Please prove that in homogeneous nucleation of solidification the critical radius and activation energy are ?? ? = (? 2?????? ????? ) ( 1 ??? ) and ??? ? = ( 16???? 3???? 2 3????? 2 ) 1 ???2 , respectively, in which ? is the surface free energy, Tm is the melting temperature, ?T is the degree of supercooling (Tm - T), and ?Hf is the latent heat of fusion.

Thermodynamics

1. Correct Answer: 32.29 ± 4%

A 1.4 m3 tank fills through inlet A while supplying water through outlets B and C at the rates given below. Determine how long (minutes) it will take until the tank is full if initially the tank contains 277 kg of water. The flow rates are given in kg/min where "t" is in minutes.

All flows are at 20 C.

Mass flow rate of A = 3.5 + 2.1*t

Mass flow rate of B = 1.5

Mass flow rate of C = 1.2

2.

Correct Answer: -99.69 ± 1%

Air enters a compressor at 152 kPa and 290 K and exits at a temperature of 507.6 K. Determine the power (kW) for the compressor if the inlet volumetric flow rate is 0.244 m3 /s and the heat transfer through the shell of the compressor to the surroundings is 1.35 kW. Use the ideal gas tables (variable specific heats).

3.

(ans:19.6)

A well-insulated, full, water tank containing 198 kg of water initially at 44^oC is being supplied with 15.6^oC water at a rate of 4 kg/min. Water is exiting the tank at the same flow rate so that the mass of water in the tank remains constant. Circulation in the tank keeps the water at a uniform temperature. The specific heat of the water is given as C = 4.2 kJ/kg-K. Determine the time (minutes) at which the water temperature drops to 34.7^oC.

Note: The energy of water in the tank is given as: E = m_cv*C*T

The solution for an equation of the form: a*dT/dt + T +b = 0     is

T(t) = k1*exp(-t/a) + k2

For this problem, the given constraints are:

T(t=0) = T_initial

T(t=infinity) = T_inlet

Hint: Use the given constraints to determine the constants k1 and k2

This is problem 7-6 from El-Wakil’s Powerplant Technology book -- a wet cooling tower receives 1.5x10⁶ lb_m/min of condenser water at 96 degFahrenheit, and 1.25x10⁶ lb_m/min of air at 1 standard atmosphere, 62 degFahrenheit, and 50 percent relative humidity. The air leaves saturated at 82 degFahrenheit. Calculate (a) the exit water temperature, in degrees Fahrenheit, and (b) the percent condenser cooling water makeup due to evaporation.

This is problem 7-5 from El-Wakil’s Powerplant Technology book -- an included-draft cooling tower cools 90,000 gallons per minute of water from 84 to 68 degFahrenheit. Air at 29.75 inHg absolute pressure, 70 degFahrenheit dry bulb and 60 degFahrenheit wet bulb, enters the tower and leaves saturated at 80 degFahrenheit. Find (a) the volume flow rate of air, in cubic feet per minute, and (b) the makeup water required, in pound mass per hour.

Compare the three types of lubrication systems for plain bearings using sketches and Bearing Parameter/ Stribeck Curve.

What are Fixed side and Floating side bearing arrangement? Explain their applications with sketches.

An airfoil profile to be used on a wind turbine blade is tested in a wind tunnel. The prototype (full-scale) airfoil section has a chord length of 2m and moves at 50 m/s relative to the wind, the wind tunnel model has a chord length of 0.4m. The temperature for the model test is the same as for prototype operation.

(a) What criterion should be used to obtain dynamic similarity in the experiment? (Write out the criterion in an equation.) (b) What velocity should the wind tunnel be operated at to have dynamic similarity for the scale model? (assuming tests at atmospheric pressure.) (c) The wind tunnel available for this test can only be operated at 100 m/s, but it can also be pressurized. What pressure should be used in the wind tunnel to have dynamic similarity? (Assume the air behaves like an ideal gas.)

Along, square, electrical heating element standing on a corner with one side of the square heating element being 25mm, thermal conductivity k = 240 W/m ? K, density ñ = 2700 kg/m3, and specific heat cp = 900 J/kg ? K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 30°C and 10 m/s, respectively.

(a) Neglecting radiation, estimate the steady-state surface temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1000 W/m. ?

(b) If the heater is activated from an initial temperature of 30°C, estimate the time required for the surface temperature to come within 20°C of its steady-state value. ?

what are the differences of all these cooling load calculation methods? What are the full name of these methods and the strength and limitation of these approaches?

a)HB method

b)CLTD method

c)RTS method

Answer the following questions:

1. What is PFCU functions and State the advantage and Disadvantages of PFCU?

2. What do you understand about fly by wire?

Answer the questions in paragraph form.

Copied answer will get 60%

A manufacturer wishes to choose between two ceramics for a certain application. Data for the two ceramics tested under identical conditions were as follows:

The service conditions are geometrically identical to the test conditions and impose a stress of 300 MPa. By constructing Weibull graphs with S = 1/2 for mean fracture stress or any other method, decide which ceramic will be more reliable and compare the probabilities of failure at 300 MPa. At what stress would the two ceramics give equal performance?

Answer: Stress for equal performance = 349 MPa

Use the Navier-Stokes equations to show how pressure varies with x, y and z in a hydrostatic fluid.

A velocity field is described by the following equations: ?? = 10y/(x^2 +y^2) , ?? = -10x/(x^2+y^2) , and w=0 (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m3 , and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.

For the case of incompressible flow, write all 3 components of the Navier-Stokes equations and the complete form of the differential continuity equation.