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Mechanics
a)Draw the shear force & bending moment diagrams for a built-in beam spanning 8 meters and carrying a distributed load of 6 kN/m and a central load of 30kN,
b) find the maximum deflection of this beam if E=21 000kN/cm^2 and I=25 000cm^6
A large thin plate with a central crack 2a=50 mm, loaded by remote tensile stress. crack started to propagate at S=150 Mpa, material E=210 Gpa, S yield strngth= 500 Mpa. How to Know if it plane stress or strain and is it appropriate foe LEFM. finally how to find K1C?
Surveying:
The length intercepted (R) on the stadia staff is 1.8m, the vertical angle +80degrees 26', the instrument constant (i) is 0.225 and the stadia constant (s) is 100. If the elevation of the instrument point is 151,90m , what is the elevation of the stadia point?
The vertical angle that the line of sight makes with the horizontal is +20degrees 45' and the length intercepted on the stadia is 1,945m. If the instrument constant is 0,375 and the stadia constant 102, determine
a) the horizontal distance of staff from centre of instrument
b) the elevation of stadia point above the instrument point
Convolve the following two sequences
x(n) = ((1/3)^n) u(n) + ((1/2)^-n) u(-n-1), h(n) = (1/2)n u(n)
Find the Z-transform of these sequences. Clearly identify the ROC and
locate the poles and zeros.
a) x(n) = ((-1)^n) (2^-n)u(n)
b) x(n) = (1/2)^n.
c) x(n) = (-(1/2)^n) u(-n+2)
d) x(n) = (1/2)^n [u(n) – u(n-5)]
Seven terminals in an on-line system are attached to a communications line to the
central computer. Exactly four of these terminals are ready to transmit a
message. Assume that each terminal is equally likely to be in the ready state (i.e.
have a message to transmit). The central computer polls the terminals in a fixed
sequence without repetition. Let X be the # of terminals polled until the first
ready terminal is located (For example if the second terminal polled is ready,
then X=2, etc…)
a) Find the PMF (Probability Mass Function) of X
b) Find the mean and the Variance of X.
A bowl contains 10 Red balls and B blue balls. 5 balls are selected at random
(without replacement). Let X be the number of blue balls selected. Find the
average value of X. Find the Variance of X. Now assume you select 5 balls with
replacement (i.e. you pick up a ball, note its color, and then put it back again). Find
E(X) and VAR (X) for this case.
Two couples act on the beam as shown. If the magnitude of F is 350 lb, determine the resultant
couple moment.
An isothermal reversible reaction (A ↔ B) is carried out in an aqueous solution. The reaction is first-order in both directions. The forward rate constant is 1 h–1 and the equilibrium constant is 1. The feed to the plant contains 100 kg-mol/m3 of A and enters at the rate of 120 m3/h. The reactor is a stirred tank of volume 180 m3. The exit stream then goes to a separator, where the concentration of A (CA) is doubled and 30 m3/h is sent back to the CSTR in a continuous operation.
a. Find the conversion.
b. Compare this conversion with what you will get if there is no recycle.