Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant. This velocity potential is commonly used to describe flow impinging upon a plate. Derive an equation for dP/dy, the pressure gradient in the y-direction, if the fluid has density, rho.

A quality mixture of water is contained in a piston cylinder system at a pressure of 3 bar. The initial volume of the system is 3 m3, and saturated liquid occupies 0.3 m3. Heat is added to the system and the volume is allowed to triple before a stop is reached. The final state of the system is at pressure of 30 bar. If the external pressure is 1 bar determine the followng: (a) The amount of heat added to the system; and (b) the amound of work performed by the system.

A 1 036-kg satellite orbits the Earth at a constant altitude of 110-km. (a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 194 km? MJ? (b) What is the change in the system's kinetic energy? MJ? (c) What is the change in the system's potential energy? MJ?

Consider 0.8 kg of N₂ at 300 K, 1 bar contained in a rigid tank connected by a valve to another rigid tank holding 0.3 kg of CO₂ at 300 K, 1 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 290 K.
Determine:
(a) the volume of each tank, in m³.
(b) the final pressure, in bar.
(c) the magnitude of the heat transfer to or from the gases during the process, in kJ.
(d) the entropy change of each gas and of the overall system, in kJ/K.

Suppose that the gears in Figure 15.28 (page 669 of textbook) are identical, each having an 8-in diameter, 80 teeth and 20° pressure angle. Assume that their finish and accuracy correspond to about the best that is commercially obtainable with a shaping cutter. (a). Which of the gears is the most vulnerable to tooth-bending fatigue failure? Why? (b). If the motor rotates 1200 rpm, determine the proper values for V, P, p, Kv, and J.

(Figure Numbers are from Juvinall and Marshek, Fifth Edition)

The accessory drive unit of a large aircraft engine involves an identical pair of 20° full-depth spur gears. The gears have 50 teeth and rotate together at 5000 rpm. The diametral pitch is 12 and the face width 1.5 in. The gears are made of alloy steel, casehardened to 62Rc (680 Bhn). Although the case extends throughout the fillet, it is conservatively decided to use the core hardness of 500 Bhn for calculating bending fatigue strength. The tooth profiles are finished with a fine-grinding operation that gives a degree of precision justifying the use of curve A of Figure 15.24 and the assumption that teeth share the load. The loading involves only very mild shock, justifying the use of Ko = 1.1.

(a). Estimate the horsepower that can be transmitted with 99% reliability, based on tooth bending fatigue.

(b). Estimate the horsepower that can be transmitted for 109 cycles with 90% reliability, based on surface fatigue.

Briefly describe and explain the driving force for the electrochemical crevice corrosion happened in the riveted structure in water, as shown in Figure 17.16 in Callister 9th Ed. Book, use Nernst equation as you see necessary.

Use MATLAB DSOLVE to solve the folloing ODE and plot it:

300x'' + 60x' + 6840 = f(t)

Write a MATLAB function that uses my_sine(x,n) to plot the approximation of the sinefunction from−3π/2 to 3π/2 with increments equal to Δx,where Δx and n(the number ofterms used in the series approximation) should be input arguments of the function andshould be specified by the user.

What is diametral pitch, and why is it an important parameter in a gear mesh?

For the factors / conditions listed, select those that tend to alleviate creep deformation for a metal sample with a random polycrystalline microstructure.

a. Raise the service temperature that the part is exposed to.

b. Substitute the metal for one with a higher melting point.

c. Decrease the applied stress on the metal part.

d. Decrease the average grain size of the metal part.

e. Increase the grain count of the metal part (for a fixed volume).

f. Apply an insulative (non-structural) ceramic coating to the part.

g. Switch to a single crystal or textured polycrystalline microstructure.

Solution for problem one (P1) below:

ME 311 Thermodynamics I 1 Homework 5 Problem from Cengel and Boles 8th Edition

P1) Carbon dioxide flows steadily in a pipe at 3000 kPa, 31 °C, and at a rate of 1.5 kg/s.

Determine the density of carbon dioxide using

(a) the ideal gas law

and

(b) the compressibility chart.

Liquid mercury at 0.5 kg/s is to be heated from 300 to
400 K by passing it through a 50-mm-diameter tube
whose surface is maintained at 450 K. Calculate the
required tube length by using an appropriate liquid
metal convection heat transfer correlation. Compare
your result with that which would have been obtained
by using a correlation appropriate for Pr>= 0.7.

(A) Derive Bernoulli's Equation from Pressure, Kinetic Energy and Potential Energy

(B) Express Bernoulli's equation:

- Per unit mass

-Per unit volume

- In terms of heads

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