bridge opening is a function of hydraulic properties, fluid characteristics and channel geometries as follows: fi(ht, ho, B, Va, ha,hu, p,H,g) = 0 Where h, is the bridge deck thickness, h, is the bridge deck height, B is the bridge opening, Va is the downstream velocity, ha is the downstream water level, hu is the upstream water level, p is the mass density, u is the water dynamic viscosity and g is the gravitational acceleration. Use Buckingham n theorem to express the dimensionless terms through the abovementioned variables.arrow_forwardGiven: Consider an adiabatic steam turbine operating at steady-flow conditions. The known operating conditions are: Inlet conditions Exit (outlet) conditions Pressure (MPa) Temperature (°C) Velocity (m/s) Steam quality Mass flow rate (kg/s) Elevation (height) (m) 10 450 0.010 80.01 50.01 91.9 % 12.01 9.0 9.0 Required: Draw clear and consistent schematic for the problem representing the inlet and exit (outlet) conditions and label your schematic with the given conditions. Analyze the problem systematically using step-by-step CV energy and mass analyses, justify the equations, state your assumptions, and determine the following (circle your final answers): (a) The specific enthalpy values at inlet and exit of the turbine. (b) The mass flow rate of steam at exit. (c) The specific heat transfer. (d) The rate of change in the kinetic energy of the steam between inlet and exit. (e) The power output generated by the turbine. (f) The specific work output. (g) The specific volumes at inlet and…arrow_forward
- You have two toys with two different shapes; one is shaped like a solid cylinder and the other like a solid sphere. The two toys have the same volume (V(cylinder) = V(sphere)) and same radius (R(cylinder)=R(sphere)). They both generate the same total heat (q(cylinder)=q(sphere)) and are made from the same material (k(cylinder)=k(sphere)). a) Determine whether the sphere toy or the cylinder toy has the higher heat flux anywhere in the toy b) Calculate the ratio of the maximum heat fluxes between them Hint: Assume the ends of the cylinder toy to be perfectly insulated.arrow_forwardA system consisting of a power cycle and a heat pump cycle, each operating between hot and cold reservoirs whose temperature are 500 K and 300 K, respectively. All energy transfers are positive in the directions of the arrows. The accompanying table provides two sets of steady-state data, in kW. For each set of data, determine if the system is operating in accord with the first and second laws of thermodynamics. Power cycle QHQc W cycle (a) 60 40 20 (b) 120 80 40 Heat pump cycle QHQ'cW'cycle 60 20 80 20 80 100 Power cycle- Hot reservoir, TH= 500 K O'H J Qc o'c Cold reservoir, Te= 300 K W cycle Heat pumparrow_forward3G 4G 9:1V docs.google.com/forms :D Mechanics / صباحي *مطلوب Untitled Section F1 F2 a F3 B. d b C F4 D Consider the following values: - F5 a = 13 m; b = 8 m; c = 10 m; d = 5 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30° , 0 = 60° B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) 19.2 kN.m b) 32.7 kN.m c) 44.6 kN.m d) 29.8 kN.m e) 14.1 kN.m f) 21.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 98.8 kN.m b) 23.7 kN.m c) 81.6 kN.m d) 65.6 kN.m e) 91.1 kN.m f) 74.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 125.7 kN.m b) 111.1 kN.m c) 74.6 kN.m d) 109.4 kN.m e) 24.1 kN.m f) 65.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 17.8 kN.m b) 88.7 kN.m c) 10.6 kN.m d) 59.5 kN.m e) 29.1 kN.m f) 70.1 kN.m 5] What is the moment of the force F2 about point E? Activate V ) 21.3 kN.m Go to Setting…arrow_forward
- Thermodynamics Answer the following problem with complete solutions. Write legibly A gas goes through the following thermodynamic processes: A to B: constant-temperature compression; B to C: constant-volume cooling; C to A: constant-pressure expansion. The pressure and volume at state C are 1.4 bars and 0.028 m^3, respectively. The net work during the C-to-A process is 10.5 kJ. What net work is derived from one complete A-B-C cycle?arrow_forward2. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C3Q(t)- a(T – T) dt %3D | where T is the slab temperature in °R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/ºR, Ts = 530°R and a = 5x10-8 Btu/h-°R*. %3D %3D %3D (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.arrow_forwardQ\. The first law of thermodynamics involves three main components, if we know the behavior of two components, estimate the behavior of the third component. ( Conclusion ) : a. If heat is added to the system, then the internal energy of the system increases. ..... .. b. If heat leaves the system, then the internal energy of the system decreases .... c. If the work is done by the system, then the internal energy of the system decreases ... ....... d. If the work is done on the system, then the internal energy of the system increases.. .......arrow_forward
- within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of A gas three processes: Process 1-2: Constant volume, V = 0.06 m², U2 - U, = 40.4 kJ Process 2-3: Expansion with PV = constant, U3 - U2= 0 Process 3-1: Constant pressure, P =3 bar, W31 = (-20) kJ There are no significant changes in kinetic or potential energy. %3D Identify the process on a sketch of p-V diagram plotted for the cycle. Formulate the expression for heat transfer for process 2-3 and process 3-1. (Hint: Apply first law of thermodynamics for closed systems) (a) (b) (c) Solve to find the net-work for the cycle and heat transfer for the process 2-3 and Heat transfer for process 3-1, in kJ Identify if the above system executes a power cycle or a refrigeration cycle. Give (d) reason.arrow_forward1. Use total differential to estimate the change: in calculating the value of f (x, y, z) = 3x?yz³ when (x, y, z) change from A (-1, 2, 1) to B (-0.998, 2.003, 0.999). in the volume, V, of a pyramid with square base when its height, h, is increased from 2 to 2.2m and its base dimension, x, is decreased from 1 to 0.9 m. The volume (a) (b) of pyramid is given by V = x²h. 3arrow_forward3. Laws on Conservation. Using the energy model sketched below plus concepts of energy conservation, consider the impact of a dirty war on the global energy. To start, assume that the impact of this war has created an atmosphere that absorbs 75% of the incoming sunlight, while the albedo is reduced to nearly 20%. Let's assume that Earth's ability to reflect incoming solar radiation is negligible. The Earth's surface radiates 240 W/m2, all of which is absorbed by the atmosphere. Assuming that Earth can be modeled as a blackbody emitter and incoming/outgoing energy as shown in the schematic, find the following quantities: a) The "nuclear winter" temperature [°C] of the surface of the Earth b) X, the rate [W/m²] at which radiation is emitted from the atmosphere to space c) Y, the rate [W/m²] of absorption of short-wavelength solar radiation at the Earth's surface d) Z, the rate [W/m2] at which the atmosphere radiates energy to the Earth's surface Incoming 342 W/m² Reflected to space X…arrow_forward
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