A hollow, round column has length (L = 1500 mm), outside diameter (do = 20 mm) and inside diameter (di = 14 mm). If the column is made of steel (E = 207 GPa, Sy = 300 MPa), then determine if it is a Johnson or an Euler column and find the critical load Pcr for each of the following end-conditions:

(a) Pinned-pinned

(b) Fixed-pinned

(c) Fixed-fixed

(d) Fixed-free

Noncubic ceramics are birefringent. Explain why this is important for polycrystalline alumina nose cones.

Explain briefly why the transparency range of single-crystal NaCl is much greater than for single- crystal MgO.

A sheet of metal of 2 m ´ 2 m and 1.5 mm thickness is being tested in a wind tunnel.

a. Calculate the critical velocity, in m/s, at which the boundary layer will remain laminar.

b. For an upstream velocity of 35 m/s, what percentage of the metal sheet surface will have a laminar boundary layer.

c. For each of the previous cases (all laminar B.L and mixed laminar/turbulent B.L), calculate the drag force on the plate, in N. Use Table 9.3 to calculate the appropriate drag coefficients.

Consider a spherical vessel filled with a substance which is generating heat at a uniform rate of 10^5 W/m^3. The substance has a thermal conductivity of 20 W/mK, and the vessel has a thermal conductivity of 15 W/mK.

The inner radius of the container is 0.5m and the outer radius is 0.6 m.

The container is surrounded by a fluid with convection coefficient of 1000 W/m^2K and T_inf = 25 Celsius.

Determine the temperature distribution T(r) by solving the differential equation, and evaluating the given boundary conditions

Perform sit-­up exercises under the following conditions: 1) arms folded across the chest, 2) hands behind the neck, 3) holding a five­ pound weight above the head. Write a paragraph explaining your findings and draw a free body diagram showing the Applied Force, Resistance, and Axis of rotation.

Explanation:

?Free body diagram:

Derive an expression for the U factor if the inside and outside surfaces of the tubes in a heat exchanger are finned and have fin efficiencies of ?_i and ?_o on the inside and the outside, and A_f,i and A_f,o as the finned area on the inside and the outside, respectively, and similarly A_u,i and A_u,o as the unfinned area on the inside and the outside, respectively.

Please post all steps taken. Thanks!

A single axis personal transport device starts from rest with the rider leaning slightly forward. Together, the two wheels weigh 25 lbs, and each has a radius of 10 in. The mass moment of inertia of the wheels

about the axle is 0.15 slug ft². The combined weight of the rest of the device and the rider (excluding the wheels) is 200 lbs, and the center of gravity G of this weight is located at x = 4 in. in front of the

axle A and y = 36 in. above the ground. An initial clockwise torque M is applied by the motor to the wheels. The coefficients of static and kinetic friction are 0.7 and 0.6, respectively.

4. Given a system of five (5) 3500-lb, 700 feet per minute (fpm) elevator cars. Gearless traction motors are being used for this system. Each car operates approximately 65% of the time and while in operation, each car draws 96% of the full load. Calculate

a. Heat generated in the machine room during peak periods. Assume solid-state control is used. (5 points)

b. Assume the following operation profile during a 24-hour day

5 hours peak use

3 hours of 70% peak

4 hours of 50% peak

12 hours of 10% peak

Calculate the approximate monthly energy cost using the electricity rate of $0.10/kWh assuming 25 days of operation per calendar month (10 points)

The strength coefficient (K) and the work hardening exponent (n) for a stainless steel were determined during the analysis of the data from a tensile test using a standard tensile specimen. The flow curve parameters for the stainless steel are K= 1250 MPa and n = 0.4. A compression test is performed on a specimen of the stainless steel. If the starting height and diameter of the specimen are 80 mm and 18 mm, respectively and the final height of the specimen is 60 mm, calculate the load that was applied to the specimen. Assume that the cross-section of the compression is uniform from top to bottom during the test.

What are the main differences between natural and forced convection flows? In the lab experiments, explain how we did use one experimental test rig to demonstrate the characteristics of both flows. ?

The erosion rate of a streambank is calculated by the excess shear stress equation: e=k(a-c) where e is the erosion rate in m/s, k is the erodibility coefficient in m^3/ N s, a is the applied shear stress (Pa) and c is the critical shear stress (Pa). The applied shear stress is calculated using the equation a=den*g*d*s where den is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), d is the depth of water (m) and s is the bed slope (m/m). The critical shear stress is a function of the silt and clay content of the streambank and is calculated using the following equation: c=0.1+0.1779(SC%)+0.0028(SC%)2-2.34E-5(SC%)3 where SC% is the percent of the streambank that is silt and clay. The erodibility coefficient is calculated using the equation k=0.20*c^-0.5. Develop a program in MATLAB that calculates the erosion rate of a streambank. The user should enter the following values: depth of water, bed slope and percent of silt and clay. The program should write out “The erosion rate is:”, the rate calculated and the units. Test the program using the following: d=1, s=.001, SC=35 and d=0.1, s=.004, SC=50. Document the erosion rate. Paste all input and output code into this Word document.

Given a system of five (5) 3500-lb, 700 feet per minute (fpm) elevator cars. Gearless traction motors are being used for this system.   Each car operates approximately 65% of the time and while in operation, each car draws 96% of the full load. Calculate

Heat generated in the machine room during peak periods. Assume solid-state control is used. (5 points)

Assume the following operation profile during a 24-hour day

5 hours peak use

3 hours of 70% peak

4 hours of 50% peak

12 hours of 10% peak

Calculate the approximate monthly energy cost using the electricity rate of $0.10/kWh assuming 25 days of operation per calendar month (10 points)

Air enters a thin-walled, 5-mm diameter, 2-m-long tube at a uniform inlet temperature of 100°C. A constant heat flux is applied to the air from the tube surface. The mean temperature of air at halfway along the tube (at 1 m length) is reported as 126°C. If the tube surface temperature at the exit is 160°C and the local heat transfer coefficient at the exit is 29.5 W/m^2K, determine

a) the applied heat flux,

b) the rate of energy increase in air from the entrance to the exit of the tube,

c) the mass flow rate of air in the tube,

d) the local heat transfer coefficient at halfway along the tube (at 1 m length),

e) the surface temperature of the tube at halfway along the tube (at 1 m length).

Assume steady-state conditions and constant air properties.