Mechanical Engineering Answers

At a particular point in a structural member a two dimensional stress system exists where sigma x=60N/mm^2 sigma y=-40N/mm^2 and shear stress (xy) =50N/mm^2 if young's modulus =200000N/mm^2 and poisson's ratio =0.3 calculate the direct strain in the x and y directions and the shear strain at the point.

Listed below is a combination of stresses acting at a point and referred to axes x and y in an elastic material. Using Mohr’s circle of stress determine the principal stresses at the point and their directions for each combination. 

i) sigma x=-60 N/mm^2, sigma y=-36N/mm^2, shear stress (xy) =5N/mm^2

ii) sigma x=30 N/mm^2, sigma y=-50N/mm^2, shear stress (xy) =30N/mm^2

In crank and slotted lever quick return mechanism, the crank length is (100 +X )mm and the distance between the fixed center is (225+X)mm. The length of the slotted lever is (525+X)mm. Determine the ration of time of cutting stroke to time of return stroke. Also calculate the length of the stroke . Note where X is two digit number made from the last two digit of the registration number of the students For example if the reg. no. of the student is 11912081 then X=81 and crank length is 80+81=161mm Draw the neat and clean diagram with proper scale. Rough drawings will not be considered. 

 The velocity components in a two dimensional flow are :

U = 8x^2 y - 8/3 y^3 And

V = -8xy^3 + 8/3 x^3.

Show that these velocity components represents a possible case of an irrotational flow.

For the velocity components given as : u = ay sin xy, v = ax sin xy. Obtain an expression for the velocity potential function.

The stream function for a two-dimensional flow is given by ψ = 8xy, calculate the velocity at the point p(4, 5). Find the velocity potential function ϕ.

If for a two-dimensional potential flow, the velocity potential is given by ϕ = 4x(3y - 4), determine the velocity at the point (2, 3) . Determine also the value of stream function ψ at the poins (2, 3).

The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience coverage are given in the table below:

TV newspaper radio

Cost per advertisement $2000 $600 $300

Audience/advertisemet $100,000 $40,000$18,000

The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

(a) Formulate the problem above in mathematical model.

(b) Formulate the problem in standard form.

(c) Solve this business problem using the Simplex method.

reverse bending stress of 300 N/mm2 is acting on 55 mm diameter steel. the ultimate strenth of steel is 590 N/mm2. Consider the factors ka= 0.45,Kb=0.85,Kc=0.89 and remaining factor are 1. Calculate the life of the bar for the reliability of 90%.

A pipe, through which water is flowing, is having diameters 20 cm and 10 cm at the cross-section 1and 2 respectively. The velocity of water at section 1 is given 4.0 m/sec. Find the velocity head at section 1 and 2 and also rate of discharge.