Calculate the fatigue stress concentration for a steel filleted shaft that is loaded axially.

Given Data:

Sut = 690 MPa

D (for larger cross-section) = 54 mm

d (for smaller cross-section) = 40 mm

r(fillet radius) = 3 mm

A vertical composite rod made up from a solid part connected in series with a hollow part
is fixed at its top end and has a collar attached at the lower end.
The following data is average

 solid rod length 320 mm;
 solid rod diameter 50 mm;
 hollow rod length 280 mm;
 hollow rod diameters 50 mm and 28 mm;

Draw a neat sketch of the arrangement and for an applied load of 1,5 kN calculate:

4.1 the maximum stress and resilience of the compound rod, when the weight
is applied suddenly without impact; (7)

4.2 the maximum stress in the compound rod, when the weight is allowed
to fall freely through a height h = 20 mm (7)
Assume E = 200 GPa.

The flowing formulae may be used:
1 2
2 2
;
2
;
2
AL U U U
E
U
E
L
AL w h
E
    





 
  

Water at a mean temperature of 80 °C and a mean velocity of 0.15 m/s flows inside a 2.5 cm ID and 3.3 cm OD, copper tube. Atmospheric air at 20 °C and a velocity of 10 m/s flows across the tube. Calculate the overall heat transfer coefficient based on the outer surface and the rate of heat loss per 1 m length of the tube for inside and outside fouling factor 0.00018 m2. What is the percent reduction in the overall heat transfer coefficient due to the dirty conditions in the heat exchanger? (Assume that the value the waterside heat transfer coefficient is 250 W/m2.°C and that of the airside is 75 W/m2.°C.

A 50-tooth spur gear is in mesh with a 27-tooth pinion. The gears have a diametral pitch of 5 teeth/in, and a pressure angle of φ = 25°. The gears transmit 80 HP at 4000 pinion rpm.

Find the factors of safety against bending and surface failure. Assume that the teeth are full depth, Qv = 10, a through hardened to 360 HB steel gear, and a carburized and case hardened steel pinion. Assume a face width of 3.0 in, a 99.9% reliability, and a life of 9 5 10 × cycles.

A pair of helical gears is used with the following properties: 14.5 degree normal pressure angle, 45 degree helix angle, diametral pitch of 8 teeth/in, 1.5-in face width, and normal diametral pitch of 11.31 teeth/in. The pinion has 12 teeth and a 1.5in pitch diameter, and the gear has 32 teeth and a 4.0 in pitch diameter. Both gears have full-depth teeth. If a right-hand pinion and a left hand gear are placed in mesh, find the transverse contact ratio, the normal contact ratio, the axial contact ratio, and the total contact ratio.

An AISI 1010 carbon steel plate of 1 by 1 m size and of 6 mm thickness is hung vertically after a heat treatment to 300°C uniform temperature. It is cooled by ambient air at 20°C flowing parallel to the plate in transverse direction.

a) Considering both forced and natural convection, for 8 m/s transverse air velocity, determine the rate of heat transfer from the plate and the corresponding instantaneous rate of change of the plate temperature.

b) For the transverse air velocities in 1-15 m/s range, plot the heat transfer coefficients from the plate associated with forced convection, natural convection and mixed convection on the same graph.

5 t/hr of soybean oil is pumped through a smooth stainless steel pipe 5 cm in diameter at 30C.

A) What will the coefficient of friction be?

B) If by heating the oil its viscosity can be reduced by a factor of 5 and its density by 5%, how will the fraction be affected?

C) Suppose the pipe is not smooth as originally thought. how would the assumed fraction be affected?

D) If the pumping distance were extended by 50% and the pipe's diameter changed to 7 cm, how will the pressure drop (as a result of friction) be affected?

A transformer that is 10 cm long, 6.2 cm wide, and 5 cm high is to be cooled by attaching a 10 cm x 6.2 cm wide gold heat sink to its top surface. The heat sink has seven fins, which are 5 mm high, 2 mm thick, and 10 cm long. A fan blows air at 25°C with a velocity of 6 m/s parallel to the passages between the fins. The heat sink is to dissipate 12 W of heat and the base temperature of the heat sink is not to exceed 45 °C to maintain safe operation. Is this design enough to cool the transformer to safe levels?

 I have to write a review paper of one measurement technique (any device you feel interested in or have experience with), which could be what I have learned in Mechanical Measurement course.
The main content should include how it operates, its application, changes in design with time, and future direction. Although I have to focus on recent and future development.

Would you give me any examples of devices or suggest essay topics ?

Describe the mathematical models of the boundary value problem to evaluate the elastic deflection of the beam based on Euler-Bernoulli and Timoshenko theories with finite difference discretisation (for numerical integration and differentiation)

Exhaust gases from a manufacturing plant are being discharged through a 10-m-tall exhaust stack with outer diameter of 1.2 m. The exhaust gases are discharged at a rate of 1.2 kg/s, while temperature drop between inlet and exit of the exhaust stack is 30°C, and the constant pressure specific heat of the exhaust gasses is 1600 J/kg·K. On a particular day, wind at 27°C is blowing across the exhaust stack with a velocity of 10 m/s, while the outer surface of the exhaust stack experiences radiation with the surrounding at 27°C. Solar radiation is incident on the exhaust stack outer surface at a rate of 1400 W/m2, and both the emissivity and solar absorptivity of the outer surface are 0.9. Determine the exhaust stack outer surface temperature in oC. The properties of air at 80°C are k = 0.02953 W/m?K, v = 2.097 × 10?5 m2/s, and Pr = 0.7154. (Round the final answer to two decimal places.)

Can you rewrite this MATLAB code using a for loop instead of a while loop?

%formatting
clc, clear, format compact;

%define variables
k=1;
b=-2;
x=-1;
y=-2;

%while loop initialization
for k <= 3
disp([num2str(k), ' ',num2str(b),' ',num2str(x),' ',num2str(y),]);
y = x^2 -3;
if y< b
b = y;
end
x = x+1;
k = k+1;
end

The machine repair model may often be used to approximate the behavior of a computer’s CPU (central processing unit). Suppose that 20 terminals (assumed to always be busy) feed the CPU. After the CPU responds to a user, he or she takes an average of 80 seconds before sending another request to the CPU (this is called the think time). The CPU takes an average of 2 seconds to respond to any request.

On the average, how long will a user have to wait before the CPU acts on his or her request? How will your answer change if there are 30 terminals? 40 terminals?

Of course, you must make appropriate assumptions about exponentiality to answer this question