Mechanical Engineering Answers

A thin copper tube, 14 mm internal diameter and 0,5 mm wall thickness has closed ends and rotates at 1200 r/min while it is subjected to an internal gauge pressure of 222 Pa. Calculate the total hoop stress in the wall of the tube if the density of copper is 8900 kg/m³.

a spherical pressure vessel is constructed by bolting two hemispheres together along rigid flanges as shown in the sketch. the sphere has an internal diameter of 1.5 and the plate thickness is 5 mm. Allowable tensile stresses are 45 MPa in the shell and 80 MPa in the bolts. calculate the allowable gauge pressure.

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The following data refer to two close-coiled helical steel springs.

SPRING

FREE HEIGHT

d

D

N

1

55 mm

4,75 mm

30 mm

8

2

48 mm

5,3 mm

44 mm

6

One spring is placed inside the other, not touching each other, and compressed between a pair of parallel plates until the distance between the plates is 40 mm. Make a neat detailed sketch of the spring and plate assembly. If G = 83 GPa for both springs, calculate the following:

5.1 The force applied to the spring assembly. ​​​​​/4/

5.2 The shear stress induced in each spring.​​​​​​/3/

5.3 The total strain energy stored in the spring assembly.​​​​/3/

5.4 The stiffness of each spring.​​​​​​​/3/

5.5​The equivalent stiffness of a single spring that can be substituted in place of these springs.​​​​

a. The results/ observation of several tensile tests performed. Compare and contrast theoretical material properties: modules of elasticity (205GPa), yield stress (300MPa) and ultimate tensile stress (500MPa) of metal (ferrite stainless steels Grade 409) of the specimens 1 and specimen 16 and using the destructive tensile test results in the graph for relevant specimens.

b. Describe how the Archimedes’ principle-based test can be used to determine the density of two material samples using the following data. Compare your results with the given densities if there are variations, and mention possible reasons for that.

Proposed an NDT method can be used to prove your reasons. Compare and contrast your method with the method above.

A. Metal sample 1 data: Steel cylindrical sample (diameter 20mm, length 100mm and mass 252.80grams, density 8050kg/m3)

B. Non-metal sample 2 data: Nylon hollow shaft (internal diameter 10mm, outer diameter 16mm, length 300mm, mass 42.40g and density 1.15g/cm3)

Calculate the mass moment of inertia for the components and axes given below: a) A 3 kg rod which is 1.5m long about its centre b) A 2kg metal plate 300mmx400mm about an axis perpendicular to the plane of the plate through its centre. c) A 500g disc of diameter 100mm about an axis perpendicular to the plane of the plate through its centre. 

A horizontal 2 m diameter conduit is half filled with a liquid (specific gravity = 1.6) and is

capped at both ends with plane vertical surfaces. The air pressure in the conduit above the

liquid surface is 200 kPa. Determine the resultant force of the fluid acting on one end of the

caps, and locate this force relative to the bottom of the conduit.

An open topped tank with a base area of 1 m2 contains a layer of water 0.5 m deep below an oil

later 1 m deep, as shown in the figure below. Determine the absolute pressure at 0.5 m below

the surface and at the bottom of the tank. Assume the densities of water and oil are 1000 kg/m3

and 850 kg/m3 respectively. Also determine the total weight of the fluid if the base area is 1 m2

This task related to destructive and non-destructive test methods that can be used to identify properties of metal and non-metals, and compare and contrast theoretical given values with the practical data give.

a. Figure 11 shows results/ observation of several tensile tests performed. Compare and contrast theoretical material properties: modules of elasticity (205GPa), yield stress (300MPa) and ultimate tensile stress (500MPa) of metal (ferrite stainless steels Grade 409) of the specimens 1 and specimen 16 shown in Figure 11(Left) and using the destructive tensile test results in the graph (Figure 11-Right) for relevant specimens.